Obtain the dimensional equation for universal gas constant. - Vidyadip

MCQ

Obtain the dimensional equation for universal gas constant.

✓
$[\text{ML}^2\text{T}^{-2}]\text{ mol }^{-1}\text{K}^{-1}$
B
$[\text{M}^2\text{LT}^{-1}\text{mol }^{-2}\text{K}^{-2}]$
C
$[\text{ML}^{2}\text{L}\text{T}^{-1}\text{ mol}^{-1}\text{K}^{-1}]$
D
$[\text{ML}^{3}\text{L}\text{T}^{-1}\text{ mol}^{-1}\text{K}^{-2}]$

✓

Answer

Correct option: A.

$[\text{ML}^2\text{T}^{-2}]\text{ mol }^{-1}\text{K}^{-1}$

According to ideal gas equation for universal gas constant.
i.e., $\text{pV = nR}T,$ where $n$ is the number of moles of gases.
$\text{R}=\frac{(\text{p})(\text{V})}{(\text{n})(\text{T})}=\frac{[\text{ML}^{-1}\text{T}^2][\text{L}^3]}{{[\text{mol}][\text{K}]}}$
$=[\text{ML}^2\text{T}^{-2}\text{mol}^{-1}\text{K}^{-1}]$

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