If two mole of an ideal gas at `546 K` occupies a volume of `44.8 litres`, the pressure must be :

Options

A. 2 atm
B. 3 atm
C. 4 atm
D. 1 atm

Answer

To find the pressure of the ideal gas using the ideal gas equation, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature (in Kelvin)

2. **Identify the given values**:
- Number of moles, \( n = 2 \) moles
- Volume, \( V = 44.8 \) liters
- Temperature, \( T = 546 \) K
- Ideal gas constant, \( R = 0.0821 \) L·atm/(K·mol)

3. **Rearrange the Ideal Gas Law to solve for Pressure \( P \)**:
\[ P = \frac{nRT}{V} \]

4. **Substitute the known values into the equation**:
\[ P = \frac{(2 \text{ moles}) \times (0.0821 \text{ L·atm/(K·mol)}) \times (546 \text{ K})}{44.8 \text{ L}} \]

5. **Calculate the numerator**:
\[ 2 \times 0.0821 \times 546 = 89.6 \]

6. **Now divide by the volume**:
\[ P = \frac{89.6}{44.8} \]

7. **Perform the division**:
\[ P = 2 \text{ atm} \]

### Final Answer:
The pressure of the gas is \( 2 \text{ atm} \).

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