If `0.24 g` of a volatile liquid upon vaporization gives `45 ml` of vapors at `NTP`, what will be the vapor density of the substance? (Density of `H_(2) = 0.089 f L^(-1)`)

Options

A. `112`
B. `37.3`
C. `59.9`
D. `56`

Explanation

To find the vapor density of the volatile liquid, we can follow these steps:

### Step 1: Understand the formula for vapor density
The vapor density (D) of a substance can be calculated using the formula:
\[ D = \frac{\text{mass of vapor}}{\text{mass of equal volume of hydrogen}} \]

### Step 2: Identify the mass of the vapor
From the question, we know that the mass of the volatile liquid that vaporized is:
\[ \text{Mass of vapor} = 0.24 \, \text{g} \]

### Step 3: Calculate the mass of an equal volume of hydrogen
We need to find the mass of hydrogen that occupies the same volume as the vapor. The volume of vapor given is:
\[ \text{Volume of vapor} = 45 \, \text{ml} = 45 \times 10^{-3} \, \text{L} \]

Using the density of hydrogen at NTP, which is given as \( 0.089 \, \text{g/L} \), we can calculate the mass of hydrogen:
\[ \text{Mass of hydrogen} = \text{Density of H}_2 \times \text{Volume of H}_2 \]
\[ \text{Mass of hydrogen} = 0.089 \, \text{g/L} \times 45 \times 10^{-3} \, \text{L} \]
\[ \text{Mass of hydrogen} = 0.089 \times 0.045 \]
\[ \text{Mass of hydrogen} = 0.004005 \, \text{g} \]

### Step 4: Substitute values into the vapor density formula
Now we can substitute the mass of the vapor and the mass of hydrogen into the vapor density formula:
\[ D = \frac{0.24 \, \text{g}}{0.004005 \, \text{g}} \]

### Step 5: Calculate the vapor density
Calculating the above expression:
\[ D = \frac{0.24}{0.004005} \approx 59.9 \]

### Final Answer
The vapor density of the volatile liquid is approximately:
\[ \text{Vapor Density} \approx 59.9 \]