Answer:
Sure, I can help you with that.
The given conditions are:
200 cm of hydrogen diffuses in 2 seconds
Vapour density of gas X = 25
RMM of hydrogen = 2
We need to determine the time it takes for 490 cm³ of gas X to diffuse under the same conditions.
The formula for Graham's Law of Diffusion is:
r1/r2 = √(M2/M1)
where:
r1 is the rate of diffusion of gas 1
r2 is the rate of diffusion of gas 2
M1 is the molar mass of gas 1
M2 is the molar mass of gas 2
In this case, gas 1 is hydrogen and gas 2 is X.
The molar mass of hydrogen is 2 g/mol and the molar mass of X is 25 g/mol.
Plugging these values into the formula, we get:
r1/r2 = √(M2/M1) = √(25/2) = 5/2
We know that 200 cm³ of hydrogen diffuses in 2 seconds. So, the rate of diffusion of hydrogen is 200/2 = 100 cm³/s.
The rate of diffusion of gas X is 5/2 * 100 cm³/s = 250 cm³/s.
Therefore, it will take 490/250 = 1.96 seconds for 490 cm³ of gas X to diffuse under the same conditions.
Hydrogen: Molar mass = 2 g/mol, Rate of diffusion = 100 cm³/s, Time = 2 seconds.
- Gas X: Molar mass = 25 g/mol, Rate of diffusion = 250 cm³/s, Time = 1.96 seconds.