An unknown gas diffuses ar a rate of 0.5 times that of nitrogen at the same temperature and pressure. Calculate the molar mass of the unknown gas.
(rate unknown/rate N2) = sqrt (molar mas N2/molar mass unknown)
Substitute and solve for molar mass unknown.
To calculate the molar mass of the unknown gas, we need to use Graham's Law of Diffusion. According to Graham's Law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Let's assume that the molar mass of nitrogen (N2) is M1, and the molar mass of the unknown gas is M2. The rate of diffusion of the unknown gas (r2) is given as 0.5 times the rate of diffusion of nitrogen (r1).
According to Graham's Law:
r2/r1 = √(M1/M2)
Substituting the given values:
0.5 = √(M1/M2)
Squaring both sides of the equation:
0.5^2 = M1/M2
0.25 = M1/M2
Cross-multiplying:
M1 = 0.25 * M2
Now, we need to know the molar mass of nitrogen (N2) to find the molar mass of the unknown gas. The molar mass of nitrogen is approximately 28 g/mol.
Substituting the value of M1:
28 g/mol = 0.25 * M2
Dividing both sides by 0.25:
M2 = 28 g/mol / 0.25
M2 = 112 g/mol
Therefore, the molar mass of the unknown gas is approximately 112 g/mol.
To find the 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.
Let's assume that the molar mass of nitrogen (N2) is M1 and the molar mass of the unknown gas is M2. The rate of diffusion of the unknown gas is given as 0.5 times that of nitrogen.
According to Graham's Law:
(rate of diffusion of unknown gas) / (rate of diffusion of nitrogen) = √(Molar mass of nitrogen / Molar mass of unknown gas)
Therefore, we can write the equation as:
0.5 = √(M1 / M2)
To solve for the molar mass of the unknown gas (M2), we need to isolate it in the equation.
Let's square both sides of the equation:
(0.5)^2 = (√(M1 / M2))^2
Simplifying the equation:
0.25 = M1 / M2
Now, we can rearrange the equation to solve for M2:
M2 = M1 / 0.25
So, the molar mass of the unknown gas (M2) can be calculated by dividing the molar mass of nitrogen (M1) by 0.25.
Please provide the molar mass of nitrogen (M1) to continue the calculation.