a sample of hydrogen effuses through a porous container about 9 times faster than an unknown gas. Estimate the molar mass of the unknown gas.
To estimate 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 assume the molar mass of hydrogen gas (H2) is M. Since the rate of effusion of hydrogen gas is 9 times faster than the unknown gas, we can write the following equation:
Rate of effusion of hydrogen (H2) / Rate of effusion of unknown gas = √(Molar mass of unknown gas / Molar mass of hydrogen gas)
Substituting the given information:
9 = √(Molar mass of unknown gas / M)
Squaring both sides of the equation:
9^2 = Molar mass of unknown gas / M
81 = Molar mass of unknown gas / M
To estimate the molar mass of the unknown gas, we need to find the Molar mass of unknown gas (in grams/mole) divided by the molar mass of hydrogen gas (in grams/mole), which will give us the molar mass ratio.
Let's assume the molar mass of hydrogen gas is approximately 2 g/mol.
81 = molar mass of unknown gas / 2
Solving for the molar mass of the unknown gas:
molar mass of unknown gas = 81 * 2
molar mass of unknown gas = 162 g/mol
Therefore, the estimated molar mass of the unknown gas is 162 g/mol.
To estimate the molar mass of the unknown gas, we can use Graham's Law of Effusion, which states:
Rate1 / Rate2 = sqrt(MolarMass2 / MolarMass1)
In this case, we are given that the effusion rate of hydrogen (H2) is 9 times faster than the unknown gas. Therefore, we can set up the equation as follows:
9 / 1 = sqrt(MolarMassUnknown / MolarMassHydrogen)
Since the molar mass of hydrogen is approximately 2 g/mol, we can substitute this value into the equation:
9 = sqrt(MolarMassUnknown / 2)
To solve for the molar mass of the unknown gas, we square both sides of the equation:
81 = MolarMassUnknown / 2
Now, we can solve for MolarMassUnknown by multiplying both sides of the equation by 2:
162 = MolarMassUnknown
Therefore, the estimated molar mass of the unknown gas is 162 g/mol.
rateH2/rateunk = sqrt (M unk)/MH2)
The problem doesn't give a rate; therefore, choose a convenient number, such as 1L/1 sec for H2 which makes the unknown 1L/9 sec since it is 9 times slower.