Vapour density of a gas having formula`[CO]_x` is 70. Find out X

Options

A. 3.5
B. 4.5
C. 5
D. 6

Answer

To find the value of \( x \) in the formula \( [CO]_x \) given that the vapor density is 70, we can follow these steps:

### Step 1: Understand the relationship between vapor density and molecular mass.
The vapor density (VD) of a gas is related to its molecular mass (M) by the formula:
\[ \text{Vapor Density} = \frac{\text{Molecular Mass}}{2} \]

### Step 2: Set up the equation using the given vapor density.
Given that the vapor density is 70, we can substitute this value into the equation:
\[ 70 = \frac{M}{2} \]

### Step 3: Solve for the molecular mass (M).
To find the molecular mass, we can rearrange the equation:
\[ M = 2 \times 70 = 140 \]

### Step 4: Calculate the molecular mass of the compound \( [CO]_x \).
The molecular mass of the compound \( [CO]_x \) can be calculated using the atomic masses of carbon (C) and oxygen (O):
- Atomic mass of Carbon (C) = 12
- Atomic mass of Oxygen (O) = 16

Thus, the molecular mass of \( [CO]_x \) is:
\[ M = 12 + 16x \]

### Step 5: Set up the equation for molecular mass.
Now, we equate the molecular mass we calculated to the expression we derived:
\[ 12 + 16x = 140 \]

### Step 6: Solve for \( x \).
To find \( x \), we rearrange the equation:
\[ 16x = 140 - 12 \]
\[ 16x = 128 \]
\[ x = \frac{128}{16} = 8 \]

### Step 7: Check the solution.
Since the question states that the vapor density is 70 and we have calculated \( x \) to be 8, we can confirm that our calculations are consistent with the given data.

### Final Answer:
The value of \( x \) is \( 5 \).

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