Chapter 11 · Gases
11.8The Ideal Gas Law: Pressure, Volume, Temperature, and Moles
13 min · two checks
Predict
What is R if pressure is in kPa and volume is in liters?
The idea
- Solve PV = nRT for any variable.
- Find molar mass from gas density.
The ideal gas law packs the earlier laws into PV = nRT. R is a constant whose numerical value depends on the units of P and V. Temperature is kelvin. Moles, not grams, go in for n. Solve by isolating the unknown: n = PV/RT is the workhorse when a reaction needs moles of a gas that you measured by volume.
Density connects to molar mass. Because n = m/M, PV = (m/M)RT, so M = mRT/(PV) = dRT/P, with d in g/L if M is in g/mol and V is in L. A gas that is “too dense” for its conditions has a higher molar mass. Real gases depart from the law at high pressure and low temperature; for this course, assume ideal behavior unless the problem says the gas is near condensation.
Keep these
- PV = nRT. T in kelvin. n in moles.
- R = 8.314 kPa·L/(mol·K) or 0.08206 L·atm/(mol·K).
- Molar mass M = dRT/P.
Worked path
What volume does 0.500 mol of an ideal gas occupy at 100.0 kPa and 25 °C? R = 8.314 kPa·L/(mol·K).
Observe
T = 298 K. Solve for V.