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Dimensional Analysis

At 273 K temp...

Question

At $273 K$ temperature and $76 c m H g$ pressure, the density of a gas is $1.964 g L^{- 1} .$ The gas is :

C H_{4}

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C O

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H e

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C O_{2}

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Solution

The correct option is D $C O_{2}$
We know,
$P V = n R T$
$\Rightarrow P V = \frac{W}{M} R T$
Or, $M = \frac{d R T}{P}$
Given, $d = 1.964 g / l$
$P = 76 c m = 760 m m H g = 1 a t m$
$R = 0.0821 l a t m K^{- 1} m o l^{- 1}$
$T = 273 K$
$∴ M = \frac{1.964 \times 0.0821 \times 273}{1} \approx 44$
So, gas is $C O_{2}$

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