How many moles of He gas occupy 22.4 litres at `30^(@)C` and one atmospheric pressure

Options

A. 0.9
B. 1.11
C. 0.11
D. 1

Answer

To find out how many moles of helium gas occupy 22.4 liters at 30°C and one atmospheric pressure, we can use the ideal gas equation:

### Step-by-Step Solution:

1. **Identify the Ideal Gas Equation**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature (in Kelvin)

2. **Convert Temperature to Kelvin**:
The temperature in Celsius needs to be converted to Kelvin using the formula:
\[ T(K) = T(°C) + 273.15 \]
For 30°C:
\[ T = 30 + 273.15 = 303.15 \, K \]

3. **Identify Given Values**:
- Pressure, \( P = 1 \, atm \)
- Volume, \( V = 22.4 \, L \)
- Temperature, \( T = 303.15 \, K \)
- Ideal gas constant, \( R = 0.0821 \, L \cdot atm/(K \cdot mol) \)

4. **Rearrange the Ideal Gas Equation to Solve for n**:
We need to find \( n \):
\[ n = \frac{PV}{RT} \]

5. **Substitute the Values into the Equation**:
Substitute \( P \), \( V \), \( R \), and \( T \) into the equation:
\[ n = \frac{(1 \, atm)(22.4 \, L)}{(0.0821 \, L \cdot atm/(K \cdot mol))(303.15 \, K)} \]

6. **Calculate the Moles**:
Now, calculate \( n \):
\[ n = \frac{22.4}{0.0821 \times 303.15} \]
First, calculate the denominator:
\[ 0.0821 \times 303.15 \approx 24.736 \]
Now, divide:
\[ n \approx \frac{22.4}{24.736} \approx 0.905 \, moles \]

### Final Answer:
Approximately 0.905 moles of helium gas occupy 22.4 liters at 30°C and one atmospheric pressure.

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