Gas Laws and Partial Pressure
Identify what stays constant, use absolute temperature, and connect gas equations to particle motion and real situations.
Gas Laws and Partial Pressure
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A gas-law equation is useful only after you identify what is held constant
Temperature must be in kelvins. Gas laws describe macroscopic patterns, while the particle model explains them: pressure comes from wall collisions, temperature reflects average kinetic energy, and volume determines the space available to particles.
For nonreacting gas mixtures, Dalton’s law gives Ptotal = P₁ + P₂ + …, while Pi = XiPtotal and Xi = ni/ntotal.
Name the constants first
A rigid tank fixes volume; a flexible balloon often stays near external pressure; an “isothermal” change fixes temperature; a sealed container fixes amount of gas.
Never use Celsius in a proportion
Convert using K = °C + 273. A change from 20°C to 40°C is 293 K to 313 K—not a doubling of temperature.
Use arrows before algebra to catch impossible answers
Problem: A gas is compressed at constant temperature.
Identify the law: T and n are constant → Boyle’s law.
Predict first: Volume goes down, so pressure must go up.
Calculate: If volume becomes one-fourth as large, pressure becomes four times as large.
Check: Reject any answer showing both pressure and volume decreasing under the stated conditions.
Why it works
A qualitative prediction exposes unit, inversion, and calculator errors before they become final answers.
Five forms you should recognize
Problem: A gas occupies 4.0 L at 100 kPa and is compressed to 2.0 L at constant temperature.
P₂ = 100(4.0)/2.0 = 200 kPaHalving volume doubles pressure.
Problem: A 3.0 L balloon warms from 300 K to 400 K at constant pressure.
V₂ = 3.0(400/300) = 4.0 LProblem: A sealed rigid tank warms from 300 K to 450 K while starting at 120 kPa.
P₂ = 120(450/300) = 180 kPaProblem: Gas A has mole fraction 0.30 at a total pressure of 500 kPa.
P_A = 0.30(500) = 150 kPaProblem: Total pressure is 101 kPa and water-vapor pressure is 3 kPa.
P_dry gas = 101 − 3 = 98 kPaCheck before you commit
- Using Celsius in gas-law ratios
- Choosing a law before identifying constants
- Forgetting the inverse pressure–volume relationship
- Treating partial pressures as averages instead of contributions
- Assuming heating always raises pressure even when volume can change
- Using the pressure of wet gas as though no water vapor were present
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Gas Laws and Partial Pressure FAQ
Why does pressure rise in a heated rigid tank?
Particles move faster and strike the fixed walls more often and with greater momentum change.
Are real gases always ideal?
No. Ideal behavior is an approximation that works best at relatively low pressure and high temperature.
Why does a balloon expand at high altitude?
Lower external pressure allows the trapped gas to occupy a larger volume.
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