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How do we calculate the volumes of gases in a reaction, and how do gases in a mixture share the total pressure?

Use molar volume in gas stoichiometry to find reacting gas volumes, and apply Dalton's law of partial pressures to a mixture of gases (MA STE supporting content, gas behavior and stoichiometry).

A standard-level answer on gas stoichiometry and Dalton's law for Massachusetts high school chemistry: using the molar volume at STP to convert between moles and gas volumes in a reaction, applying coefficient volume ratios, and using Dalton's law of partial pressures for gas mixtures, grounded in the framework's gas content.

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  1. What this topic is asking
  2. Gas stoichiometry with molar volume
  3. The volume-ratio shortcut
  4. Dalton's law of partial pressures
  5. Try this

What this topic is asking

This page brings the gas laws and stoichiometry together. A Massachusetts high school chemistry course expects you to calculate the volumes of gases in a reaction using the molar volume, to use the shortcut that coefficient ratios are also volume ratios for gases, and to apply Dalton's law of partial pressures to a mixture of gases.

Gas stoichiometry with molar volume

The path is the same mole bridge as before, with one extra step for any gas:

  1. Convert the known to moles. For a gas at STP, divide its volume by 22.4 L/mol.
  2. Apply the mole ratio from the balanced equation.
  3. Convert the moles of the unknown to the units asked. For a gas at STP, multiply by 22.4 L/mol to get a volume.

This lets you start from a gas volume and finish at a mass, or start from a mass and finish at a gas volume, just by inserting the molar volume at the right point. The general method is set out in stoichiometric calculations.

The volume-ratio shortcut

Because equal volumes contain equal moles at the same conditions, the coefficients can be read straight as a volume ratio. For 2H2+O2→2H2O(g)2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O(g)}, 2 volumes of hydrogen react with 1 volume of oxygen to give 2 volumes of steam. So 10 L of hydrogen needs 5 L of oxygen and makes 10 L of steam, with no need to find moles. This shortcut works only when all the relevant substances are gases at matched conditions.

Dalton's law of partial pressures

Each gas in a mixture moves and collides independently, so each contributes its own partial pressure to the total. Air, for example, has a total pressure that is the sum of the partial pressures of nitrogen, oxygen, and the rest. A common use is collecting a gas over water: the measured pressure includes water vapor, so the gas's own pressure is the total minus the known vapor pressure of water.

Try this

Q1. A mixture contains helium at 30 kPa, neon at 50 kPa, and argon at 20 kPa. Find the total pressure. [1]

  • Cue. 30+50+20=10030 + 50 + 20 = 100 kPa (Dalton's law).

Q2. At STP, how many liters of carbon dioxide form when 5.0 L of methane burns completely? [1]

  • Cue. Ratio of CH4\text{CH}_4 to CO2\text{CO}_2 is 1 to 1, so 5.0 L.

Exam-style practice questions

Practice questions written in the style of MA DESE exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

MA Chemistry (style)3 marksFor N2+3H2→2NH3\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3, all gases at STP: (a) State the volume ratio of hydrogen to ammonia. (b) What volume of ammonia forms from 6.0 L of hydrogen? (c) Explain why the coefficient ratio also works for volumes.
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A 3-point gas-stoichiometry item.

(a) 1 point: the volume ratio of H2\text{H}_2 to NH3\text{NH}_3 is 3 to 2, the same as the coefficient ratio.
(b) 1 point: 6.0×23=4.06.0 \times \dfrac{2}{3} = 4.0 L of ammonia.
(c) 1 point: at the same temperature and pressure, equal volumes of gas contain equal numbers of moles (Avogadro), so the mole ratio is also the volume ratio. Markers reward citing equal volumes for equal moles.

MA Chemistry (style)2 marksA container holds oxygen at 60 kPa and nitrogen at 40 kPa. (a) State the total pressure. (b) Name the law used.
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A 2-point Dalton's law item.

(a) 1 point: total pressure =60+40=100= 60 + 40 = 100 kPa.
(b) 1 point: Dalton's law of partial pressures (the total pressure is the sum of the partial pressures of the gases in the mixture). Markers reward adding the partial pressures and naming Dalton's law.

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