the molar mass of an unknown gas was measured by an effusion experiment. it took 63s for te gas to effuse. where as nitrogen gas took 48sec. what is the molar mass of the gas?
32g/mol
37g/mol
24g/mol
16g/mol
48g/mol
rateu/raten = sqrt(molar mass N2/molar mass U)
u = unknown
n = nirtogen
48
To calculate the molar mass of the unknown gas, we can use Graham's Law of Effusion. According to Graham's Law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Let's denote the molar mass of the unknown gas as M. According to the problem, the time it took for the unknown gas to effuse is 63 seconds, while nitrogen gas took 48 seconds. Therefore, we can set up a ratio of the square roots of the molar masses and the times:
√M_unknown gas / √M_nitrogen gas = t_nitrogen gas / t_unknown gas
Substituting the known values into the equation:
√M_unknown gas / √28 g/mol = 48 s / 63 s
Simplifying, we get:
√M_unknown gas / √28 g/mol = 4/3
Now, let's solve for √M_unknown gas:
√M_unknown gas = (√28 g/mol) * (4/3)
√M_unknown gas = (√112 g/mol) / 3
√M_unknown gas ≈ 10.583 / 3
√M_unknown gas ≈ 3.528
Finally, to find the molar mass of the unknown gas, we square the value of √M_unknown gas:
M_unknown gas ≈ (3.528)^2
M_unknown gas ≈ 12.443 g/mol
Rounding to the nearest whole number, the molar mass of the unknown gas is approximately 12 g/mol.
None of the provided answer options match this calculated value, so the correct answer may not be available.
To determine the molar mass of the unknown gas, we can use Graham's law of effusion. According to Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The formula can be written as:
Rate1 / Rate2 = √(Molar mass2 / Molar mass1)
Let's use this formula to find the molar mass of the unknown gas in comparison to nitrogen gas:
Rate1 (unknown gas) / Rate2 (nitrogen gas) = √(Molar mass of nitrogen gas / Molar mass of unknown gas)
Given that the unknown gas took 63 seconds to effuse and nitrogen gas took 48 seconds, we can substitute these values into the formula:
63 / 48 = √(28 g/mol / Molar mass of unknown gas)
To solve for the molar mass of the unknown gas, we need to isolate the unknown gas's molar mass on one side of the equation:
√(28 g/mol / Molar mass of unknown gas) = 63 / 48
Square both sides of the equation to remove the square root:
28 g/mol / Molar mass of unknown gas = (63 / 48)^2
Simplify the right side of the equation:
28 g/mol / Molar mass of unknown gas = 1.3125
Now, we can solve for the molar mass of the unknown gas by isolating it on one side:
Molar mass of unknown gas = 28 g/mol / 1.3125
Calculating this expression will give us the molar mass of the unknown gas:
Molar mass of unknown gas = 21.333 g/mol
Since none of the options provided match this result, it seems that an error may have occurred in the calculations or in the provided options. Please double-check the information and calculations to determine the correct molar mass for the unknown gas.