What is the volume of moles of gas that exerts atm of pressure at K? R = L.atm/mol.K

1. Identify the relevant formula: This problem involves the amount of gas, pressure, temperature, and the gas constant, which points to the Ideal Gas Law: $PV = nRT$.
2. Identify the given values:
- Number of moles, $n = 0.789$ mol
- Pressure, $P = 1.15$ atm
- Temperature, $T = 376$ K
- Ideal gas constant, $R = 0.08206 \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}}$
3. Rearrange the formula to solve for Volume (V): Divide both sides of the Ideal Gas Law equation by P: $V = \frac{nRT}{P}$.
4. Substitute the given values into the rearranged formula:
$$V = \frac{(0.789 \text{ mol}) \times (0.08206 \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}}) \times (376 \text{ K})}{1.15 \text{ atm}}$$
5. Perform the calculation:
- First, calculate the numerator: $0.789 \times 0.08206 \times 376 \approx 24.356$
- Now, divide the numerator by the pressure: $V = \frac{24.356}{1.15} \approx 21.179$ L
6. Round to an appropriate number of significant figures: The given values have three significant figures (0.789, 1.15, 376). Therefore, the answer should also be rounded to three significant figures. $21.179$ L rounds to $21.2$ L.