200cm3 of a diffused through a porous plug in 5s under the same condition 450cm3of oxygen diffused in 5s. Calculate the relative molecular mass of the gas
First, we need to use Graham's law of diffusion to find the ratio of the rates of diffusion of the two gases:
Rate of gas A / Rate of gas B = sqrt (Molar mass of gas B / Molar mass of gas A)
We know that the rate of oxygen (gas B) is 450 cm3 in 5 seconds, or 90 cm3/s.
Let x be the relative molecular mass of the other gas (gas A), and let its rate of diffusion be y cm3/s.
Then, we can write:
y / 90 = sqrt (32 / x)
where 32 is the molar mass of oxygen (in g/mol).
Next, we can use the given data that 200 cm3 of gas A diffused in 5 seconds to solve for y:
y / 90 = 200 / 450
y = 80 cm3/s
Substituting into the previous equation, we can solve for x:
80 / 90 = sqrt (32 / x)
x = (32 * 90^2) / 80^2
x = 36
Therefore, the relative molecular mass of gas A is 36.
To calculate the relative molecular mass of the gas, we need to use Graham's law of diffusion.
According to Graham's law of diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Let's assume the molar mass of the gas we want to find is M. The rate of diffusion (r) of a gas is given by:
r = V / t
Where:
- r is the rate of diffusion
- V is the volume of the gas diffused
- t is the time taken for diffusion
For the first gas:
r1 = V1 / t1
For the second gas:
r2 = V2 / t2
We are given the following information:
V1 = 200 cm^3
t1 = 5 s
V2 = 450 cm^3
t2 = 5 s
We can calculate the rate of diffusion for both gases:
r1 = 200 cm^3 / 5 s = 40 cm^3/s
r2 = 450 cm^3 / 5 s = 90 cm^3/s
Now, we can use Graham's law to find the relative molecular mass (M) of the gas:
r1 / r2 = √(M2 / M1)
40 / 90 = √(M2 / M1)
Cross-multiplying:
40 * M1 = 90 * M2
M2 / M1 = 40 / 90
M2 = (40 / 90) * M1
Since we don't know the molar mass of the second gas (M2), let's assume M1 = 28 g/mol, which is the molar mass of nitrogen gas (N2).
M2 = (40 / 90) * 28 g/mol
M2 ≈ 12.4 g/mol
Therefore, the relative molecular mass of the gas is approximately 12.4 g/mol.