# Equilibrium of stearic acid dimerization when dissolved in hexane

• ada0713
In summary, the conversation discusses the reaction of stearic acid in hexane and the estimation of equilibrium constant at different temperatures. The reaction is exothermic and the equilibrium constant decreases when the temperature increases from 28°C to 38°C. The method for eliminating answer choices is to compare them to the Kc value at 28°C. The most reasonable answer choice is 2) 1.9 * 10^3.
ada0713

## Homework Statement

Stearic acid, nature's most common fatty acid, dimerizes when dissolved in hexane:
2C17H35COOH --> (C17H35COOH)2 H°rxn = -172 kJ
The equilibrium constant for this reaction at 28°C is 2900. Estimate the equilibrium constant at 38°C.

1) 4.7 *10^5
2) 1.9 * 10^3
3) 2.6 *10^4
4) 18
5) 3.2 *10^2

## The Attempt at a Solution

The reaction is exothermic( since delta H is negative)
therefore the actual equation will look like:

2C17H35COOH --> (C17H35COOH)2 + heat

If the temperature chanages from 28C to 38C it means that
the heat is added to the system, thus, the equilibrium will shift towards left.
this will cause the reactant to increase
making Kc to decrease. (since Kc= product/reactant)

So I eliminated answer choices that are larger than 2900 (the Kc at 28C).
And I'm left with 2, 4, and 5.
The anwer choice 2 seems to be the most reasonable
since it decrease by 100, and the other answers seem to decrease too much.
But I'm not positive about my decision.
Is there any way to actually caculate Kc value, or is my method correct?

Help!

Last edited:
Does anyone know how to slove this question?

Your method is correct. The equilibrium constant at a higher temperature will be lower due to the shift towards the reactants. Choice 2, 1.9 * 10^3, is the most reasonable answer. However, if you wanted to calculate the exact value, you could use the Van't Hoff equation:

ln(K2/K1) = -(ΔH°/R)(1/T2 - 1/T1)

where K1 and K2 are the equilibrium constants at temperatures T1 and T2 respectively, ΔH° is the enthalpy change of the reaction, and R is the gas constant. Rearranging for K2, we get:

K2 = K1 * e^[(ΔH°/R)(1/T2 - 1/T1)]

Plugging in the values given in the problem, we get:

K2 = (2900) * e^[(172000/8.314)(1/311 - 1/301)] = 1914.9

which is closest to choice 2, 1.9 * 10^3.

## 1. What is the purpose of studying the equilibrium of stearic acid dimerization when dissolved in hexane?

The purpose of this study is to understand the chemical equilibrium between stearic acid molecules when they are dissolved in hexane. This can provide insight into the behavior of the molecules and their interactions in a solvent, which can have practical applications in fields such as pharmaceuticals and materials science.

## 2. How is the equilibrium constant determined in this experiment?

The equilibrium constant is determined by measuring the concentrations of stearic acid and its dimer at equilibrium in a solution of hexane. This can be done through various methods such as spectroscopy or titration, and the value of the equilibrium constant can then be calculated using the concentrations and the balanced chemical equation for the dimerization reaction.

## 3. What factors can affect the equilibrium of stearic acid dimerization in hexane?

The equilibrium of stearic acid dimerization in hexane can be affected by factors such as temperature, concentration of stearic acid and hexane, presence of other solvents or impurities, and the presence of catalysts or inhibitors. These factors can shift the equilibrium towards the formation of more or less dimer, affecting the overall yield of the reaction.

## 4. What is the significance of the stearic acid dimerization equilibrium constant?

The equilibrium constant for stearic acid dimerization in hexane represents the ratio of products (dimer) to reactants (stearic acid) at equilibrium. This value can provide information about the stability and strength of the dimerization reaction, and can also be used to predict the direction of the reaction under different conditions.

## 5. How can the equilibrium of stearic acid dimerization be manipulated?

The equilibrium of stearic acid dimerization can be manipulated by changing the conditions of the reaction. For example, by increasing the temperature, the equilibrium can shift towards the formation of more dimer. Additionally, by adding a catalyst, the equilibrium can be shifted towards the formation of more dimer at a faster rate. However, any changes made to the equilibrium must be carefully controlled to avoid altering the results of the experiment.

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