The ideal gas constant R has units of which of the following?

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Multiple Choice

The ideal gas constant R has units of which of the following?

Explanation:
The units come from the equation PV = nRT. Pressure times volume has the same units as energy: in SI, pressure is in pascals (N/m^2) and volume in cubic meters, so P·V = (N/m^2)·m^3 = N·m = J. Since this equals nRT, the gas constant R must convert energy to amount and temperature, giving units of J per mole per kelvin. So R has units J/(mol·K). It's common to also see N·m/(mol·K) since J = N·m, and even kg·m^2/(s^2·mol·K) is the same as J/(mol·K). The standard expression is J/(mol·K).

The units come from the equation PV = nRT. Pressure times volume has the same units as energy: in SI, pressure is in pascals (N/m^2) and volume in cubic meters, so P·V = (N/m^2)·m^3 = N·m = J. Since this equals nRT, the gas constant R must convert energy to amount and temperature, giving units of J per mole per kelvin. So R has units J/(mol·K). It's common to also see N·m/(mol·K) since J = N·m, and even kg·m^2/(s^2·mol·K) is the same as J/(mol·K). The standard expression is J/(mol·K).

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