Stearic acid (C18H36O2) is a fatty acid, a molecule with a long hydrocarbon chain and an organic acid group (COOH) at the end. It is used to make cosmetics, ointments, soaps, and candles and is found in animal tissue as part of many saturated fats. In fact, when you eat meat, you are ingesting some fats containing stearic acid. Determine the ΔHrxn for this combustion given the following information:

ΔHf of stearic acid = -948 kJ/mol,
ΔHf of CO2 = -394 kJ/mol,
ΔHf of water = -242 kJ/mol.

Calculate the heat (q) released in kJ when 206 g of stearic acid reacts with 943.2 g of oxygen.

-7612.5 kJ.

Explanation:

Equation of the reaction:

C18H36O2 + 26O2(g) --> 18H2O(g) + 18CO2(g)

ΔHrxn = ΔHp - ΔHr

ΔH (combustion) = [18*(ΔHf of CO2) + 18*(ΔHf of H2O)] - [1*(ΔHf of C18H36O2) + 26*(ΔHf of O2)]

= [18 * (-394) + 18 * (-242)] - [1 * (-948) + 26 * (0)]

= [(-7092) + (-4356)] - (-948)]

= -10500 kJ/mol

Molar mass:

C18H36O2;

= (18*12) + (36*1) + (2*16)

= 284 g/mol

O2:

= (2 * 16)

= 32 g/mol

Number of moles = mass/molar mass

C18H36O2:

= 206/284

= 0.725 mol.

O2:

= 943.2/32

= 29.475 mol

Finding the limiting reagent,

By stoichiometry, 1 mole of steric acid combusted in 26 moles of oxygen.

Therefore,

= 29.475 mol of O2 * 1 mol of steric acid/26 mol of O2

= 1.134 mol of steric acid(only 0.725 mol is present)

Steric acid is the limiting reagent.

q = n * ΔHrxn

= 0.725 * -10500

= -7612.5 kJ.