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:

$\begin{gathered} \frac{PV}{nT}=\frac{\text{nRT}}{nT} \\ \\ \frac{PV}{nT}=R \end{gathered}$

Then, R is:

$R=\frac{PV}{nT}$

Use the given units in the equation above:

$R=\frac{N\cdot m^3}{mol\cdot K}$

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