Under certain conditions, neon (Ne) gas diffuses at a rate of 4.5 centimeters per second. Under the same conditions, an unknown gas diffuses at a rate of 10.1 centimeters per second. What is the approximate molar mass of the unknown gas?
(rate1/rate2) = sqrt(M2/M1)
M2 = molar mass of gas 2. M1 = molar mass gas 2.
Ne = 20.2
mv^2 = const
m ~ 1/v^2
(4.5/10.1)^2 = 0.198
20.2 * 0.198 = 4.0 g/mol (Helium)
that is an incorrect answer
To determine the approximate molar mass of the unknown gas, we can use Graham's Law of Diffusion.
Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, this can be represented as:
Rate1 / Rate2 = sqrt(Molar mass2 / Molar mass1)
In this case, we are given the rates of diffusion for neon (Rate1) and the unknown gas (Rate2). Let's substitute these values into the equation:
4.5 / 10.1 = sqrt(Molar mass of unknown gas / Molar mass of neon)
Simplifying, we get:
0.446 = sqrt(Molar mass of unknown gas / 20.18)
To isolate the molar mass of the unknown gas, we square both sides:
(0.446)^2 = Molar mass of unknown gas / 20.18
0.199 = Molar mass of unknown gas / 20.18
Now, let's solve for the molar mass of the unknown gas:
Molar mass of unknown gas = 0.199 * 20.18
Molar mass of unknown gas ≈ 4.01 g/mol
Therefore, the approximate molar mass of the unknown gas is 4.01 g/mol.