Stearic acid (C18 H36 O2) is a fatty acid, a molecule with a long hydrocarbon chain and an organ

Stearic acid (C18 H36 O2) is a fatty acid, a molecule with a...

Stearic acid $\left(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\right)$ 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. (a) Write a balanced equation for the combustion of stearic acid to gaseous products. (b) Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for this combustion $\left(\Delta H_{\mathrm{f}}^{\circ} \text { of } \mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}=\right.$ $-948 \mathrm{kJ} / \mathrm{mol} )$ (c) Calculate the heat $(q)$ released in $\mathrm{kJ}$ and kcal when 1.00 $\mathrm{g}$ of stearic acid is burned completely. (d) A candy bar contains 11.0 $\mathrm{g}$ of fat and provides $100 .$ Cal from fat; is this consistent with your answer for part ( $(\mathrm{c}) ?$

Stearic acid $\left(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\right)$ 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.
(a) Write a balanced equation for the combustion of stearic acid to gaseous products.
(b) Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for this combustion $\left(\Delta H_{\mathrm{f}}^{\circ} \text { of } \mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}=\right.$ $-948 \mathrm{kJ} / \mathrm{mol} )$
(c) Calculate the heat $(q)$ released in $\mathrm{kJ}$ and kcal when 1.00 $\mathrm{g}$ of stearic acid is burned completely.
(d) A candy bar contains 11.0 $\mathrm{g}$ of fat and provides $100 .$ Cal from fat; is this consistent with your answer for part ( $(\mathrm{c}) ?$

Key Concepts

Energy Content and Nutritional Analysis

Energy content in nutritional analysis involves determining how much energy is released from fat, carbohydrate, or protein oxidation. This concept connects chemical thermodynamics with dietary caloric values, allowing for a comparison between calculated energy outputs from combustion and the labeled energy provided in food products.

Calorimetry and Unit Conversions

Calorimetry is the experimental measurement of the heat released or absorbed during a chemical reaction. This concept requires understanding the conversion of energy units, such as converting joules to calories or kilojoules to kilocalories, which is essential for comparing experimental data with theoretical predictions.

Combustion Reactions

Combustion reactions are chemical processes in which a substance reacts rapidly with oxygen to produce energy in the form of heat and light, typically yielding gaseous products like carbon dioxide and water. These reactions are central in understanding energy release in organic compounds and are often used to analyze fuel efficiency and thermal energy generation.

Stoichiometry and Balanced Equations

Stoichiometry involves the calculation of reactants and products in a chemical reaction based on the conservation of mass. Writing a balanced chemical equation is crucial because it ensures that all atoms are accounted for on both sides of the reaction, allowing for accurate determination of the amounts of reactants needed and products formed.

Enthalpy of Formation and Reaction Enthalpy

Enthalpy of formation is the change in enthalpy when one mole of a compound is formed from its constituent elements in their standard states. By using these values, one can calculate the overall enthalpy change (?H_rxn) for a reaction, which indicates whether the process is exothermic (releases heat) or endothermic (absorbs heat).

Transcript

00:01 Hey guys, so in this question, we're given stearic acid, and we're asked to do four different things with this.

00:05 First, we have to find a balanced equation for its combustion reaction.

00:10 Second, we need to find the delta h of the reaction.

00:15 And then we had to find how much heat is produced when one gram of stearic acid is burned, and as well as comparing how a candy bar and its 11 grams of fat will, is it consistent to the.

00:30 The amount of heat that's produced that we found in part c.

00:34 So i will go over all of them and try my best to explain how to do each step.

00:41 So in part a, we have stearic acid, which is c -18 h -36 -o2.

00:53 And it's combusting, so that means it's reacting with oxygen, and a combustion reaction produces carbon dioxide and water.

01:06 And these are gases since we need to know that since this is a thermochemistry question and we need to know what state they are in.

01:16 So to balance this out, i'm going to go ahead and put an 18 by the carbon dioxide to balance the carbons, as well as an 18 in front of the hydrogens to balance out the hydrogens.

01:30 Now to balance out the carbon or the, excuse me, the oxygens, there are 54 oxygens on the right side of the equation.

01:38 And to make it even on the left side, we have to put a coefficient of 26 in front of our oxygen.

01:49 So that is our balanced equation for the combustion of stearic acid.

01:54 Now for part b, we have to find the delta h reaction at standard conditions.

02:03 So that is equal to our delta h products minus our delta h of our region.

02:11 Now we just need to look for these values in the book, and we're also given the delta h formation for our stearic acid.

02:27 So i'll go ahead and plug these into our equation.

02:31 So for carbon dioxide, we have a coefficient of 18, so we have to include that in this equation.

02:38 So it's 18 times negative 393 .5 plus 18.

02:47 Times negative 241 .8 for water and that is subtracted from a negative 948 for styric acid.

03:04 Now all of these values are in kilojoules and i just didn't write the units throughout the equation just to save some room.

03:15 Now plugging all of this into our calculator, we find that this is equal to negative 10 ,487 kilojoules...

Please give Ace some feedback