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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
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two vessels of volumes 16.4 L and 5 L contain two ideal gases of molec...
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, 

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Most Upvoted Answer
Two vessels of volumes 16.4 L and 5 L contain two ideal gases of molec...
Given Data:
- Volume of vessel 1 (V1) = 16.4 L
- Volume of vessel 2 (V2) = 5 L
- Temperature of gas in vessel 1 (T1) = 27 °C
- Temperature of gas in vessel 2 (T2) = 227 °C
- Pressure of gas in vessel 1 (P1) = 1.5 atm
- Pressure of gas in vessel 2 (P2) = 4.1 atm

Explanation:
1. Using the ideal gas law equation, \(PV = nRT\), where:
- P is the pressure
- V is the volume
- n is the number of moles of gas
- R is the ideal gas constant
- T is the temperature in Kelvin
2. We know that the number of molecules is directly proportional to the number of moles of gas.
\(n = \frac{PV}{RT}\)
3. The ratio of the number of molecules of gas in vessel 1 to that of vessel 2 can be calculated as:
\(\frac{n_1}{n_2} = \frac{P_1V_1}{RT_1} \times \frac{RT_2}{P_2V_2}\)
4. Plugging in the values, we get:
\(\frac{n_1}{n_2} = \frac{1.5 \times 16.4}{0.0821 \times (27 + 273)} \times \frac{0.0821 \times (227 + 273)}{4.1 \times 5}\)
5. Solving the above equation, we get:
\(\frac{n_1}{n_2} = 2\)
Therefore, the ratio of the number of molecules of gas in vessel 1 to that of vessel 2 is 2, which corresponds to option 'A'.
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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 isa)2b)1c)1/2d)1/3Correct answer is option 'A'. Can you explain this answer?
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