To calculate the minimum mass of hydrogen gas required to produce 507 kJ of heat, we use the ratio of heat produced per gram of hydrogen, according to the enthalpy change in the balanced chemical equation. Solving for the unknown mass gives us a minimum of 4.2429 g, which means the correct answer is 4.5 grams, the smallest option that is greater than the calculated mass.
Step-by-step explanation:
The question asks for the minimum mass of hydrogen gas required to produce 507 kJ of heat, given that the reaction of hydrogen gas with oxygen to form water has an enthalpy change (ΔH) of -483.5 kJ. To solve this, we need to use the stoichiometry of the balanced chemical equation and the fact that enthalpy is an extensive property, which means it is proportional to the amount of reactants used.
First, we establish the proportionality between the enthalpy given in the equation and the amount of heat we need to produce, which is:
483.5 kJ heat produced by 4.04 g of H₂ (from the balanced equation)
The ratio between the required heat and the heat produced by the given mass of hydrogen is:
507 kJ / 483.5 kJ = x g H₂ / 4.04 g H₂
Solving for x gives us the mass of hydrogen needed to produce the required amount of heat:
x = (507 kJ * 4.04 g H₂) / 483.5 kJ = 4.2429 g H₂
Since the options are given in whole numbers, the minimum mass that would suffice to produce at least 507 kJ of heat, without having any excess, would be 4.5 grams (Option A).