To find the number of moles of an ideal gas, we can use the Ideal Gas Law, which is represented by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant, which is \( 0.0821 , \text{L} \cdot \text{atm} / (\text{K} \cdot \text{mol}) \)
- \( T \) = temperature (in Kelvin)
Given:
- \( P = 0.50 , \text{atm} \)
- \( V = 0.45 , \text{L} \)
- \( T = 273 , \text{K} \)
Now, we can rearrange the Ideal Gas Law to solve for \( n \):
\[ n = \frac{PV}{RT} \]
Now substituting the values into the equation:
\[ n = \frac{(0.50 , \text{atm})(0.45 , \text{L})}{(0.0821 , \text{L} \cdot \text{atm} / (\text{K} \cdot \text{mol}))(273 , \text{K})} \]
Calculating the denominator:
\[ R \cdot T = 0.0821 \cdot 273 \approx 22.4143 , \text{L} \cdot \text{atm} / \text{mol} \]
Now substitute back into the equation for \( n \):
\[ n = \frac{(0.50 \cdot 0.45)}{22.4143} \]
Calculating the numerator:
\[ 0.50 \cdot 0.45 = 0.225 \]
Now:
\[ n = \frac{0.225}{22.4143} \approx 0.01003 , \text{mol} \]
Rounding gives \( n \approx 0.01 , \text{mol} \).
Therefore, the number of moles of the ideal gas present in the sample is approximately 0.01 mol.