The relative rate of diffusion between two gases is 1.656. If the lighter gas is methane (molecular mass=16.05g/mol), what is the molecular mass of the other gas? What might the other gas be?
(rate1/rate2)=1.656=sqrt(M2/16)
Solve for M2.
To find the molecular mass of the other gas, we can use Graham's law of diffusion.
Graham's law states that the rates of diffusion of two gases are inversely proportional to the square root of their molar masses. Mathematically, it can be expressed as:
Rate1 / Rate2 = sqrt (MolarMass2 / MolarMass1)
Given that the relative rate of diffusion (Rate1 / Rate2) is 1.656, and the molar mass of methane (MolarMass1) is 16.05 g/mol, we can plug in these values into Graham's law equation:
1.656 = sqrt (MolarMass2 / 16.05)
To solve for MolarMass2, we need to isolate it by squaring both sides:
(1.656)^2 = MolarMass2 / 16.05
2.739936 = MolarMass2 / 16.05
Now, we can solve for MolarMass2:
MolarMass2 = 2.739936 * 16.05
MolarMass2 = 43.9987868 g/mol
So, the molecular mass of the other gas is approximately 43.999 g/mol.
To determine what the other gas might be, we could use the periodic table and look for an element with a similar molar mass. In this case, we find that the closest match is carbon dioxide (CO2), which has a molar mass of approximately 44 g/mol. Therefore, it is likely that the other gas is carbon dioxide (CO2).