A mixture of methane and ethane in the mole ratio of x : y has a mean molecular mass equal to 20. What would be the mean molecular mass of a mixture of the same gases present in the ratio y : x?a)20b)22c)24d)None of theseCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Mean molecular mass of a mixture of gases is calculated by taking the weighted average of the individual molecular masses of the gases present in the mixture.

Given:
Mole ratio of methane to ethane = x : y
Mean molecular mass of the mixture = 20

To find:
Mean molecular mass of the mixture in the ratio y : x

Let's assume the molecular masses of methane and ethane are M1 and M2 respectively.

Weighted average of the molecular masses of the mixture can be calculated using the following formula:

Mean molecular mass = (x * M1 + y * M2) / (x + y)

According to the given information, the mean molecular mass of the mixture is 20:

20 = (x * M1 + y * M2) / (x + y) ........(1)

We need to find the mean molecular mass of the mixture in the ratio y : x. Let's represent it as MM:

MM = (y * M1 + x * M2) / (y + x) ........(2)

We can find the relationship between MM and 20 by rearranging equation (1) as follows:

20 = (x * M1 + y * M2) / (x + y)
20 * (x + y) = x * M1 + y * M2
20x + 20y = x * M1 + y * M2 ........(3)

Now, let's rearrange equation (2) to match the form of equation (3):

MM = (y * M1 + x * M2) / (y + x)
MM * (y + x) = y * M1 + x * M2
MMy + MMx = y * M1 + x * M2 ........(4)

Comparing equations (3) and (4), we can see that the left-hand side of both equations is the same (20x + 20y = MMy + MMx). However, the right-hand side of both equations is different.

Since the right-hand sides of equations (3) and (4) are not equal, the mean molecular mass of the mixture in the ratio y : x is not equal to 20. Therefore, the correct answer is option D: None of these.

Answer

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