In what ratio by mass, the gases CO and 2 butene `(C_4 H_8)` be mixed in a vessel so that they cause same partial pressures ?

Options

A. `1:1`
B. `2:1`
C. `1:2`
D. `1:3`

Answer

To solve the problem of finding the mass ratio of CO (carbon monoxide) and 2-butene (C₄H₈) that will cause the same partial pressures in a vessel, we can follow these steps:

### Step 1: Understand the relationship between partial pressures and moles
According to Dalton's Law of Partial Pressures, the partial pressure of a gas is directly proportional to the number of moles of that gas. Therefore, for CO and C₄H₈ to exert the same partial pressure, the number of moles of CO must equal the number of moles of C₄H₈.

### Step 2: Write the formula for moles
The number of moles (n) of a gas can be calculated using the formula:
\[ n = \frac{W}{M} \]
where:
- \( W \) = mass of the gas
- \( M \) = molar mass of the gas

### Step 3: Calculate the molar masses
- The molar mass of CO (carbon monoxide) is 28 g/mol.
- The molar mass of C₄H₈ (2-butene) is 56 g/mol.

### Step 4: Set up the equation for moles
Let \( W_1 \) be the mass of CO and \( W_2 \) be the mass of C₄H₈. According to our understanding from Step 1, we can write:
\[ \frac{W_1}{M_{CO}} = \frac{W_2}{M_{C_4H_8}} \]
Substituting the molar masses:
\[ \frac{W_1}{28} = \frac{W_2}{56} \]

### Step 5: Cross-multiply to find the mass ratio
Cross-multiplying gives us:
\[ 56W_1 = 28W_2 \]

### Step 6: Rearranging the equation
Rearranging the equation to find the ratio of \( W_1 \) to \( W_2 \):
\[ \frac{W_1}{W_2} = \frac{28}{56} = \frac{1}{2} \]

### Conclusion
Thus, the mass ratio of CO to 2-butene (C₄H₈) is 1:2.

### Final Answer
The gases CO and 2-butene should be mixed in a ratio of **1:2 by mass**.

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