For an ideal gas, what is the relationship among P, V, n, R, and T and what are common unit choices for R?

• A. PV = nRT; R = 0.082057 L atm mol−1 K−1 or R = 8.314 J mol−1 K−1.
• B. PV = nRT; R = 1.
• C. PV = nRT^2.
• D. P + V = nRT.

Answer: (A)

For an ideal gas, the relationship among pressure, volume, amount of substance, the gas constant, and temperature is PV = nRT. The key is that units must balance on both sides, so the value of R depends on the units you’re using. If pressure is in atmospheres and volume in liters, R is 0.082057 L·atm·mol⁻¹·K⁻¹. If you work in SI units with pressure in pascals and volume in cubic meters, R is 8.314 J·mol⁻¹·K⁻¹ (since 1 J = 1 Pa·m³). The other forms fail because they either mis-handle the units (such as squaring the temperature), combine terms with incompatible operations (adding P and V), or rely on a dimensionless R, which would not make the equation dimensionally consistent.