ideal gas constant
Summary
The ideal gas constant R is the proportionality constant in PV = nRT. It is 8.314 J/(mol·K), or 0.0821 L·atm/(mol·K). It is the same for every ideal gas, and only its numerical value changes with the units, so match R to the units of P and V.
Detail
Meaning: R links pressure, volume, amount and temperature in the ideal gas law. It does not depend on which gas is present. It is an energy per mole per kelvin, so the same constant appears wherever the MCAT relates energy to temperature. Common values: 8.314 J/(mol·K), which equals 8.314 m³·Pa/(mol·K) 0.0821 L·atm/(mol·K)
Equation: PV = nRT, where P is pressure (Pa), V is volume (m³), n is amount of gas (mol), R is the ideal gas constant (J/(mol·K)), and T is absolute temperature (K). R is also the product of Avogadro's number and Boltzmann's constant.
On the MCAT: Gas-law questions ask for n, P, V or T, and the main task is choosing the R that fits the units given. R also shows up outside gas laws: ΔG = ΔG° + RT ln Q, ΔG° = −RT ln Keq, the Arrhenius equation k = Ae^(−Ea/RT), and average kinetic energy of one mole of gas = (3/2)RT. In urms = √(3RT/M), M must be in kg/mol when R is in J/(mol·K).
Common confusion: Students think R changes with the gas or with conditions. It does not. Only its numerical value changes with the units used. Two errors are common: using 0.0821 when pressure is in kPa or volume is in mL, and putting temperature in °C. T must be in kelvin. In thermodynamics, use 8.314 J/(mol·K), and convert to kJ if ΔG° is given in kJ/mol.
Sources
- Chemistry: The Central Science
- Chemistry: Atoms First
- General Chemistry: Principles and Modern Applications
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.