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States of Matter
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09/09/2021 7:17 pm
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Two vessels of volumes 16.4 L and 5 L contain two ideal gases of molecular existence at the respective temperature of 27°C and 227°C and exert 1.5 and 4.1 atmospheres respectively. The ratio of the number of molecules of the former to that of the later is
(a) 2
(b) 1
(c) 1/2
(d) 1/3
1 Answer
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09/09/2021 7:23 pm
Correct answer: (a) 2
Explanation:
Given conditions
V1 = 16.4 L, V2 = 5 L
P1 = 1.5 atm, P2 = 4.1 atm
T1 = 273 + 27 = 300 K,
T2 = 273 + 227 = 500 K
Applying gas equation,
\(\frac{P_1V_1}{P_2V_2}\) = \(\frac{n_1T_1}{n_2T_2}\)
\(\frac{n_1}{n_2}\) = \(\frac{P_1V_1T_1}{P_2V_2T_2}\)
∴ \(\frac{1.5 \times 16.4 \times 500}{4.1 \times 5 \times 300}\) = \(\frac{2}{1}\)