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The pressure P, volume V and temperature T of a gas in the jar A and other gas in the jar B at Pressure 2P, volume V/4 and temperature 2T, then the ratio of number of molecules in jar A and B will be.
Select one:
  • a)
    4 : 1
  • b)
    2 : 1
  • c)
    1 : 3
  • d)
    1 : 2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The pressure P, volume V and temperature T of a gas in the jar A and o...
V = nRT    (n = number of moles)
 (N = Number of molecules, NA = Avogadro number)
∴ 

The correct answer is: 4 : 1
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Most Upvoted Answer
The pressure P, volume V and temperature T of a gas in the jar A and o...
Explanation:

Given:
Pressure in jar A (P1) = P
Volume in jar A (V1) = V
Temperature in jar A (T1) = T

Pressure in jar B (P2) = 2P
Volume in jar B (V2) = V/4
Temperature in jar B (T2) = 2T

We know that the ideal gas law equation is given by:

PV = nRT

Where:
P = Pressure of the gas
V = Volume of the gas
n = Number of moles of the gas
R = Ideal gas constant
T = Temperature of the gas

We can rewrite the equation as:

n = PV/RT

Now, let's calculate the number of molecules in jar A and jar B.

Number of molecules in jar A (n1):
n1 = (P1 * V1)/(R * T1)

Number of molecules in jar B (n2):
n2 = (P2 * V2)/(R * T2)

Ratio of number of molecules in jar A and jar B:

n1/n2 = [(P1 * V1)/(R * T1)] / [(P2 * V2)/(R * T2)]

Cancel out the common terms:

n1/n2 = (P1 * V1 * T2) / (P2 * V2 * T1)

Substitute the given values:

n1/n2 = (P * V * T2) / (2P * V/4 * T1)

n1/n2 = (P * V * T2) / (2P * V/4 * T1)

n1/n2 = (4 * P * V * T2) / (2P * V * T1)

Cancel out the common terms:

n1/n2 = (4 * T2) / (2 * T1)

Simplify:

n1/n2 = 2

Therefore, the ratio of the number of molecules in jar A to jar B is 2:1, which corresponds to option b) 2:1.
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