60 cm of hydrogen diffused through a porous membrane in 10 minutes. The same volume of gas G diffused through the same membrane in 37.4 minutes. Determine the relative molecular mass of
60 cm of hydrogen diffused through a porous membrane in 10 minutes. The same volume of gas G diffused through the same membrane in 37.4 minutes. Determine the relative molecular mass of g (h equal to 1)
To determine the relative molecular mass of gas G, we can use Graham's law of diffusion. According to Graham's law, the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass.
Let's assign the rate of diffusion of hydrogen (H₂) as r₁ and the rate of diffusion of gas G as r₂. We can set up the following equation based on Graham's law:
r₁/r₂ = √(M₂/M₁)
Given that r₁ = 60 cm and r₂ = 37.4 cm (since both gases diffused through the same membrane), M₁ is the molar mass of hydrogen (H₂), and we need to solve for M₂, which is the molar mass of gas G.
Now, let's plug in the values into the equation and solve for M₂:
60/37.4 = √(M₂/2)
Simplifying further:
1.604 = √(M₂/2)
To eliminate the square root, we square both sides:
2.57 = M₂/2
Now, solve for M₂ by multiplying both sides by 2:
M₂ = 2 × 2.57
M₂ = 5.14
Therefore, the relative molecular mass of gas G is approximately 5.14.
To determine the relative molecular mass of gas G, we can use Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
The formula for Graham's law of diffusion is:
Rate1 / Rate2 = √(Molar Mass2 / Molar Mass1)
Let's denote the molar mass of gas G as Molar Mass2 and the molar mass of hydrogen as Molar Mass1.
Given:
Rate1 (rate of diffusion of hydrogen) = 60 cm/10 min = 6 cm/min
Rate2 (rate of diffusion of gas G) = Same volume of gas, so Rate2 = 60 cm/37.4 min = 1.604 cm/min
Plugging these values into the formula:
6 / 1.604 = √(Molar Mass2 / Molar Mass1)
To find the ratio of the molar masses, we square both sides of the equation:
(6 / 1.604)² = (Molar Mass2 / Molar Mass1)²
36 / 2.573616 = Molar Mass2 / Molar Mass1
Simplifying this equation:
2.573616 = Molar Mass2 / Molar Mass1
Since we're trying to find the relative molecular mass of gas G, we can rewrite this as:
Relative Molecular Mass of G / Molar Mass of Hydrogen = 2.573616
Therefore, the relative molecular mass of gas G is approximately 2.573616 times the molar mass of hydrogen.
rate 1 = H2 = 60/10 = ?
rate 2 = G = 60/37.4 = ?
(rate1/rate2) = sqrt(MMG/MMH2) where MMG is molar mass G and MMH2 = molar mass H2.
You know molar mass H2. The only unknown is MMG.