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Chapter 15: Problem 74

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
The equilibrium constant for the reaction is 1.16 and at equilibrium, 53.7% of fructose is converted to glucose.

Step by step solution

01

Calculation of Change in Concentration

The initial concentration of fructose, \(C_{f-initial} = 0.244 M\) and the concentration at equilibrium, \(C_{f-equilibrium} = 0.113 M\). So, the change in concentration \(\Delta C_f = C_{f-initial} - C_{f-equilibrium} = 0.244 M - 0.113 M = 0.131 M\). Since fructose is converting to glucose, this is also the concentration of glucose at equilibrium.
02

Calculation of the Equilibrium Constant

The equilibrium constant \(K_c\) for the reaction is given by the ratio of the concentration of products \(glucose\) to reactants \(fructose\) at equilibrium. Here the stoichiometry is one-to-one, so we have \(K_c = [Glucose] / [Fructose]\) where the square brackets denote concentrations at equilibrium. Substituting the values, we get \(K_c = 0.131 / 0.113 = 1.16\).
03

Calculation of Percentage Conversion

The percentage conversion of fructose to glucose is the ratio of the change in fructose concentration to the initial concentration, multiplied by 100. So we get Percent Conversion = \(\Delta C_f / C_{f-initial} * 100 = 0.131 / 0.244 * 100 = 53.7%\). This means that 53.7% of the fructose has been converted into glucose at equilibrium.

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Most popular questions from this chapter

At \(25^{\circ} \mathrm{C}\), a mixture of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) gases are in equilibrium in a cylinder fitted with a movable piston. The concentrations are: \(\left[\mathrm{NO}_{2}\right]=0.0475 \mathrm{M}\) and \(\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=0.491 \mathrm{M}\). The volume of the gas mixture is halved by pushing down on the piston at constant temperature. Calculate the concentrations of the gases when equilibrium is reestablished. Will the color become darker or lighter after the change? [Hint: \(K_{\mathrm{c}}\) for the dissociation of \(\mathrm{N}_{2} \mathrm{O}_{4}\) is \(4.63 \times\) \(10^{-3} . \mathrm{N}_{2} \mathrm{O}_{4}(g)\) is colorless and \(\mathrm{NO}_{2}(g)\) has a brown color.]

Consider this reaction at equilibrium in a closed container: $$ \mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) $$ What would happen if (a) the volume is increased, (b) some \(\mathrm{CaO}\) is added to the mixture, (c) some \(\mathrm{CaCO}_{3}\) is removed, (d) some \(\mathrm{CO}_{2}\) is added to the mixture, (e) a few drops of an \(\mathrm{NaOH}\) solution are added to the mixture, (f) a few drops of an \(\mathrm{HCl}\) solution are added to the mixture (ignore the reaction between \(\mathrm{CO}_{2}\) and water \(),(\mathrm{g})\) the temperature is increased?

The equilibrium constant \(K_{P}\) for the following reaction is found to be \(4.31 \times 10^{-4}\) at \(375^{\circ} \mathrm{C}\) : $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ In a certain experiment a student starts with 0.862 atm of \(\mathrm{N}_{2}\) and 0.373 atm of \(\mathrm{H}_{2}\) in a constant-volume vessel at \(375^{\circ} \mathrm{C}\). Calculate the partial pressures of all species when equilibrium is reached.

At \(1024^{\circ} \mathrm{C}\), the pressure of oxygen gas from the decomposition of copper(II) oxide \((\mathrm{CuO})\) is \(0.49 \mathrm{~atm}\) $$ 4 \mathrm{CuO}(s) \rightleftharpoons 2 \mathrm{Cu}_{2} \mathrm{O}(s)+\mathrm{O}_{2}(g) $$ (a) What is the \(K_{P}\) for the reaction? (b) Calculate the fraction of \(\mathrm{CuO}\) decomposed if 0.16 mole of it is placed in a 2.0 - \(L\) flask at \(1024^{\circ} \mathrm{C}\). (c) What would be the fraction if a 1.0 -mole sample of \(\mathrm{CuO}\) were used? (d) What is the smallest amount of \(\mathrm{CuO}\) (in moles) that would establish the equilibrium?

Consider the potential energy diagrams for two types of reactions \(\mathrm{A} \rightleftharpoons \mathrm{B}\). In each case, answer the following questions for the system at equilibrium. (a) How would a catalyst affect the forward and reverse rates of the reaction? (b) How would a catalyst affect the energies of the reactant and product? (c) How would an increase in temperature affect the equilibrium constant? (d) If the only effect of a catalyst is to lower the activation energies for the forward and reverse reactions, show that the equilibrium constant remains unchanged if a catalyst is added to the reacting mixture.
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