The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight of X is:a)64.0b)32.0c)4.0d)8.0Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Answer

Because of rate is inversly proportional to square root of molecular waightGiven. R1=2 R2. And M1=16  then 2 R2/R2= sq.root of M2/M1,,,put velue ans 64

Answer

Introduction:
The rate of diffusion of a gas is directly proportional to the square root of its molar mass. Therefore, if we know the rate of diffusion of one gas and the rate of diffusion of another gas at a given temperature, we can determine the relative molecular weights of the two gases.

Given information:
The rate of diffusion of methane (CH4) is twice that of gas X at a given temperature.

Solution:
To determine the molecular weight of gas X, we need to compare its rate of diffusion to that of methane.

Step 1: Use the rate of diffusion ratio
The rate of diffusion of methane is given as twice that of gas X. Let's call the rate of diffusion of methane as rCH4 and the rate of diffusion of gas X as rX.

rCH4 = 2 * rX

Step 2: Use the formula for rate 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. Therefore, we can write the following equation:

rCH4 / rX = √(MX / MCH4)

Where MX is the molar mass of gas X and MCH4 is the molar mass of methane.

Step 3: Substitute the given information
From the given information, we know that rCH4 = 2 * rX. Substituting this into the equation above, we get:

2 * rX / rX = √(MX / MCH4)

2 = √(MX / MCH4)

Step 4: Solve for MX / MCH4
To solve for MX / MCH4, we square both sides of the equation:

2^2 = (√(MX / MCH4))^2

4 = MX / MCH4

Step 5: Determine the molecular weight of gas X
Now we have the ratio of the molecular weight of gas X to the molecular weight of methane:

MX / MCH4 = 4

Since the molecular weight of methane (MCH4) is 16 g/mol, we can solve for MX:

MX = 4 * MCH4

MX = 4 * 16 g/mol

MX = 64 g/mol

Conclusion:
Therefore, the molecular weight of gas X is 64.0 g/mol, which corresponds to option A.

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