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At identical temp and pressure the rate of diffusion of hydrogen gas is 5.19 times that of hydrocarbon having molecular formula CnH2n-2. What is value of ‘n’ ?
Correct answer is '4'. Can you explain this answer?
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In order to find the value of n, we can use Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Let's assume the molar mass of the hydrocarbon is M and the molar mass of hydrogen gas is 2.02 g/mol (approximately).
According to Graham's law, the rate of diffusion of hydrogen gas (RH2) is 5.19 times that of the hydrocarbon (RHc).
Therefore, we can write the equation:
RH2 = 5.19 * RHc
The rate of diffusion is inversely proportional to the square root of the molar mass, so we can also write the equation:
√2.02 = 5.19 * √M
Simplifying the equation:
√M = √2.02 / 5.19
Squaring both sides of the equation:
M = (2.02 / 5.19)^2
Calculating the value:
M = 0.7796 g/mol
Now, let's substitute the value of M into the molecular formula of the hydrocarbon:
CnH2n-2
The molar mass of the hydrocarbon is:
M = n * 12.01 + (2n - 2) * 1.01
Substituting the value of M:
0.7796 = n * 12.01 + (2n - 2) * 1.01
Simplifying the equation:
0.7796 = 12.01n + 2.02n - 2.02
14.03n = 2.7996
Dividing both sides of the equation by 14.03:
n = 0.1996
Therefore, the value of n is approximately 0.1996.
Let's assume the molar mass of the hydrocarbon is M and the molar mass of hydrogen gas is 2.02 g/mol (approximately).
According to Graham's law, the rate of diffusion of hydrogen gas (RH2) is 5.19 times that of the hydrocarbon (RHc).
Therefore, we can write the equation:
RH2 = 5.19 * RHc
The rate of diffusion is inversely proportional to the square root of the molar mass, so we can also write the equation:
√2.02 = 5.19 * √M
Simplifying the equation:
√M = √2.02 / 5.19
Squaring both sides of the equation:
M = (2.02 / 5.19)^2
Calculating the value:
M = 0.7796 g/mol
Now, let's substitute the value of M into the molecular formula of the hydrocarbon:
CnH2n-2
The molar mass of the hydrocarbon is:
M = n * 12.01 + (2n - 2) * 1.01
Substituting the value of M:
0.7796 = n * 12.01 + (2n - 2) * 1.01
Simplifying the equation:
0.7796 = 12.01n + 2.02n - 2.02
14.03n = 2.7996
Dividing both sides of the equation by 14.03:
n = 0.1996
Therefore, the value of n is approximately 0.1996.
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At identical temp and pressure the rate of diffusion of hydrogen gas is 5.19 times that of hydrocarbon having molecular formula CnH2n-2. What is value of ‘n’ ?Correct answer is '4'. Can you explain this answer?
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