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.
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.
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.
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.