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Chapter 14: Problem 86

When dissolved in water, glucose (corn sugar) and fructose (fruit sugar) exist in equilibrium as follows: fructose \(\rightleftharpoons\) glucose A chemist prepared a \(0.244 M\) fructose solution at \(25^{\circ} \mathrm{C}\). At equilibrium, it was found that its concentration had decreased to \(0.113 M .\) (a) Calculate the equilibrium constant for the reaction. (b) At equilibrium, what percentage of fructose was converted to glucose?

Short Answer

Expert verified
So, (a) the equilibrium constant for the reaction is approximately 1.16, and (b) 53.7% of fructose was converted to glucose at equilibrium.

Step by step solution

01

Understanding the reaction and what happens at equilibrium

Fructose and glucose are in equilibrium in the solution. Therefore, the change in the concentration of fructose will be equal to the change in the concentration of glucose. When equilibrium is reached, the concentration of fructose has decreased from 0.244 M to 0.113 M, which mean the change in concentration is 0.244-0.113 = 0.131 M. We can conclude that 0.131 M of fructose has been converted into glucose.
02

Calculating the equilibrium constant (K)

The equilibrium constant (K) is calculated by using the concentrations at equilibrium. It is the ratio of the concentration of the products to the concentration of the reactants. However, in this case, the reactant and the product is the same substance in different forms. The equilibrium constant (K) can be defined by the equilibrium concentrations as \[K = [glucose] / [fructose]\]. We can substitute the equilibrium concentrations into the equation to get \[K = 0.131 / 0.113\].
03

Solve for the equilibrium constant (K)

K is calculated to be 1.16, approximately.
04

Calculate the percentage of fructose transformed into glucose

The percentage of fructose converted to glucose can be worked out from the initial and final concentration. The change of concentration divided by the initial concentration will give us the fraction transformed. Multiplying it by 100 will give us the percentage. Therefore: \[Percentage \ transformation = (0.244 - 0.113) / 0.244 * 100\% \]
05

Solve for the percentage of fructose transformed into glucose

Percentage transformation is calculated to be 53.7% approximately.

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Most popular questions from this chapter

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