If two moles of an ideal gas at 500 K occupies a volume of 41 litres, the pressure of the gas is `(R = 0.082 L atm K^(-1) mol^(-1))`

Options

A. 2 atm
B. 3 atm
C. 4 atm
D. 5 atm

Explanation

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

### Step-by-Step Solution:

1. **Write the Ideal Gas Equation**:
The ideal gas equation is given by:
\[ PV = nRT \]
where:
- \( P \) = pressure of the gas (in atm)
- \( V \) = volume of the gas (in liters)
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant (0.082 L atm K\(^{-1}\) mol\(^{-1}\))
- \( T \) = temperature of the gas (in Kelvin)

2. **Identify the Given Values**:
From the problem, we have:
- \( n = 2 \) moles
- \( T = 500 \) K
- \( V = 41 \) liters
- \( R = 0.082 \) L atm K\(^{-1}\) mol\(^{-1}\)

3. **Rearrange the Ideal Gas Equation to Solve for Pressure**:
To find the pressure \( P \), we can rearrange the equation:
\[ P = \frac{nRT}{V} \]

4. **Substitute the Known Values into the Equation**:
Now, substitute the values into the equation:
\[ P = \frac{(2 \text{ moles}) \times (0.082 \text{ L atm K}^{-1} \text{ mol}^{-1}) \times (500 \text{ K})}{41 \text{ L}} \]

5. **Calculate the Numerator**:
First, calculate the numerator:
\[ 2 \times 0.082 \times 500 = 82 \]

6. **Calculate the Pressure**:
Now, divide the numerator by the volume:
\[ P = \frac{82}{41} = 2 \text{ atm} \]

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

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