Question

A gummy bear contains 5.24 g of sucrose (342.3 g/mol). When the gummy bear reacts with potassium chlorate (KClO₃​) has a standard enthalpy change of −5960 kJ when 1 mol of sucrose reacts with 8 mol of KClO₃​ such that the following balanced equation can be generated:

C₁₂H₂₂​O₁₁​(aq)+8KClO₃​(aq)→12CO₂ ​(g)+11H₂​O(i)+8KCl(aq)
If 15.9 g of potassium chlorate are used what is the change in enthalpy per mole of water produced?
a. −1020 kJ/mol
b. −271 kJ/mol
c. −512 kJ/mol
d. −542 kJ/mol
e. 256 kJ/mol
f. 1080 kJ/mol

Answer 1

The change in enthalpy per mole of water produced when 15.9 g of potassium chlorate and 5.24 g of sucrose react is −542 kJ/mol, corresponding to choice d.

Step-by-step explanation:

The question asks us to calculate the change in enthalpy per mole of water produced when 15.9 g of potassium chlorate reacts with 5.24 g of sucrose based on the thermodynamic equation:

C12H22O11 (aq) + 8KClO3(aq) → 12CO2(g) + 11H2O(l) + 8KCl(aq)

.

First, we determine the molar masses of the reactants: sucrose (342.3 g/mol) and potassium chlorate (KClO3, 122.55 g/mol). The number of moles of sucrose is 5.24 g / 342.3 g/mol = 0.0153 mol. The number of moles of KClO3 is 15.9 g / 122.55 g/mol = 0.1297 mol.

We then check for the limiting reactant by comparing the stoichiometric ratios. The balanced reaction requires 8 moles of KClO3 for every mole of sucrose, which would be 0.0153 mol sucrose * 8 = 0.1224 mol KClO3. Since we have more than 0.1224 mol KClO3, sucrose is the limiting reactant.

Using the given standard enthalpy change of −5960 kJ for 1 mol of sucrose reaction, the enthalpy change for the amount of sucrose we have (0.0153 mol) is −5960 kJ * 0.0153 mol = −90.7 kJ. This reaction produces 11 moles of water for every mole of sucrose, thus the water produced from our sucrose is 0.0153 mol * 11 = 0.1683 mol.

Finally, we find the change in enthalpy per mole of water produced by dividing the total enthalpy change by the moles of water: −90.7 kJ / 0.1683 mol = −542 kJ/mol. Therefore, the answer is −542 kJ/mol of water produced, which corresponds to choice d.