A sample of unknown gas effuses in 10.6 min. An equal volume of H2 in the same apparatus under the same conditions effuses in 2.42 min. What is the molar mass of the unknown gas?
(rateu/ratek) = sqrt(Mk/Mu)
u = unknown
k = known
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. Mathematically, it can be expressed as:
Rate1 / Rate2 = √(Molar Mass2 / Molar Mass1)
In this case, we have the following information:
Rate1 = rate of effusion of the unknown gas
Rate2 = rate of effusion of H2
Molar Mass2 = molar mass of H2 (2.02 g/mol) (Note: the molar mass of H2 can be found in the periodic table)
Let's plug in the values we have:
Rate1 / Rate2 = √(Molar Mass2 / Molar Mass1)
Rate1 / 2.42 = √(2.02 / Molar Mass1)
Now, we need to rearrange the equation to solve for the molar mass of the unknown gas (Molar Mass1):
√(2.02 / Molar Mass1) = Rate1 / 2.42
To eliminate the square root, we'll square both sides of the equation:
2.02 / Molar Mass1 = (Rate1 / 2.42)^2
Now, rearrange the equation to solve for Molar Mass1:
Molar Mass1 = (2.02 / (Rate1 / 2.42)^2)
Given that the unknown gas effuses in 10.6 min, we substitute this value into the equation:
Molar Mass1 = (2.02 / (10.6 / 2.42)^2)
Now, we can evaluate this equation to find the molar mass of the unknown gas.