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Q.

A compressed cylinder of gas contains 1.50x10³g of N₂gas at a pressure of 2.0 x 10⁷pa and a temperature of 17.1^oC. What volume of gas has been released into the atmosphere if the final pressure in the cylinder is 1.80 x10⁵ Pa? Assume ideal behavior and that the gas temperature is unchanged.

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a

1264 L

b

12600 L

c

45 L

d

126 L

answer is A.

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Detailed Solution

$\begin{array}{l} n_{N_{2}} = \frac{1.50 \times 10^{3}}{28} = 53 .57 mole \\ \frac{P_{1}}{P_{2}} = \frac{n_{1}}{n_{2}} \\ n_{2} = \frac{1 .8}{200} \times 53 .57 = 0 .48213 \\ n_{N_{2}} escape = 53.57 - 0.48213 = 53 .087 \\ volume = \frac{nRT}{p} = \frac{53.087 \times 0.0821 \times (17.1 + 273)}{1 atm} = 1264 L \end{array}$

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