Final answer:
Approximately 35.48 grams of C2H6 are required to produce 1842 kJ of heat in the reaction 2C2H6(g) + 7O2(g) → 4CO2(g) + 6H2O(l) with an enthalpy change of -3121 kJ.
Step-by-step explanation:
The student has asked how many grams of C2H6 are required to produce 1842 kJ of heat in the given reaction. The reaction is 2C2H6(g) + 7O2(g) → 4CO2(g) + 6H2O(l) with an enthalpy change (Hr×n) of -3121 kJ.
To solve this, we need to calculate the grams of C2H6 needed using stoichiometry and proportional reasoning.
Let's begin by determining how much heat is produced by one mole of C2H6. From the reaction, we can see that 2 moles of C2H6 produce -3121 kJ of heat:
- 2 moles C2H6 → -3121 kJ
- 1 mole C2H6 → -1560.5 kJ
Now, using the proportion, we can calculate the moles of C2H6 needed to produce 1842 kJ of heat:
-1560.5 kJ / 1 mol C2H6 = 1842 kJ / x mol C2H6
x = 1842 kJ × (1 mol C2H6 / -1560.5 kJ)
x = -1.18 mol C2H6 (Since heat is being released, we consider the negative sign for correct stoichiometric calculations)
To find the grams of C2H6, we use the molar mass of C2H6 (30.07 g/mol):
Mass of C2H6 = -1.18 mol × 30.07 g/mol
= -35.48 g C2H6
Therefore, approximately 35.48 grams of C2H6 are required to produce 1842 kJ of heat in the reaction.