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 gas formula \( \text{CO}_x \) given that its vapor density is 70, we can follow these steps:

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

### Step 2: Calculate the molecular weight using the vapor density
Given that the vapor density of the gas is 70, we can calculate the molecular weight:
\[ \text{Molecular Weight} = 2 \times 70 = 140 \]

### Step 3: Write the expression for the molecular weight of the gas \( \text{CO}_x \)
The molecular weight of \( \text{CO}_x \) can be expressed as:
\[ \text{Molecular Weight} = \text{Molar mass of C} + x \times \text{Molar mass of O} \]
Where:
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Oxygen (O) = 16 g/mol

Thus, the molecular weight of \( \text{CO}_x \) is:
\[ \text{Molecular Weight} = 12 + 16x \]

### Step 4: Set up the equation
Now, we can set the molecular weight we calculated equal to the expression we derived for \( \text{CO}_x \):
\[ 12 + 16x = 140 \]

### Step 5: Solve for \( x \)
To find \( x \), we will rearrange the equation:
\[ 16x = 140 - 12 \]
\[ 16x = 128 \]
Now, divide both sides by 16:
\[ x = \frac{128}{16} = 8 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{8} \]