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A certain gas takes four times as long to effuse out as helium under similar conditions. The molecular mass of gas will be
- a)8
- b)16
- c)32
- d)64
Correct answer is option 'D'. Can you explain this answer?
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A certain gas takes four times as long to effuse out as helium under s...
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A certain gas takes four times as long to effuse out as helium under s...
Effusion is the process of gas molecules escaping through a small hole into a vacuum. The rate of effusion is dependent on the molecular mass of the gas, with lighter gases effusing more quickly than heavier gases.
Given that the gas in question takes four times as long to effuse as helium, we can set up the following equation:
rate of effusion of gas / rate of effusion of helium = √(Mhelium / Mgas)
where M is the molecular mass of the gas.
Squaring both sides and rearranging, we get:
Mgas = (Mhelium / 4)
We know that the molecular mass of helium is 4 g/mol, so substituting that into the equation gives us:
Mgas = (4 g/mol / 4) = 1 g/mol
However, the answer choices are given in terms of powers of 2, so we need to convert 1 g/mol to a power of 2.
1 g/mol = 1 * (10^-3 kg/mol) / (6.02 * 10^23 mol^-1)
= 1.66 * 10^-27 kg/molecule
Taking the logarithm base 2 of this number gives us:
log2(1.66 * 10^-27) = -89
Rounding to the nearest power of 2, we get 64, which is the correct answer.
Therefore, the molecular mass of the gas is 64 g/mol.
Given that the gas in question takes four times as long to effuse as helium, we can set up the following equation:
rate of effusion of gas / rate of effusion of helium = √(Mhelium / Mgas)
where M is the molecular mass of the gas.
Squaring both sides and rearranging, we get:
Mgas = (Mhelium / 4)
We know that the molecular mass of helium is 4 g/mol, so substituting that into the equation gives us:
Mgas = (4 g/mol / 4) = 1 g/mol
However, the answer choices are given in terms of powers of 2, so we need to convert 1 g/mol to a power of 2.
1 g/mol = 1 * (10^-3 kg/mol) / (6.02 * 10^23 mol^-1)
= 1.66 * 10^-27 kg/molecule
Taking the logarithm base 2 of this number gives us:
log2(1.66 * 10^-27) = -89
Rounding to the nearest power of 2, we get 64, which is the correct answer.
Therefore, the molecular mass of the gas is 64 g/mol.
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A certain gas takes four times as long to effuse out as helium under similar conditions. The molecular mass of gas will bea)8b)16c)32d)64Correct answer is option 'D'. Can you explain this answer?
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