Provide the different values and units of the universal gas constant $R$.
(N/A) The universal gas constant $R$ is defined by the ideal gas equation $PV = nRT$,which implies $R = \frac{PV}{nT}$. Its value depends on the units used for pressure,volume,and temperature. The following table summarizes the common values of $R$:
| Condition | Value and Unit of $R$ |
|---|---|
| $(i)$ Pressure in $atm$,Volume in $L$ | $0.0821 \ L \ atm \ K^{-1} \ mol^{-1}$ |
| $(ii)$ Pressure in $bar$,Volume in $L$ | $0.08314 \ L \ bar \ K^{-1} \ mol^{-1}$ |
| $(iii)$ $SI$ Units (Pressure in $Pa$,Volume in $m^3$) | $8.314 \ J \ K^{-1} \ mol^{-1}$ |
| $(iv)$ Energy in $calories$ | $1.987 \ cal \ K^{-1} \ mol^{-1}$ |
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