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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.

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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

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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,

\(\frac{P_1V_1}{P_2V_2}\) = \(\frac{n_1T_1}{n_2T_2}\)

\(\frac{n_1}{n_2}\) = \(\frac{P_1V_1T_1}{P_2V_2T_2}\)

∴ \(\frac{1.5 \times 16.4 \times 500}{4.1 \times 5 \times 300}\) = \(\frac{2}{1}\)

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