1. **State the problem:** We need to find the mass of 3 L of hydrogen gas at 300°C and pressure $2 \times 10^{4}$ Pa. Given molar mass $M = 2$ g/mol and gas constant $R = 8.314$ J/(mol·K). 2. **Convert temperature to Kelvin:** $$T = 300 + 273.15 = 573.15\,K$$ 3. **Use the ideal gas law:** $$PV = nRT$$ where $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is gas constant, and $T$ is temperature. 4. **Convert volume to cubic meters:** $$V = 3\,L = 3 \times 10^{-3}\,m^{3}$$ 5. **Calculate number of moles $n$:** $$n = \frac{PV}{RT} = \frac{(2 \times 10^{4})(3 \times 10^{-3})}{8.314 \times 573.15}$$ 6. **Calculate numerator:** $$2 \times 10^{4} \times 3 \times 10^{-3} = 60$$ 7. **Calculate denominator:** $$8.314 \times 573.15 \approx 4765.5$$ 8. **Calculate moles:** $$n = \frac{60}{4765.5} \approx 0.01259\,mol$$ 9. **Calculate mass:** $$m = n \times M = 0.01259 \times 2 = 0.02518\,g$$ **Final answer:** The mass of hydrogen is approximately $0.0252$ grams.