A gas X diffuse through porous partition at the rate of 3 cm3 per second. Under the same condition hydrogen diffused at the rate of 15 cm3 per second.
What is the 42. relative molecular mass of X.
5
12
18
45
50
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Given that r1 = 3cm³/s, r2 = 15cm³/s, M1 = ? M2 = 2
Where:
r1 = rate of diffusion of the unknown gas
r2 = rate of diffusion of hydrogen
M1 = Molar mass of the unknown gas
M2 = Molar mass of hydrogen
From Graham's law of diffusion
Rate = √M where M is molar mass.
For two gases, the law can be expressed as
R1/R2 = √M2/M1
3/15 = √2/M1
Squaring both sides to remove the square root, we have
(3/15)² = (√2/M1)²
9/225 = 2/M1
M1 = 225 × 2/9
M1 = 50
Relative Molecular Mass of the unknown gas = 50
A gas X diffuse through porous partition at the rate of 3 cm3 per second. Under the same condition hydrogen diffused at the rate of 15 cm3 per second.
What is the 42. relative molecular mass of X.
A. 5
B. 12
C. 18
D. 45
E. 50
To find the relative molecular mass of gas X, we can use Graham's law of diffusion:
Graham's Law
Rate1 / Rate2 = √(M2 / M1)
Where:
- Rate1 is the rate of diffusion of gas X (3 cm³/s)
- Rate2 is the rate of diffusion of hydrogen (15 cm³/s)
- M1 is the molecular mass of gas X (unknown)
- M2 is the molecular mass of hydrogen (2 g/mol)
Rearranging the equation
We can rearrange the equation to solve for M1:
M1 = M2 x (Rate2 / Rate1)²
Plugging in values
M1 = 2 g/mol x (15 cm³/s / 3 cm³/s)²
= 2 g/mol x (5)²
= 2 g/mol x 25
= 50 g/mol
So, the relative molecular mass of gas X is 50 g/mol.
