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Q.

The capacity of a vessel is 3 L. It contains 6 g oxygen, 8g nitrogen and 5 g CO₂ mixture at 27^oC. If R = 8.31 J/mol K, then the pressure in the vessel in N/m² will be (approx.)

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a

$5 \times 10^{5}$

b

$5 \times 10^{4}$

c

$10^{6}$

d

$10^{5}$

answer is A.

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Detailed Solution

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By Dalton's law

$\begin{array}{l} P = P_{1} + P_{2} + P_{3} = \frac{μ_{1} RT}{V} + \frac{μ_{2} RT}{V} + \frac{μ_{3} RT}{V} \\ = \frac{RT}{V} [μ_{1} + μ_{2} + μ_{3}] = \frac{RT}{V} [\frac{m_{1}}{M_{1}} + \frac{m_{2}}{M_{2}} + \frac{m_{3}}{M_{3}}] = \frac{8.31 \times 300}{3 \times 10^{- 3}} [\frac{6}{32} + \frac{8}{28} + \frac{5}{44}] \\ = 498 \times 10^{3} = 500 \times 10^{3} = 5 \times 10^{5} N / m^{2} \end{array}$

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