Equal weight of `CO and CH_(4)` are mixed together in an empty container at 300K. The fraction of total pressure exerted by `CH_(4)` is

Options

A. ` ( 16 ) /( 17 ) `
B. ` ( 7 ) /( 11 ) `
C. ` ( 8 ) /(9 ) `
D. ` ( 5 )/( 16 ) `

Explanation

To solve the problem of finding the fraction of total pressure exerted by methane (CH₄) when equal weights of carbon monoxide (CO) and methane are mixed, we can follow these steps:

### Step 1: Define the weights of CO and CH₄
Let the weight of CO be \( A \) grams and the weight of CH₄ also be \( A \) grams since they are equal.

### Step 2: Calculate the number of moles of CO and CH₄
- The molar mass of CO is 28 g/mol.
- The molar mass of CH₄ is 16 g/mol.

Using the formula for moles:
\[ \text{Moles of CO} = \frac{A}{28} \]
\[ \text{Moles of CH₄} = \frac{A}{16} \]

### Step 3: Calculate the total number of moles
The total number of moles \( n_{\text{total}} \) is the sum of the moles of CO and CH₄:
\[ n_{\text{total}} = \text{Moles of CO} + \text{Moles of CH₄} = \frac{A}{28} + \frac{A}{16} \]

To add these fractions, we need a common denominator. The least common multiple of 28 and 16 is 112:
\[ n_{\text{total}} = \frac{4A}{112} + \frac{7A}{112} = \frac{11A}{112} \]

### Step 4: Calculate the mole fraction of CH₄
The mole fraction \( X_{\text{CH₄}} \) is given by the formula:
\[ X_{\text{CH₄}} = \frac{\text{Moles of CH₄}}{n_{\text{total}}} \]
Substituting the values we calculated:
\[ X_{\text{CH₄}} = \frac{\frac{A}{16}}{\frac{11A}{112}} = \frac{A}{16} \times \frac{112}{11A} = \frac{112}{176} = \frac{7}{11} \]

### Step 5: Calculate the fraction of total pressure exerted by CH₄
According to Dalton's Law of Partial Pressures, the fraction of total pressure exerted by a gas is equal to its mole fraction. Therefore, the fraction of total pressure exerted by CH₄ is:
\[ \text{Fraction of pressure by CH₄} = X_{\text{CH₄}} = \frac{7}{11} \]

### Final Answer
The fraction of total pressure exerted by methane (CH₄) is \( \frac{7}{11} \).

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