If 4 moles of an ideal gas at 300 K occupy volume of 89 . 6 L , then pressure of the gas will be (A) 2 atm (B) 1 atm (c) 1.099 atm (D) 2.910 atm

Options

A. 2 atm
B. 1 atm
C. 1.099 atm
D. 2.910 atm

Explanation

To find the pressure of the ideal gas, we can use the Ideal Gas Law, which is expressed as:

\[ PV = nRT \]

Where:
- \( P \) = pressure of the gas (in atm)
- \( V \) = volume of the gas (in liters)
- \( n \) = number of moles of the gas
- \( R \) = ideal gas constant (0.0821 atm·L/(mol·K))
- \( T \) = temperature of the gas (in Kelvin)

### Step-by-step Solution:

1. **Identify the given values:**
- Number of moles, \( n = 4 \) moles
- Temperature, \( T = 300 \) K
- Volume, \( V = 89.6 \) L
- Ideal gas constant, \( R = 0.0821 \) atm·L/(mol·K)

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

3. **Substitute the known values into the equation:**
\[ P = \frac{4 \, \text{moles} \times 0.0821 \, \text{atm·L/(mol·K)} \times 300 \, \text{K}}{89.6 \, \text{L}} \]

4. **Calculate the numerator:**
\[ 4 \times 0.0821 \times 300 = 98.52 \, \text{atm·L} \]

5. **Now divide by the volume:**
\[ P = \frac{98.52 \, \text{atm·L}}{89.6 \, \text{L}} \approx 1.099 \, \text{atm} \]

6. **Conclusion:**
The pressure of the gas is approximately \( 1.099 \, \text{atm} \).

### Final Answer:
(C) 1.099 atm

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