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Partial Pressure and Dalton's Law Worked Examples cheat sheet - grade 11-12

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Chemistry Grade 11-12

Partial Pressure and Dalton's Law Worked Examples Cheat Sheet

A printable reference covering Dalton's law, partial pressure, mole fraction, collected gas corrections, and worked gas mixture examples for grades 11-12.

TopicsPressureThermodynamicsStates of MatterMoleculesRatios and ProportionsChemistryStudy Guide
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Partial pressure describes how much pressure one gas contributes inside a mixture of gases. Dalton's law is important because many chemistry problems involve air, collected gases, or reacting gases mixed in the same container. This cheat sheet helps students organize gas mixture calculations and choose the right formula for each situation.

Worked-example skills are especially useful for laboratory problems involving gases collected over water.

The core idea is that the total pressure of a gas mixture equals the sum of the pressures from each gas. A gas's partial pressure can also be found from its mole fraction using Pi=XiPtotalP_i = X_iP_{\text{total}}. For gases collected over water, the dry gas pressure is found by subtracting water vapor pressure: Pgas=Ptotal−PH2OP_{\text{gas}} = P_{\text{total}} - P_{\text{H}_2\text{O}}.

These relationships connect pressure, moles, and composition in ideal gas mixtures.

Key Facts

  • Dalton's law states that the total pressure of a gas mixture is Ptotal=P1+P2+P3+⋯P_{\text{total}} = P_1 + P_2 + P_3 + \cdots.
  • The partial pressure of a gas is the pressure it would exert if it alone occupied the same volume at the same temperature.
  • Mole fraction is calculated with Xi=nintotalX_i = \frac{n_i}{n_{\text{total}}}, where nin_i is the moles of one gas.
  • Partial pressure from mole fraction is calculated with Pi=XiPtotalP_i = X_iP_{\text{total}}.
  • The sum of all mole fractions in a gas mixture is X1+X2+X3+⋯=1X_1 + X_2 + X_3 + \cdots = 1.
  • For a gas collected over water, the dry gas pressure is Pgas=Ptotal−PH2OP_{\text{gas}} = P_{\text{total}} - P_{\text{H}_2\text{O}}.
  • If gases are in the same container at the same temperature and volume, their partial pressures are proportional to their moles, so P1P2=n1n2\frac{P_1}{P_2} = \frac{n_1}{n_2}.
  • Pressure units must match before using Dalton's law, such as converting 760 mmHg=1 atm=101.3 kPa760\ \text{mmHg} = 1\ \text{atm} = 101.3\ \text{kPa}.

Vocabulary

Partial pressure
The pressure contributed by one gas in a mixture of gases.
Dalton's law
The rule that the total pressure of a gas mixture equals the sum of the partial pressures of all gases present.
Mole fraction
The ratio of moles of one gas to the total moles of all gases in the mixture, written as Xi=nintotalX_i = \frac{n_i}{n_{\text{total}}}.
Total pressure
The combined pressure exerted by every gas particle in a gas mixture.
Water vapor pressure
The pressure exerted by water vapor, which must be subtracted when a gas is collected over water.
Ideal gas mixture
A mixture of gases that behaves as if each gas particle moves independently and does not chemically react with the others.

Common Mistakes to Avoid

  • Adding mole fractions to pressures directly is wrong because mole fraction has no units while pressure does. Use Pi=XiPtotalP_i = X_iP_{\text{total}} to convert mole fraction into partial pressure.
  • Forgetting to subtract water vapor pressure gives a wet gas pressure instead of the dry gas pressure. For gas collected over water, use Pgas=Ptotal−PH2OP_{\text{gas}} = P_{\text{total}} - P_{\text{H}_2\text{O}}.
  • Using mismatched pressure units causes incorrect totals. Convert all pressures to the same unit before applying Ptotal=P1+P2+P3+⋯P_{\text{total}} = P_1 + P_2 + P_3 + \cdots.
  • Treating partial pressure as dependent on gas identity is misleading for ideal gases. At the same temperature and volume, partial pressure depends on the number of moles, not whether the gas is N2\text{N}_2, O2\text{O}_2, or another gas.
  • Rounding mole fractions too early can change the final pressure noticeably. Keep extra digits during calculations and round only the final answer to the correct significant figures.

Practice Questions

  1. 1 A mixture contains 0.40 mol0.40\ \text{mol} of O2\text{O}_2 and 0.60 mol0.60\ \text{mol} of N2\text{N}_2 at a total pressure of 2.50 atm2.50\ \text{atm}. What is the partial pressure of O2\text{O}_2?
  2. 2 A gas sample is collected over water at 25∘C25^\circ\text{C} when the total pressure is 98.7 kPa98.7\ \text{kPa}. If PH2O=3.17 kPaP_{\text{H}_2\text{O}} = 3.17\ \text{kPa}, what is the pressure of the dry gas?
  3. 3 A container has PHe=220 mmHgP_{\text{He}} = 220\ \text{mmHg}, PNe=315 mmHgP_{\text{Ne}} = 315\ \text{mmHg}, and PAr=0.280 atmP_{\text{Ar}} = 0.280\ \text{atm}. What is the total pressure in mmHg\text{mmHg}?
  4. 4 Explain why adding more N2\text{N}_2 to a fixed-volume container at constant temperature increases the total pressure and changes the mole fractions of the other gases.

Understanding Partial Pressure and Dalton's Law Worked Examples

At the particle level, pressure comes from gas particles striking the walls of a container. In a mixture, nitrogen particles, oxygen particles, and every other kind of particle all strike the same walls independently. Their collision effects add because the particles are mostly far apart.

This is why a gas does not need to be separated from the others to have its own pressure contribution. A gas with more particles makes more wall collisions in the same time.

At one fixed temperature and volume, doubling the moles of one gas doubles its partial pressure. This direct link between particle count and pressure makes mole ratios especially useful.

A reliable worked-example method starts by listing the gases that are actually present at the final moment. Then decide which quantity is known for each gas, such as moles, mass, volume, or pressure. Convert mass to moles before finding composition.

Add the moles to find total moles. Divide each gas's moles by total moles to find its share of the mixture. Multiply that share by total pressure to find its pressure contribution.

As a quick check, the individual pressures should add back to the measured total pressure. A larger mole fraction must give a larger partial pressure when gases share one container at the same temperature.

Gas collected over water needs extra care because the container holds two substances in the gas space. The desired gas is mixed with water vapor that came from liquid water. Water molecules escape from the liquid surface until evaporation and condensation reach a balance.

Warmer water creates more water vapor, so its vapor pressure depends strongly on temperature. Use a vapor pressure table for the actual water temperature, not room temperature guessed from memory.

Subtract the water vapor contribution before using the ideal gas law to calculate moles of the dry gas. Forgetting this correction makes the dry gas pressure too large and leads to too many calculated moles.

These ideas appear beyond classroom lab work. Air is a mixture, and oxygen's partial pressure helps explain why breathing becomes harder at high altitude. The percentage of oxygen in air changes very little with altitude, but lower total atmospheric pressure means fewer oxygen particle collisions and a lower oxygen partial pressure.

Medical gas cylinders, scuba systems, and industrial chemical processes must control gas composition for the same reason. Most school calculations treat gases as ideal, which works best at low pressure and moderate temperature.

Real gases can depart from ideal behavior when particles are crowded or strongly attracted. For typical grade eleven and grade twelve problems, careful unit conversion, correct temperature use, and a clear list of gases matter more than complicated corrections.