Question

The correct value of the gas constant $R$ is close to

• A. 0.082 L-atm $ K^{-1}\,mol^{-1} $
• B. 0.082 $ L-atm^{-1} $ K mol
• C. 0.082 L-atm K mol
• D. 0.082 $ L-atm^{-1} $ K mol

Answer 1

Answer: (A)

We know
$p V =n R T $
$R =\frac{p V}{n T} $
$R =\frac{p V}{n T} $
$=\frac{\text { pressure } \times \text { volume }}{\text { mole } \times \text { temperature }}$
$=\frac{\text { work or energy }}{\text { mole } \times \text { temperature }}$
$R$ is expressed in the unit of work or energy $mol ^{-1} K ^{-1}$.
The different values of $R$ are summarised below
$R =0.0821\, L \,atm \,mol ^{-1}{ K }^{-1} $
$=8.3143 \times 10^{7} erg\, mol ^{-1} K ^{-1} $
$=8.3143 \,J \,mol ^{-1} K ^{-1} $
$=8.3143 \,Nm \,mol ^{-1} K ^{-1}$
$=8.3143 \times 10^{-3} kJ \,mol ^{-1} K ^{-1} $
$=1.987 \,cal\, mol ^{-1} K ^{-1}$
$=5.189 \times 10^{19} eV\, mol ^{-1} K ^{-1}$