Gases Always React in Small Whole-Number Ratios by Volume
Learn Gay Lussac's law of combining volumes and Avogadro's law, use the formation of hydrogen chloride, ammonia and nitric oxide to prove that hydrogen, oxygen, nitrogen and chlorine are diatomic, apply the molar volume of 22.4 litres at STP, and solve gas volume problems step by step.
Why does one litre of nitrogen need exactly three litres of hydrogen?
Mix nitrogen and hydrogen under the right conditions and they form ammonia. Measure the gases carefully and a striking pattern appears. One litre of nitrogen always reacts with exactly three litres of hydrogen, and the ammonia produced occupies exactly two litres — provided every volume is measured at the same temperature and pressure.
**The ratio is not approximately ; it is exactly that, and other gas reactions give equally tidy ratios:
- Hydrogen and chlorine** combine as and give volumes of hydrogen chloride
- Hydrogen and oxygen combine as and give volumes of steam
- Nitrogen and oxygen combine as and give volumes of nitric oxide
Masses never behave so neatly. Eight grams of oxygen react with one gram of hydrogen — a ratio with nothing special about it. Volumes of gases give small whole numbers because equal volumes of gases contain equal numbers of molecules, so a volume ratio is really a ratio of molecules, and molecules react in whole numbers.
That single idea unlocks the whole topic.
- It explains the combining-volume ratios
- It proves that common gases such as hydrogen and oxygen exist as two-atom molecules
- It leads to the molar volume — the fact that a fixed volume of any gas, at a standard temperature and pressure, contains the same number of molecules and weighs its molecular mass in grams
- It lets you calculate volumes of gases in reactions directly from a balanced equation
Gas volumes matter in everyday life too. A cooking gas stove needs the right amount of air to burn the gas cleanly; too little air gives a yellow, sooty flame. The volume of air needed follows directly from the volume ratio in the burning equation, as a worked example below shows.
One condition runs through every statement on this page. Gas volumes change with temperature and pressure, so volumes can be compared only when they are measured under the same conditions. Every law below includes that requirement.
This page covers the first part of the ICSE Class 10 Chemistry chapter on mole concept and stoichiometry: Gay Lussac's law and Avogadro's law, the atomicity of common gases, molar volume, and volume-volume calculations.
**The ratio is not approximately ; it is exactly that, and other gas reactions give equally tidy ratios:
- Hydrogen and chlorine** combine as and give volumes of hydrogen chloride
- Hydrogen and oxygen combine as and give volumes of steam
- Nitrogen and oxygen combine as and give volumes of nitric oxide
Masses never behave so neatly. Eight grams of oxygen react with one gram of hydrogen — a ratio with nothing special about it. Volumes of gases give small whole numbers because equal volumes of gases contain equal numbers of molecules, so a volume ratio is really a ratio of molecules, and molecules react in whole numbers.
That single idea unlocks the whole topic.
- It explains the combining-volume ratios
- It proves that common gases such as hydrogen and oxygen exist as two-atom molecules
- It leads to the molar volume — the fact that a fixed volume of any gas, at a standard temperature and pressure, contains the same number of molecules and weighs its molecular mass in grams
- It lets you calculate volumes of gases in reactions directly from a balanced equation
Gas volumes matter in everyday life too. A cooking gas stove needs the right amount of air to burn the gas cleanly; too little air gives a yellow, sooty flame. The volume of air needed follows directly from the volume ratio in the burning equation, as a worked example below shows.
One condition runs through every statement on this page. Gas volumes change with temperature and pressure, so volumes can be compared only when they are measured under the same conditions. Every law below includes that requirement.
This page covers the first part of the ICSE Class 10 Chemistry chapter on mole concept and stoichiometry: Gay Lussac's law and Avogadro's law, the atomicity of common gases, molar volume, and volume-volume calculations.
What do Gay Lussac's law of combining volumes and Avogadro's law state?
Gay Lussac's law says reacting gases and gaseous products have volumes in a simple whole-number ratio; Avogadro's law says equal volumes of all gases under the same conditions contain the same number of molecules.
Gay Lussac's law of combining volumes. When gases react together, they do so in volumes which bear a simple whole-number ratio to one another and to the volumes of the gaseous products, provided all the volumes are measured at the same temperature and pressure.
Examples, with the volume ratio read straight from the coefficients:
Avogadro's law. Equal volumes of all gases, under the same conditions of temperature and pressure, contain an equal number of molecules.
How the two laws fit together. By Avogadro's law, one volume of any gas holds some number of molecules. So in the ammonia reaction:
The volume ratio and the molecule ratio are the same thing, and both are the coefficients of the balanced equation. That is why Gay Lussac's whole-number ratios happen at all.
Worked example 1. In , what volume of oxygen reacts with of carbon monoxide, and what volume of carbon dioxide forms?
Worked example 2 — volumes are not conserved. In the ammonia reaction, volumes of reactants give only volumes of product. Mass is conserved in every reaction; volume is not, because the number of molecules changes.
The boundary case — only gases count. In the burning of methane measured at room temperature,
the water condenses to a liquid, and a liquid's volume is negligible and does not follow the law. Only methane, oxygen and carbon dioxide appear in the volume ratio . Above , the water would be steam and would count as volumes.
An everyday illustration of Avogadro's law. A bicycle tube pumped with air and an identical tube filled with the same volume of helium at the same pressure and temperature contain the same number of molecules — even though the helium tube is far lighter. Equal volumes hold equal numbers, not equal masses.
Gay Lussac's law of combining volumes. When gases react together, they do so in volumes which bear a simple whole-number ratio to one another and to the volumes of the gaseous products, provided all the volumes are measured at the same temperature and pressure.
Examples, with the volume ratio read straight from the coefficients:
Avogadro's law. Equal volumes of all gases, under the same conditions of temperature and pressure, contain an equal number of molecules.
How the two laws fit together. By Avogadro's law, one volume of any gas holds some number of molecules. So in the ammonia reaction:
The volume ratio and the molecule ratio are the same thing, and both are the coefficients of the balanced equation. That is why Gay Lussac's whole-number ratios happen at all.
Worked example 1. In , what volume of oxygen reacts with of carbon monoxide, and what volume of carbon dioxide forms?
Worked example 2 — volumes are not conserved. In the ammonia reaction, volumes of reactants give only volumes of product. Mass is conserved in every reaction; volume is not, because the number of molecules changes.
The boundary case — only gases count. In the burning of methane measured at room temperature,
the water condenses to a liquid, and a liquid's volume is negligible and does not follow the law. Only methane, oxygen and carbon dioxide appear in the volume ratio . Above , the water would be steam and would count as volumes.
An everyday illustration of Avogadro's law. A bicycle tube pumped with air and an identical tube filled with the same volume of helium at the same pressure and temperature contain the same number of molecules — even though the helium tube is far lighter. Equal volumes hold equal numbers, not equal masses.
How do the HCl, NH3 and NO reactions show that hydrogen, oxygen, nitrogen and chlorine are diatomic?
Each reaction makes two molecules of product from one molecule of an element, and since every product molecule needs at least one atom of that element, the element's molecule must contain at least two atoms.
Atomicity is the number of atoms in one molecule of an element.
- Monatomic — one atom: helium, neon, argon
- Diatomic — two atoms: hydrogen, oxygen, nitrogen, chlorine
- Triatomic — three atoms: ozone,
- Polyatomic — more: phosphorus , sulphur
1. Hydrogen and chlorine, from hydrogen chloride.
Experiment: volume of hydrogen volume of chlorine volumes of hydrogen chloride.
Apply Avogadro's law: molecules of hydrogen molecules of chlorine molecules of hydrogen chloride.
**Divide by **: molecule of hydrogen molecule of chlorine molecules of hydrogen chloride.
Reason it through:
- Each molecule of hydrogen chloride contains at least one hydrogen atom
- So two molecules of hydrogen chloride contain at least two hydrogen atoms
- All of them came from one molecule of hydrogen
- So one molecule of hydrogen contains at least two atoms
The same argument, with chlorine in place of hydrogen, shows one molecule of chlorine contains at least two atoms. **Hydrogen is and chlorine is .
2. Nitrogen, from ammonia.
Experiment**: volume of nitrogen volumes of hydrogen volumes of ammonia.
By Avogadro's law: molecule of nitrogen molecules of ammonia.
Each ammonia molecule contains at least one nitrogen atom, so two contain at least two, all from one nitrogen molecule. **Nitrogen is .
3. Oxygen, from nitric oxide.
Experiment**: volume of nitrogen volume of oxygen volumes of nitric oxide.
By Avogadro's law: molecule of oxygen molecules of nitric oxide.
Each nitric oxide molecule contains at least one oxygen atom, so one oxygen molecule contains at least two atoms. **Oxygen is ** — and the same reaction confirms nitrogen as .
Worked check — do the diatomic formulae give the right volume ratios? Writing the equations with diatomic molecules:
Atoms: hydrogen , chlorine ; molecules: — exactly the measured volumes. If hydrogen and chlorine were single atoms, the equation would be , predicting , which does not match the experiment.
The honest limit of the argument. The reasoning proves at least two atoms per molecule, not exactly two. Combined with the measured molecular masses — hydrogen's is and its atomic mass is — it settles the atomicity at exactly two, which is the link to vapour density in Part 2.
An everyday note. Oxygen supplied in hospital cylinders, and the oxygen in every breath, is . **Ozone, , is a different substance** made of the same element — which is exactly why atomicity has to be established rather than assumed.
Atomicity is the number of atoms in one molecule of an element.
- Monatomic — one atom: helium, neon, argon
- Diatomic — two atoms: hydrogen, oxygen, nitrogen, chlorine
- Triatomic — three atoms: ozone,
- Polyatomic — more: phosphorus , sulphur
1. Hydrogen and chlorine, from hydrogen chloride.
Experiment: volume of hydrogen volume of chlorine volumes of hydrogen chloride.
Apply Avogadro's law: molecules of hydrogen molecules of chlorine molecules of hydrogen chloride.
**Divide by **: molecule of hydrogen molecule of chlorine molecules of hydrogen chloride.
Reason it through:
- Each molecule of hydrogen chloride contains at least one hydrogen atom
- So two molecules of hydrogen chloride contain at least two hydrogen atoms
- All of them came from one molecule of hydrogen
- So one molecule of hydrogen contains at least two atoms
The same argument, with chlorine in place of hydrogen, shows one molecule of chlorine contains at least two atoms. **Hydrogen is and chlorine is .
2. Nitrogen, from ammonia.
Experiment**: volume of nitrogen volumes of hydrogen volumes of ammonia.
By Avogadro's law: molecule of nitrogen molecules of ammonia.
Each ammonia molecule contains at least one nitrogen atom, so two contain at least two, all from one nitrogen molecule. **Nitrogen is .
3. Oxygen, from nitric oxide.
Experiment**: volume of nitrogen volume of oxygen volumes of nitric oxide.
By Avogadro's law: molecule of oxygen molecules of nitric oxide.
Each nitric oxide molecule contains at least one oxygen atom, so one oxygen molecule contains at least two atoms. **Oxygen is ** — and the same reaction confirms nitrogen as .
Worked check — do the diatomic formulae give the right volume ratios? Writing the equations with diatomic molecules:
Atoms: hydrogen , chlorine ; molecules: — exactly the measured volumes. If hydrogen and chlorine were single atoms, the equation would be , predicting , which does not match the experiment.
The honest limit of the argument. The reasoning proves at least two atoms per molecule, not exactly two. Combined with the measured molecular masses — hydrogen's is and its atomic mass is — it settles the atomicity at exactly two, which is the link to vapour density in Part 2.
An everyday note. Oxygen supplied in hospital cylinders, and the oxygen in every breath, is . **Ozone, , is a different substance** made of the same element — which is exactly why atomicity has to be established rather than assumed.
Why does 22.4 litres of any gas at STP weigh its molar mass in grams?
At STP, 22.4 litres of any gas contains the same fixed number of molecules — the number in one gram molecular mass — so its mass is the molecular mass expressed in grams.
STP means standard temperature and pressure:
- Temperature , which is
- Pressure atmosphere, which is or of mercury
The molar volume. The volume occupied by one gram molecular mass of any gas at STP is ** litres. Because of Avogadro's law, it is the same for every gas.
So the mass of litres of a gas at STP equals its molecular mass in grams:
- Hydrogen**, : weighs
- Oxygen, : weighs
- Ammonia, : weighs
- Carbon dioxide, : weighs
- Chlorine, : weighs
Why this works. Take of hydrogen and of oxygen at STP. By Avogadro's law they contain the same number of molecules. Each oxygen molecule is times heavier than each hydrogen molecule, so the oxygen weighs . The same argument holds for every gas.
Worked example 1 — volume to mass. Find the mass of of carbon dioxide at STP.
Worked example 2 — mass to volume. Find the volume of of oxygen at STP.
Worked example 3 — molecular mass from a measured mass. of a gas at STP weighs . Find its molecular mass.
**Molecular mass — which matches sulphur dioxide.
Worked example 4 — density of a gas at STP.** Find the density of ammonia at STP.
The boundary cases to state precisely.
- **The value litres applies only at STP.** At room temperature, about , and the same pressure, one gram molecular mass of gas occupies more, about litres
- It applies only to gases. Water is a liquid at , and of it occupies about , nowhere near litres
An everyday sense of the size. litres is about the volume of eleven two-litre water bottles — roughly a small bucket. **That bucketful of oxygen at STP would weigh **, about as much as a few coins, while the same bucket of hydrogen would weigh just .
STP means standard temperature and pressure:
- Temperature , which is
- Pressure atmosphere, which is or of mercury
The molar volume. The volume occupied by one gram molecular mass of any gas at STP is ** litres. Because of Avogadro's law, it is the same for every gas.
So the mass of litres of a gas at STP equals its molecular mass in grams:
- Hydrogen**, : weighs
- Oxygen, : weighs
- Ammonia, : weighs
- Carbon dioxide, : weighs
- Chlorine, : weighs
Why this works. Take of hydrogen and of oxygen at STP. By Avogadro's law they contain the same number of molecules. Each oxygen molecule is times heavier than each hydrogen molecule, so the oxygen weighs . The same argument holds for every gas.
Worked example 1 — volume to mass. Find the mass of of carbon dioxide at STP.
Worked example 2 — mass to volume. Find the volume of of oxygen at STP.
Worked example 3 — molecular mass from a measured mass. of a gas at STP weighs . Find its molecular mass.
**Molecular mass — which matches sulphur dioxide.
Worked example 4 — density of a gas at STP.** Find the density of ammonia at STP.
The boundary cases to state precisely.
- **The value litres applies only at STP.** At room temperature, about , and the same pressure, one gram molecular mass of gas occupies more, about litres
- It applies only to gases. Water is a liquid at , and of it occupies about , nowhere near litres
An everyday sense of the size. litres is about the volume of eleven two-litre water bottles — roughly a small bucket. **That bucketful of oxygen at STP would weigh **, about as much as a few coins, while the same bucket of hydrogen would weigh just .
How do you solve volume–volume problems using Gay Lussac's law and molar volume?
Balance the equation, read the volume ratio from the coefficients, find which gas runs out first, and calculate every volume used, formed and left over — counting only substances that are gases at the measuring temperature.
The method:
- Write the balanced equation
- Read the volume ratio from the coefficients of the gases
- Find the limiting gas if both reactant volumes are given
- Calculate volumes used, formed and remaining
- Decide which products are gases at the temperature of measurement
Worked example 1 — a straight ratio. What volume of oxygen burns of carbon monoxide, and what volume of carbon dioxide forms?
Worked example 2 — one gas in excess. of nitrogen and of hydrogen react completely as far as possible. Find the final volume.
- ** of nitrogen would need of hydrogen** — only is present, so hydrogen is limiting
- Nitrogen used: ; nitrogen left:
- Ammonia formed:
- Final volume:
Worked example 3 — a product that condenses. of methane is burnt in of oxygen, and the volume is measured at room temperature.
- Oxygen used: ; oxygen left:
- Carbon dioxide formed:
- Water is liquid at room temperature, so it adds no gas volume
- Final gas volume:
- If the gas is then passed through potassium hydroxide solution, which absorbs carbon dioxide, ** of oxygen remains
Worked example 4 — air for a gas stove.** What volume of air is needed to burn of methane, taking air as one-fifth oxygen by volume?
Ten volumes of air for every volume of methane — the reason a gas burner has openings that draw in plenty of air.
Worked example 5 — the gas in cooking cylinders. Liquefied petroleum gas is mainly butane and propane. Find the volume of oxygen needed and carbon dioxide formed when of butane burns.
Worked example 6 — steam counts above 100 °C. of hydrogen and of oxygen are exploded and the volume measured at .
- ** of hydrogen needs of oxygen — hydrogen is limiting
- Oxygen left**:
- Steam formed: , which counts at
- Final volume:
- Cooled to room temperature, the steam condenses and only of oxygen remains
Worked example 7 — working backwards. What volumes of nitrogen and hydrogen produce of ammonia?
The boundary case running through examples 3 and 6. The same reaction gives different final volumes at different temperatures, because water's state changes. Always check the temperature of measurement before adding up the gas volumes.
The method:
- Write the balanced equation
- Read the volume ratio from the coefficients of the gases
- Find the limiting gas if both reactant volumes are given
- Calculate volumes used, formed and remaining
- Decide which products are gases at the temperature of measurement
Worked example 1 — a straight ratio. What volume of oxygen burns of carbon monoxide, and what volume of carbon dioxide forms?
Worked example 2 — one gas in excess. of nitrogen and of hydrogen react completely as far as possible. Find the final volume.
- ** of nitrogen would need of hydrogen** — only is present, so hydrogen is limiting
- Nitrogen used: ; nitrogen left:
- Ammonia formed:
- Final volume:
Worked example 3 — a product that condenses. of methane is burnt in of oxygen, and the volume is measured at room temperature.
- Oxygen used: ; oxygen left:
- Carbon dioxide formed:
- Water is liquid at room temperature, so it adds no gas volume
- Final gas volume:
- If the gas is then passed through potassium hydroxide solution, which absorbs carbon dioxide, ** of oxygen remains
Worked example 4 — air for a gas stove.** What volume of air is needed to burn of methane, taking air as one-fifth oxygen by volume?
Ten volumes of air for every volume of methane — the reason a gas burner has openings that draw in plenty of air.
Worked example 5 — the gas in cooking cylinders. Liquefied petroleum gas is mainly butane and propane. Find the volume of oxygen needed and carbon dioxide formed when of butane burns.
Worked example 6 — steam counts above 100 °C. of hydrogen and of oxygen are exploded and the volume measured at .
- ** of hydrogen needs of oxygen — hydrogen is limiting
- Oxygen left**:
- Steam formed: , which counts at
- Final volume:
- Cooled to room temperature, the steam condenses and only of oxygen remains
Worked example 7 — working backwards. What volumes of nitrogen and hydrogen produce of ammonia?
The boundary case running through examples 3 and 6. The same reaction gives different final volumes at different temperatures, because water's state changes. Always check the temperature of measurement before adding up the gas volumes.
Exam tip
What layout gets every mark in a gas volume problem?
Write the balanced equation, put the volume ratio under the formulae, then set out used, formed and left as separate lines with units.
- State both laws with their condition — same temperature and pressure — or the definition loses a mark
- Write the balanced equation first, and underline the gases
- Write the volume ratio under the equation from the coefficients
- Identify the limiting gas by comparing what each reactant would need
- Give volumes used, formed and left on separate lines
- Leave liquid water out of volumes measured below , and include steam above it
- Mention what an absorbent removes — potassium hydroxide absorbs carbon dioxide
- In atomicity proofs, write all three lines: volumes, molecules, one molecule — then argue at least two atoms
- **Use only at STP and only for gases
- Give units on every answer** — , or
The misconception to name. Volumes of gases are not conserved in a reaction. One volume of nitrogen and three of hydrogen give two volumes of ammonia, not four. Adding reactant volumes to find the product volume is the most common wrong method, and it contradicts the very law the question is testing.
A second trap. Treating the limiting gas as the one with the smaller volume. In worked example 2, nitrogen and hydrogen have equal volumes, yet hydrogen runs out, because the reaction needs three times as much of it. Always compare against the ratio, not against each other.
- State both laws with their condition — same temperature and pressure — or the definition loses a mark
- Write the balanced equation first, and underline the gases
- Write the volume ratio under the equation from the coefficients
- Identify the limiting gas by comparing what each reactant would need
- Give volumes used, formed and left on separate lines
- Leave liquid water out of volumes measured below , and include steam above it
- Mention what an absorbent removes — potassium hydroxide absorbs carbon dioxide
- In atomicity proofs, write all three lines: volumes, molecules, one molecule — then argue at least two atoms
- **Use only at STP and only for gases
- Give units on every answer** — , or
The misconception to name. Volumes of gases are not conserved in a reaction. One volume of nitrogen and three of hydrogen give two volumes of ammonia, not four. Adding reactant volumes to find the product volume is the most common wrong method, and it contradicts the very law the question is testing.
A second trap. Treating the limiting gas as the one with the smaller volume. In worked example 2, nitrogen and hydrogen have equal volumes, yet hydrogen runs out, because the reaction needs three times as much of it. Always compare against the ratio, not against each other.
Did you know
Why does a balloon of carbon dioxide sink while a helium balloon floats?
Fill one balloon with helium and an identical balloon with carbon dioxide to the same size. By Avogadro's law, at the same temperature and pressure the two balloons contain exactly the same number of gas molecules. Yet let go and one soars to the ceiling while the other drops to the floor.
Same number of molecules, very different masses per molecule.
- A helium atom has a mass of about
- A carbon dioxide molecule has a mass of — eleven times more
- Air, a mixture mainly of nitrogen and oxygen, has an average molecular mass of about
At STP, the molar volume turns those masses straight into densities:
A gas lighter than air rises through it, and a gas heavier than air sinks. Helium is roughly seven times lighter than air, so its balloon floats; carbon dioxide is about one and a half times heavier, so its balloon falls.
The same arithmetic explains why carbon dioxide puts out fires. Released near a flame, carbon dioxide sinks and spreads along the ground like an invisible liquid, pushing away the air and cutting the flame off from oxygen. A gas that rose would drift away uselessly.
It also explains a safety rule in wells and underground tanks. Carbon dioxide from decaying matter can collect at the bottom of a deep, still well, because it is heavier than air and does not easily mix upwards. That is why workers lower a burning candle before descending: if the flame goes out, the air below is unsafe to breathe.
**And hydrogen, at , is lighter still than helium — which is why it would lift a balloon even better. It is avoided in toy balloons for a reason from an earlier chapter**: hydrogen burns, while helium's complete outer shell makes it completely safe near a flame.
Same number of molecules, very different masses per molecule.
- A helium atom has a mass of about
- A carbon dioxide molecule has a mass of — eleven times more
- Air, a mixture mainly of nitrogen and oxygen, has an average molecular mass of about
At STP, the molar volume turns those masses straight into densities:
A gas lighter than air rises through it, and a gas heavier than air sinks. Helium is roughly seven times lighter than air, so its balloon floats; carbon dioxide is about one and a half times heavier, so its balloon falls.
The same arithmetic explains why carbon dioxide puts out fires. Released near a flame, carbon dioxide sinks and spreads along the ground like an invisible liquid, pushing away the air and cutting the flame off from oxygen. A gas that rose would drift away uselessly.
It also explains a safety rule in wells and underground tanks. Carbon dioxide from decaying matter can collect at the bottom of a deep, still well, because it is heavier than air and does not easily mix upwards. That is why workers lower a burning candle before descending: if the flame goes out, the air below is unsafe to breathe.
**And hydrogen, at , is lighter still than helium — which is why it would lift a balloon even better. It is avoided in toy balloons for a reason from an earlier chapter**: hydrogen burns, while helium's complete outer shell makes it completely safe near a flame.
Exam relevance
How does gas volume work lead into JEE and NEET Chemistry?
This is foundation work for Class 11 Some Basic Concepts of Chemistry, examined in both JEE Main and NEET Chemistry, and for the Kinetic Theory of gases in Class 11 Physics, which both exams also include.
Where the laws lead. Class 11 opens with the laws of chemical combination, and Gay Lussac's law of gaseous volumes and Avogadro's law are stated there in the same form as here. Direct questions on which law explains a given observation appear as objective items, and the reasoning that volume ratios are molecule ratios is assumed throughout.
Where the volume calculations lead. Stoichiometry and the limiting reagent are central to Class 11 and are examined repeatedly as numericals in both exams. Worked examples 2, 3 and 6 are limiting-reagent problems in their simplest form — the method of comparing each reactant against the ratio is exactly the one used with moles and masses later.
Where molar volume leads. Converting between the volume of a gas and its amount is a step inside many larger problems, from combustion analysis of organic compounds to electrolysis questions that ask for the volume of gas released. Confident use of the molar volume removes one source of error from every such question.
Where Avogadro's law leads in Physics. Class 11 Kinetic Theory writes Avogadro's law as a proportion between the volume of a gas and the number of molecules, and combines it into the ideal gas equation, . The molar volume at STP is simply that equation evaluated at one standard temperature and pressure.
Question types to expect. At this level: stating the laws, atomicity proofs, and volume-volume problems. In competitive papers: laws of chemical combination, limiting-reagent numericals, gas volumes from mass or moles, and ideal gas calculations, often as single numerical-answer questions.
The single trap that costs marks. Using litres without checking the conditions. **The modern standard pressure of bar gives a slightly larger molar volume, about litres, and room-temperature conditions give more again. Reading which conditions a question specifies decides which value is correct.
A second trap. Applying the molar volume to water or any other substance that is not a gas under the stated conditions. A question about the volume of water formed at STP expects the liquid volume**, not litres per gram molecular mass.
Board versus competitive emphasis. The ICSE paper marks the statement of each law, the three-line atomicity argument and a laid-out volume calculation; a competitive paper marks a single final number, often after combining gas volumes with masses. The transferable habit is converting every quantity into a count of molecules before comparing — because volumes, masses and moles are all just different ways of counting the same particles.
Where the laws lead. Class 11 opens with the laws of chemical combination, and Gay Lussac's law of gaseous volumes and Avogadro's law are stated there in the same form as here. Direct questions on which law explains a given observation appear as objective items, and the reasoning that volume ratios are molecule ratios is assumed throughout.
Where the volume calculations lead. Stoichiometry and the limiting reagent are central to Class 11 and are examined repeatedly as numericals in both exams. Worked examples 2, 3 and 6 are limiting-reagent problems in their simplest form — the method of comparing each reactant against the ratio is exactly the one used with moles and masses later.
Where molar volume leads. Converting between the volume of a gas and its amount is a step inside many larger problems, from combustion analysis of organic compounds to electrolysis questions that ask for the volume of gas released. Confident use of the molar volume removes one source of error from every such question.
Where Avogadro's law leads in Physics. Class 11 Kinetic Theory writes Avogadro's law as a proportion between the volume of a gas and the number of molecules, and combines it into the ideal gas equation, . The molar volume at STP is simply that equation evaluated at one standard temperature and pressure.
Question types to expect. At this level: stating the laws, atomicity proofs, and volume-volume problems. In competitive papers: laws of chemical combination, limiting-reagent numericals, gas volumes from mass or moles, and ideal gas calculations, often as single numerical-answer questions.
The single trap that costs marks. Using litres without checking the conditions. **The modern standard pressure of bar gives a slightly larger molar volume, about litres, and room-temperature conditions give more again. Reading which conditions a question specifies decides which value is correct.
A second trap. Applying the molar volume to water or any other substance that is not a gas under the stated conditions. A question about the volume of water formed at STP expects the liquid volume**, not litres per gram molecular mass.
Board versus competitive emphasis. The ICSE paper marks the statement of each law, the three-line atomicity argument and a laid-out volume calculation; a competitive paper marks a single final number, often after combining gas volumes with masses. The transferable habit is converting every quantity into a count of molecules before comparing — because volumes, masses and moles are all just different ways of counting the same particles.
Key takeaways
What must you be able to do from this part?
Two laws, one proof applied three times, one standard volume and a volume-calculation method.
- Gay Lussac's law: reacting gases and gaseous products have volumes in a simple whole-number ratio, at the same temperature and pressure
- Avogadro's law: equal volumes of all gases under the same conditions contain equal numbers of molecules
- Together: the volume ratio equals the molecule ratio equals the coefficients of the balanced equation
- Examples: is ; is ; is
- Volumes are not conserved; mass is
- Liquids do not count — water below adds no gas volume
- Atomicity is the number of atoms in one molecule of an element
- Proof: molecule of an element gives product molecules, each with at least one of its atoms, so the molecule has at least two atoms
- HCl proves and ; ammonia proves ; nitric oxide proves
- STP is () and of mercury
- Molar volume: one gram molecular mass of any gas occupies at STP, so weighs the molecular mass in grams
- ** of ** weighs ; ** of ** occupies ; ** weighing ** means molecular mass
- Density at STP is molecular mass divided by
- Method: balanced equation, volume ratio, limiting gas, used-formed-left, gases only
- **** gives with left
- ** of methane** needs of oxygen, or of air
The sharpest self-test is one reaction measured twice. Take of hydrogen and of oxygen, explode them, and find the final volume at and again at room temperature — then check that the difference between your two answers is exactly the steam.
- Gay Lussac's law: reacting gases and gaseous products have volumes in a simple whole-number ratio, at the same temperature and pressure
- Avogadro's law: equal volumes of all gases under the same conditions contain equal numbers of molecules
- Together: the volume ratio equals the molecule ratio equals the coefficients of the balanced equation
- Examples: is ; is ; is
- Volumes are not conserved; mass is
- Liquids do not count — water below adds no gas volume
- Atomicity is the number of atoms in one molecule of an element
- Proof: molecule of an element gives product molecules, each with at least one of its atoms, so the molecule has at least two atoms
- HCl proves and ; ammonia proves ; nitric oxide proves
- STP is () and of mercury
- Molar volume: one gram molecular mass of any gas occupies at STP, so weighs the molecular mass in grams
- ** of ** weighs ; ** of ** occupies ; ** weighing ** means molecular mass
- Density at STP is molecular mass divided by
- Method: balanced equation, volume ratio, limiting gas, used-formed-left, gases only
- **** gives with left
- ** of methane** needs of oxygen, or of air
The sharpest self-test is one reaction measured twice. Take of hydrogen and of oxygen, explode them, and find the final volume at and again at room temperature — then check that the difference between your two answers is exactly the steam.