To determine the number of moles of gas contained in the given container, we can use the Ideal Gas Law, which is expressed as:
\[ PV = nRT \]
Where:
- \( P \) is the pressure in atm
- \( V \) is the volume in liters
- \( n \) is the number of moles
- \( R \) is the ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) is the temperature in Kelvin
First, we need to convert the volume from mL to L:
\[ V = 750 , \text{mL} = 0.750 , \text{L} \]
Next, we convert the temperature from Celsius to Kelvin:
\[ T = -50.0 , \text{°C} + 273.15 = 223.15 , \text{K} \]
Now we can substitute \( P \), \( V \), \( R \), and \( T \) into the Ideal Gas Law to solve for \( n \):
- Substitute the known values into the equation:
\[ 0.921 , \text{atm} \times 0.750 , \text{L} = n \times 0.0821 , \text{L·atm/(K·mol)} \times 223.15 , \text{K} \]
- Calculate the left side:
\[ 0.921 \times 0.750 = 0.69075 , \text{atm·L} \]
- Calculate the right side's temperature part:
\[ 0.0821 \times 223.15 \approx 18.356265 \]
- Now, substitute back into the equation:
\[ 0.69075 = n \times 18.356265 \]
- Solve for \( n \):
\[ n = \frac{0.69075}{18.356265} \approx 0.0377 , \text{mol} \]
Thus, the number of moles of the gas contained in the 750 mL container at -50.0 °C and 0.921 atm is approximately 0.0377 moles.
The correct answer from the options is:
0.0377 mol.
1 answer