In PV = nRT, which statement about units is true?

In PV = nRT, which statement about units is true?

• A. Pressure is measured in pascals and temperature in kelvin.
• B. Volume is independent of temperature.
• C. Temperature is measured in Celsius.
• D. Pressure is measured in atmospheres.

Answer: (A)

The equation is solved most clearly when the units are consistent in the SI system. For this form, pressure in pascals, volume in cubic metres, and temperature in kelvin are used, with R = 8.314 J mol−1 K−1. Kelvin is an absolute temperature scale, so it measures temperature from zero without any offset; Celsius would shift the temperature values and disrupt the direct proportionality in PV ∝ T. With these SI units, the left-hand side PV has units of the energy-like joules, matching nRT. That’s why using pressure in pascals and temperature in kelvin is the true statement. Volume depends on temperature at fixed pressure and amount of gas, so it is not independent of temperature. Temperature in Celsius isn’t compatible with the standard form, and while you could use atmospheres and litres if you adjust R accordingly, that isn’t the universal unit requirement.

The equation is solved most clearly when the units are consistent in the SI system. For this form, pressure in pascals, volume in cubic metres, and temperature in kelvin are used, with R = 8.314 J mol−1 K−1. Kelvin is an absolute temperature scale, so it measures temperature from zero without any offset; Celsius would shift the temperature values and disrupt the direct proportionality in PV ∝ T. With these SI units, the left-hand side PV has units of the energy-like joules, matching nRT. That’s why using pressure in pascals and temperature in kelvin is the true statement. Volume depends on temperature at fixed pressure and amount of gas, so it is not independent of temperature. Temperature in Celsius isn’t compatible with the standard form, and while you could use atmospheres and litres if you adjust R accordingly, that isn’t the universal unit requirement.