Final answer:
To determine the quantity of H₂ gas in the fuel tank, we utilize the ideal gas law equation PV=nRT. We convert the pressure from psi to atm and the volume from liters to m³. By rearranging the ideal gas law equation and substituting the known values, we can determine the number of moles of H₂ gas. Finally, we use the molar mass of hydrogen to convert moles to grams.
Step-by-step explanation:
To determine the number of grams of H₂ gas in the fuel tank, we can use the ideal gas law equation PV=nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin. First, we need to convert the pressure from psi to atm by dividing by 14.7, which gives us 2850 psi ÷ 14.7 psi/atm = 193.88 atm. Next, we convert the volume from liters to m³ by multiplying by 0.001, which gives us 50.0 L × 0.001 m³/L = 0.05 m³. Now we can rearrange the ideal gas law equation to solve for the number of moles of H₂ gas: n = PV / RT. We substitute the known values as follows: n = (193.88 atm) × (0.05 m³) / (0.0821 L·atm/(mol·K) × (20°C + 273.15 K)). Solving this equation gives us the number of moles of H₂ gas. Finally, we can use the molar mass of hydrogen (2.02 g/mol) to convert moles to grams: mass = number of moles × molar mass. Plugging in the calculated number of moles, we get the final answer in grams.
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