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Chapter 13: Problem 108

For the following endothermic reaction at equilibrium: $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$ which of the following changes will increase the value of \(K ?\) a. increasing the temperature b. decreasing the temperature c. removing \(\mathrm{SO}_{3}(g)\) (constant \(T )\) d. decreasing the volume (constant \(T )\) e. adding \(\operatorname{Ne}(g)(\text { constant } T)\) f. adding \(\mathrm{SO}_{2}(g)(\text { constant } T)\) g. adding a catalyst (constant T)

Short Answer

Expert verified
In conclusion, the only change that will increase the value of \(K\) in this endothermic reaction is: a. increasing the temperature

Step by step solution

01

Understanding Le Chatelier's Principle

Le Chatelier's Principle states that if a change is applied to a system in equilibrium, the system will adjust itself to minimize the effect of the change and restore the equilibrium. It applies to temperature, concentration, volume, and pressure changes in a chemical equilibrium, but not to the addition of a catalyst.
02

Evaluate the effect of increasing temperature

For an endothermic reaction, increased temperature will shift the equilibrium to the side with more products (right side). This leads to an increase in the number of moles of \(\mathrm{SO}_2(g)\) and \(\mathrm{O}_2(g)\) and therefore results in an increase in the value of \(K\). So, option a. increasing the temperature is correct.
03

Evaluate the effect of decreasing temperature

For an endothermic reaction, a decrease in temperature will shift the equilibrium to the side with more reactants (left side). This will lead to a decrease in the value of \(K\). Option b. decreasing the temperature is incorrect.
04

Evaluate the effect of removing SO\(_3(g)\)

If we remove \(\mathrm{SO}_3(g)\), the reaction will shift towards the left side to offset the decrease in reactant concentration. However, this change will not affect the value of the equilibrium constant \(K\). The concentrations of the species will change, but the ratio at equilibrium will remain the same. Option c. removing SO\(_3(g)\) is incorrect.
05

Evaluate the effect of decreasing volume

Decreasing the volume causes an increase in pressure, and the equilibrium will shift towards the side with lesser moles of gas. In this reaction, both sides have equal number of moles of gas, so the change in volume will not affect the value of the equilibrium constant \(K\). Option d. decreasing the volume is incorrect.
06

Evaluate the effect of adding Ne(g)

Adding a noble gas (such as Ne) will not affect the equilibrium, as it does not participate in the reaction. Thus, the value of \(K\) remains unchanged. Option e. adding Ne(g) is incorrect.
07

Evaluate the effect of adding SO\(_2(g)\)

Adding \(\mathrm{SO}_2(g)\) (constant T) will shift the equilibrium to the left to offset the increase in product concentration. However, just like in step 4, this change does not affect the value of \(K\), only the concentration of species. Option f. adding SO\(_2(g)\) is incorrect.
08

Evaluate the effect of adding a catalyst

Adding a catalyst speeds up both the forward and reverse reactions, but it does not affect the equilibrium position or the value of \(K\). Option g. adding a catalyst is incorrect. In conclusion, the only change that will increase the value of \(K\) in this endothermic reaction is: a. increasing the temperature

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Most popular questions from this chapter

The hydrocarbon naphthalene was frequently used in mothballs until recently, when it was discovered that human inhalation of naphthalene vapors can lead to hemolytic anemia. Naphthalene is 93.71% carbon by mass, and a 0.256-mole sample of naphthalene has a mass of 32.8 g. What is the molecular formula of naphthalene? This compound works as a pesticide in mothballs by sublimation of the solid so that it fumigates enclosed spaces with its vapors according to the equation Naphthalene \((s) \rightleftharpoons\) naphthalene \((g)\) $K=4.29 \times 10^{-6}(\( at \)298 \mathrm{~K})\( If \)3.00 \mathrm{~g}$ solid naphthalene is placed into an en with a volume of \(5.00 \mathrm{~L}\) at $25^{\circ} \mathrm{C},$ what percentage thalene will have sublimed once equilibriur estahlished?

For the reaction $$2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ it is determined that, at equilibrium at a particular temperature, the concentrations are as follows: $[\mathrm{NO}(g)]=8.1 \times 10^{-3} \mathrm{M}\( \)\left[\mathrm{H}_{2}(g)\right]=4.1 \times 10^{-5} M,\left[\mathrm{N}_{2}(g)\right]=5.3 \times 10^{-2} M,$ and \(\left[\mathrm{H}_{2} \mathrm{O}(g)\right]-2.9 \times 10^{-3} \mathrm{M} .\) Calculate the value of \(K\) for the reaction at this temperature.

Consider the reaction $$\mathrm{P}_{4}(g) \rightleftharpoons 2 \mathrm{P}_{2}(g)$$ where \(K_{\mathrm{p}}=1.00 \times 10^{-1}\) at 1325 \(\mathrm{K}\) . In an experiment where \(\mathrm{P}_{4}(g)\) is placed into a container at 1325 \(\mathrm{K}\) , the equilibrium mixture of \(\mathrm{P}_{4}(g)\) and \(\mathrm{P}_{2}(g)\) has a total pressure of 1.00 atm. Calculate the equilibrium pressures of \(\mathrm{P}_{4}(g)\) and \(\mathrm{P}_{2}(g) .\) Calculate the fraction (by moles) of \(\mathrm{P}_{4}(g)\) that has dissociated to reach equilibrium.

At a particular temperature, \(K=2.0 \times 10^{-6}\) for the reaction $$2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g)$$ If 2.0 moles of \(\mathrm{CO}_{2}\) is initially placed into a 5.0 -L vessel, calculate the equilibrium concentrations of all species.

The value of the equilibrium constant \(K\) depends on which of the following (more than one answer may be correct)? a. the initial concentrations of the reactants b. the initial concentrations of the products c. the temperature of the system d. the nature of the reactants and products Explain.
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