1. **State the problem:** We need to find the volume of a balloon containing 0.785 moles of N₂ gas at a pressure of 1.5 atm and temperature 301 K. 2. **Formula used:** We use the Ideal Gas Law formula: $$PV = nRT$$ where: - $P$ is pressure, - $V$ is volume, - $n$ is number of moles, - $R$ is the ideal gas constant, - $T$ is temperature in Kelvin. 3. **Important rules:** - The ideal gas constant $R$ is typically $0.0821 \frac{L \cdot atm}{mol \cdot K}$ when pressure is in atm and volume in liters. - Temperature must be in Kelvin. 4. **Rearrange the formula to solve for volume $V$:** $$V = \frac{nRT}{P}$$ 5. **Substitute the known values:** $$V = \frac{0.785 \times 0.0821 \times 301}{1.5}$$ 6. **Calculate the numerator:** $$0.785 \times 0.0821 \times 301 = 19.404$$ 7. **Calculate the volume:** $$V = \frac{19.404}{1.5}$$ 8. **Simplify the fraction:** $$V = \frac{\cancel{19.404}}{\cancel{1.5}} = 12.936$$ 9. **Final answer:** The volume of the balloon is approximately **12.94 liters**.