To calculate the number of moles of an ideal gas, we can use the Ideal Gas Law, which is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure in atm
- \( V \) = volume in liters
- \( n \) = number of moles
- \( R \) = ideal gas constant = 0.0821 L·atm/(K·mol)
- \( T \) = temperature in Kelvin
Given:
- \( P = 0.50 , \text{atm} \)
- \( V = 0.45 , \text{L} \)
- \( T = 273 , \text{K} \)
We can solve for \( n \) (number of moles):
\[ n = \frac{PV}{RT} \]
Substituting in the values:
\[ n = \frac{(0.50 , \text{atm}) \times (0.45 , \text{L})}{(0.0821 , \text{L·atm/(K·mol)}) \times (273 , \text{K})} \]
Calculating the denominator:
\[ 0.0821 \times 273 \approx 22.4143 , \text{L·atm/(K·mol)} \]
Now calculating \( n \):
\[ n = \frac{0.50 \times 0.45}{22.4143} \]
\[ n = \frac{0.225}{22.4143} \approx 0.01 , \text{mol} \]
Therefore, the number of moles of the ideal gas present in a 0.45 L sample at 273 K and 0.50 atm pressure is approximately 0.01 mol.
The correct response is 0.01 mol.