The density of a gas is `1.964` `g dm^(-3)` at `273 K` and `76 cm Hg`. The gas is

Options

A. `CH_(4)`
B. `C_(2)H_(6)`
C. `CO_(2)`
D. `Xe`

Answer

To determine the gas based on the given density, we can use the formula relating density, pressure, temperature, and molar mass. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Density (D) = 1.964 g/dm³
- Temperature (T) = 273 K
- Pressure (P) = 76 cm Hg

### Step 2: Convert pressure to atmospheres
1. Since 76 cm Hg is equivalent to 1 atmosphere (atm), we can use:
\[ P = 1 \text{ atm} \]

### Step 3: Use the density formula
2. The formula relating density (D), pressure (P), molar mass (M), and the ideal gas constant (R) is:
\[ D = \frac{P \cdot M}{R \cdot T} \]
Rearranging this formula to find molar mass (M):
\[ M = \frac{D \cdot R \cdot T}{P} \]

### Step 4: Substitute the values into the formula
3. Use the ideal gas constant R = 0.0821 L·atm/(K·mol) and convert density from g/dm³ to g/L (1 g/dm³ = 1 g/L):
\[ D = 1.964 \text{ g/L} \]
Now substituting the values:
\[ M = \frac{1.964 \, \text{g/L} \cdot 0.0821 \, \text{L·atm/(K·mol)} \cdot 273 \, \text{K}}{1 \, \text{atm}} \]

### Step 5: Calculate the molar mass
4. Performing the calculation:
\[ M = \frac{1.964 \cdot 0.0821 \cdot 273}{1} \]
\[ M = \frac{44.0}{1} = 44.0 \, \text{g/mol} \]

### Step 6: Identify the gas
5. Now, we compare the calculated molar mass with the options given:
- CH₄ (Molar mass = 16 g/mol)
- C₂H₆ (Molar mass = 30 g/mol)
- CO₂ (Molar mass = 44 g/mol)
- Xenon (Molar mass = 131.3 g/mol)

The only gas with a molar mass of 44 g/mol is CO₂.

### Final Answer:
The gas is **CO₂** (Carbon Dioxide).

---