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Kinetic Theory of Gases

The molecular...

Question

The molecular weight of $O_{2}$ and $N_{2}$ are 32 and 28 respectively. At $15^{0} C$ , the pressure of 1 gm $O_{2}$ will be the same as that of 1 gm $N_{2}$ in the same bottle at the temperature ?

A

- 21^{0} C

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B

- 13^{0} C

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C

15^{0} C

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D

{56.4}^{0} V

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Solution

The correct option is B $- 13^{0} C$
Temperature of $O_{2}$ $= 273 + 15 = 298 K$
Temperature of $N_{2}$ $= x$
As $P$ $\propto$ $n T$ , as pressure is same.
$⟹ n_{1} T_{1} = n_{2} T_{2} ⟹ (\frac{1}{32}) (298) = (\frac{1}{28}) (x) ⟹ x = \frac{28}{32} \times 298 = 260.75 K$
Temperature in $^{o} C = 260.75 - 273 = - 13^{o} C$

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