First slide

Gaseous state

Question

What per cent of a sample of nitrogen must be allowed to escape if its temperature, pressure and volume are to be changed as given?

Moderate

A

16.67%
B

83.33%
C

75.00%
D

25.00%

Solution

$\frac{p_{1} V_{1}}{T_{1}} = \frac{3 \times 1 .65}{546} = 9 .066 \times 10^{- 3} \frac{p_{2} V_{2}}{T_{2}} = \frac{0 .75 \times 0 .55}{273} = 1 .51 \times 10^{- 3} < \frac{p_{1} V_{1}}{T_{1}} Hence, N_{2} gas in LHS should escape to make \frac{p_{1} v_{1}}{T_{1}} = \frac{p_{2} v_{2}}{T_{2}} . ∴ V_{1} = \frac{p_{2} V_{2} \times T_{1}}{T_{2} \times P_{1}} = \frac{0 .75 \times 0 .55 \times 546}{273 \times 3} = 0 .275 L Volume of N_{2} escaped = 1 .65 - 0 .275 = 1 .375 L Hence, fraction of N_{2} escaped = \frac{1 .375}{1 .65} = 0 .8333$

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