Final answer:
The minimum mass of hydrogen gas required to produce 507 kJ of heat is approximately 3.57 grams, calculated using the calorimetry data given.
Step-by-step explanation:
Calculating the Minimum Mass of Hydrogen Gas Required
To find the minimum mass of hydrogen gas required to produce 507 kJ of heat, we need to use the calorimetry data provided. From the reference information, a 10 gram sample of pure hydrogen burns to give 1,420 kJ of heat. We can set up a proportion to solve for the unknown mass (m) that would produce 507 kJ:
10 g / 1,420 kJ = m / 507 kJ
Cross-multiplying and solving for m yields:
m = (10 g × 507 kJ) / 1,420 kJ
m ≈ 3.57 g
To find the minimum mass of hydrogen gas required to produce 507 kJ of heat, we can use the principle of stoichiometry. First, we need to determine the heat evolved per gram of hydrogen gas using the information given. When 10 grams of hydrogen is burned completely with excess oxygen, it evolves 1,420 kJ of heat. So, the heat evolved per gram of hydrogen gas is 142 kJ/g.
Now, we can set up a proportion to find the mass of hydrogen gas. Let x be the mass of hydrogen gas in grams.
142 kJ/g = 507 kJ / x g
Cross-multiplying, we get 142x = 507, and solving for x, we find that the minimum mass of hydrogen gas required to produce 507 kJ of heat is approximately 3.57 grams.