The density of the vapour of a substance at 1 atm and 500 K is `0.36 kgm^(-2)`. If molar mass of gas is `18 g mol^(-1)` the molar volume of gas is `5 xx 10^(a) m^(3)//mol` What is the value of a ?

Explanation

To solve the problem, we need to find the value of \( a \) in the expression for molar volume \( 5 \times 10^a \, \text{m}^3/\text{mol} \). We will use the given density and molar mass to calculate the molar volume.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Density (\( \rho \)) = 0.36 kg/m³
- Molar Mass (\( M \)) = 18 g/mol = 0.018 kg/mol (since 1 g = 0.001 kg)

2. **Use the Formula for Molar Volume:**
The molar volume (\( V_m \)) can be calculated using the formula:
\[ V_m = \frac{M}{\rho} \]
where \( M \) is the molar mass and \( \rho \) is the density.

3. **Substitute the Values:**
\[ V_m = \frac{0.018 \, \text{kg/mol}}{0.36 \, \text{kg/m}^3} \]

4. **Calculate the Molar Volume:**
\[ V_m = \frac{0.018}{0.36} \, \text{m}^3/\text{mol} \]
\[ V_m = 0.05 \, \text{m}^3/\text{mol} \]

5. **Express in Scientific Notation:**
We can express \( 0.05 \, \text{m}^3/\text{mol} \) in scientific notation:
\[ 0.05 = 5 \times 10^{-2} \]
Therefore, the molar volume can be written as:
\[ V_m = 5 \times 10^{-2} \, \text{m}^3/\text{mol} \]

6. **Identify the Value of \( a \):**
From the expression \( 5 \times 10^a \, \text{m}^3/\text{mol} \), we can see that:
\[ a = -2 \]

### Final Answer:
The value of \( a \) is \( -2 \).