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A chamber containing a gas was evacuated till the vacuum attained was $10^{- 14}$ m of Hg. If the temperature of the chamber was 30°C, the number of molecules that remain in it per cubic metre is:L

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3.2 $\times$ 10¹¹

3.2 $\times$ 10¹²

2.3 $\times$ 10¹²

2.3 $\times$ 10¹⁰

answer is A.

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Detailed Solution

pV = nRT

$\Rightarrow n = \frac{pV}{RT}$

Now,

$N = n \times 6.02 \times 10^{23} = \frac{PV}{RT} \times 6.02 \times 10^{23}$

$\Rightarrow N = \frac{(10^{- 14} \times 13.6 \times 10^{3} \times 10) (1)}{(8.31) (273 + 30)} \times 6.02 \times 10^{23}$

= 3.2 $\times$ 10¹¹

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