Question

Determine the number of moles of a gas contained in a 750-mL container at -50.0 °C and 0.921 atm. Have volume include three decimal places.

26.5 mol

0.0265 mol

0.0377 mol

37.7 mol

Answer 1

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 \( n \):

1. **Substitute the known values** into the equation:

\[
0.921 \, \text{atm} \times 0.750 \, \text{L} = n \times 0.0821 \, \text{L·atm/(K·mol)} \times 223.15 \, \text{K}
\]

2. **Calculate the left side**:

\[
0.921 \times 0.750 = 0.69075 \, \text{atm·L}
\]

3. **Calculate the right side's temperature part**:

\[
0.0821 \times 223.15 \approx 18.356265
\]

4. **Now, substitute back into the equation**:

\[
0.69075 = n \times 18.356265
\]

5. **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**.