Molecular mass of a gas is 78 . Its density at `98 .^(@)C` and 1 atm will be

Options

A. `200 g L^(-1)`
B. `2 . 56 g L^(-1)`
C. `256 g L^(-1)`
D. `78 g L^(-1)`

Explanation

To find the density of a gas with a molecular mass of 78 g/mol at a temperature of 98°C and a pressure of 1 atm, we can use the ideal gas law rearranged in terms of density. The ideal gas law is given by:

\[ PV = nRT \]

Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Number of moles
- \( R \) = Ideal gas constant
- \( T \) = Temperature in Kelvin

### Step-by-Step Solution

1. **Convert Temperature to Kelvin**:
- The temperature in Celsius is given as 98°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
\[ T = 98 + 273.15 = 371.15 \, K \]

2. **Use the Ideal Gas Law**:
- The ideal gas law can be rearranged to express density (\( D \)):
\[ D = \frac{PM}{RT} \]
Where:
- \( D \) = Density
- \( P \) = Pressure (1 atm)
- \( M \) = Molar mass (78 g/mol)
- \( R \) = Ideal gas constant (0.0821 atm·L/(mol·K))
- \( T \) = Temperature in Kelvin (371.15 K)

3. **Substitute the Values**:
- Now we can substitute the known values into the equation:
\[ D = \frac{(1 \, \text{atm}) \times (78 \, \text{g/mol})}{(0.0821 \, \text{atm·L/(mol·K)}) \times (371.15 \, K)} \]

4. **Calculate the Density**:
- First, calculate the denominator:
\[ 0.0821 \times 371.15 = 30.487 \, \text{atm·L/mol} \]
- Now, calculate the density:
\[ D = \frac{78}{30.487} \approx 2.56 \, \text{g/L} \]

5. **Final Answer**:
- The density of the gas at 98°C and 1 atm is approximately **2.56 g/L**.

### Summary
The density of the gas with a molecular mass of 78 g/mol at 98°C and 1 atm is **2.56 g/L**.