Question

What must be the units of R, the gas constant, in this formula? A. Newton • meter per kelvin B. mole • kelvin per Newton • meter C. Newton • meter per mole • kelvin D. Newton • meter • kelvin per mole

Answer 1

`P=\frac{\text{nRT}}{V}`

Solve R:

Multiply both sides of the equation by V:

`\begin{gathered} PV=V\cdot\frac{\text{nRT}}{V} \\ \\ PV=nRT \end{gathered}`

Divide both sides of the equation by nT:

`\begin{gathered} (PV)/(nT)=\frac{\text{nRT}}{nT} \\ \\ (PV)/(nT)=R \end{gathered}`

Then, R is:

`R=(PV)/(nT)`

Use the given units in the equation above:

`R=(N\cdot m^3)/(mol\cdot K)`

Then, the units of R are: Newton*cubic meter per mol*Kelvin