At same temperature and pressure which of the following pairs of gases has same rate of diffusion?

C O, N_{2} O

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C O_{2}, N_{2} O

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N_{2} O, C H_{4}

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N O_{2}, S O_{2}

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Solution

The correct option is D $C O_{2}, N_{2} O$
According to Graham's law of diffusion, at same temperature and pressure.
$r \propto \frac{1}{\sqrt{M}}$
Option (A) CO, $N_{2} O$
$M_{C O} = 12 + 16 = 28$
$M_{N_{2} O} = (14 \times 2) + 16 = 44$
Option (B) $C O_{2}, N_{2} O$
$M_{C O_{2}} = 12 + (16 \times 2) = 44$ .
$M_{N_{2} O} = (14 \times 2) + 16 = 44$ .
Option (C) $N_{2} O, C H_{4}$
$M_{N_{2} O} = 44$
$M_{C H_{4}} = 12 + 4 = 16$
Option (D) $N O_{2}, S O_{2}$
$M N O_{2} = 14 + (16 \times 2) = 46$
$M S O_{2} = 32 + (16 \times 2) = 64$
In the given options, the gases $C O_{2}, N_{2} O$ have same rates of diffusion.

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