To find 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 (0.50 atm)
- \( V \) = volume in liters (0.45 L)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin (273 K)
We need to solve for \( n \):
\[ n = \frac{PV}{RT} \]
Now substituting the values into the equation:
\[ n = \frac{(0.50 , \text{atm}) \times (0.45 , \text{L})}{(0.0821 , \text{L·atm/(K·mol)}) \times (273 , \text{K})} \]
Calculating the denominator:
\[ 0.0821 , \text{L·atm/(K·mol)} \times 273 , \text{K} \approx 22.4143 , \text{L·atm/mol} \]
Now substituting everything in:
\[ n = \frac{0.50 \times 0.45}{22.4143} \approx \frac{0.225}{22.4143} \approx 0.01004 , \text{mol} \]
So, the number of moles of gas present is approximately 0.01 mol.
The correct response is:
0.01 mol