The density of chlorine relative to air is

Options

A. 2.44
B. 3
C. found only experimentally
D. 4

Answer

To find the density of chlorine relative to air, we can follow these steps:

### Step 1: Understand the Concept of Relative Density
Relative density (or specific gravity) is the ratio of the density of a substance to the density of a reference substance. In this case, we are comparing the density of chlorine (Cl₂) to the density of air.

### Step 2: Write the Formula for Relative Density
The formula for relative density (RD) is given by:
\[ \text{Relative Density} = \frac{\text{Density of Gas A}}{\text{Density of Gas B}} \]
Here, Gas A is chlorine and Gas B is air.

### Step 3: Use the Ideal Gas Law to Relate Density to Molecular Weight
From the ideal gas law (PV = nRT), we can derive that density (ρ) is proportional to the molecular weight (M) of the gas:
\[ \rho = \frac{M}{RT} \]
Thus, we can express the relative density in terms of molecular weights:
\[ \text{Relative Density} = \frac{\rho_{\text{Cl}_2}}{\rho_{\text{air}}} = \frac{M_{\text{Cl}_2}}{M_{\text{air}}} \]

### Step 4: Find the Molecular Weights
- The molecular weight of chlorine (Cl₂) is approximately 70.9 g/mol (since Cl has a molecular weight of about 35.45 g/mol).
- The molecular weight of air can be approximated as 29 g/mol (considering the average composition of air).

### Step 5: Calculate the Relative Density
Now, we can substitute the molecular weights into the relative density formula:
\[ \text{Relative Density} = \frac{M_{\text{Cl}_2}}{M_{\text{air}}} = \frac{70.9 \, \text{g/mol}}{29 \, \text{g/mol}} \]
Calculating this gives:
\[ \text{Relative Density} \approx 2.44 \]

### Conclusion
The relative density of chlorine with respect to air is approximately 2.44.

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