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Chapter 17: Problem 75

Predict the effect of decreasing the temperature on the amount(s) of reactant(s) in the following reactions: (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CHO}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-151 \mathrm{~kJ}\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(l)+\mathrm{H}_{2} \mathrm{O}(g)\) $$ \Delta H_{\mathrm{rxn}}^{\circ}=-451 \mathrm{~kJ} $$ (c) \(2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CH}_{3} \mathrm{CHO}(g)\) (exothermic) (d) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) (endothermic)

Short Answer

Expert verified
For reactions (a), (b), and (c), decreasing the temperature decreases the amount of reactants. For reaction (d), decreasing the temperature increases the amount of reactant.

Step by step solution

01

Understand Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in temperature, pressure, or concentration, the system will adjust itself to partially counteract that change. Specifically, for temperature changes: if you decrease the temperature, the equilibrium will shift in the direction that produces heat (exothermic reaction).
02

Analyze Reaction (a)

The reaction is \(\mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CHO}(g) \) with \( \Delta H_{\mathrm{rxn}} = -151 \mathrm{~kJ} \). Since the reaction is exothermic (negative \(\Delta H\)), decreasing the temperature will shift the equilibrium to the right, increasing the amount of products and decreasing the amount of reactants.
03

Analyze Reaction (b)

The reaction is \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(l)+\mathrm{H}_{2} \mathrm{O}(g) \) with \( \Delta H_{\mathrm{rxn}} = -451 \mathrm{~kJ} \). Since the reaction is exothermic, decreasing the temperature will shift the equilibrium to the right, increasing the amount of products and decreasing the amount of reactants.
04

Analyze Reaction (c)

The reaction is \(2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CH}_{3} \mathrm{CHO}(g) \) and it is given as exothermic. Decreasing the temperature will again shift the equilibrium to the right, increasing the amount of products and decreasing the amount of reactants.
05

Analyze Reaction (d)

The reaction is \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \) and it is endothermic (requires heat). Decreasing the temperature will shift the equilibrium to the left, increasing the amount of \(\mathrm{N}_{2} \mathrm{O}_{4} \) and decreasing the amount of \(\mathrm{NO}_{2} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

equilibrium shift
One of the critical concepts in chemistry is the idea of an equilibrium shift. This occurs when a system in equilibrium responds to a change in temperature, pressure, or concentration of reactants or products. According to Le Chatelier's Principle, if such a change is introduced, the system will adjust to oppose the effect of the change.
For instance, if the concentration of a reactant is increased, the system shifts to produce more products to balance the added reactant. Conversely, if the temperature is changed, the system will shift in a direction that counteracts the temperature change.
To understand this better, consider a simple reversible reaction:
\(\text{A + B} \rightleftharpoons \text{C + D} \)
If the temperature of this exothermic reaction decreases, the equilibrium will shift to the right, favoring the production of C and D. By shifting the balance, the system compensates for the lost heat, illustrating an equilibrium shift.
exothermic reaction
An exothermic reaction is a chemical reaction that releases heat into its surroundings. In such reactions, the energy of the products is lower than the energy of the reactants. This release of energy leads to a negative change in enthalpy (\( \Delta H \)) for the reaction.
For example, consider the reaction:
\(\text{C}_{2}\text{H}_{2}(g) + \text{H}_{2}\text{O}(g) \rightleftharpoons \text{CH}_{3}\text{CHO}(g) \) \( \Delta H = -151 kJ \)
The negative \( \Delta H \) indicates that this reaction is exothermic. Decreasing the temperature of such a reaction will shift the equilibrium to the right, increasing the production of products and reducing reactants. This shift happens because the system tries to counteract the loss in temperature by producing more heat.
endothermic reaction
In contrast to exothermic reactions, endothermic reactions absorb heat from their surroundings. The energy needed to form the products is higher than the energy of the reactants, resulting in a positive change in enthalpy (\( \Delta H \)).
For instance, consider the reaction:
\(\text{N}_{2}\text{O}_{4}(g) \rightleftharpoons 2 \text{NO}_{2}(g) \) (endothermic)
Since this reaction requires heat, decreasing the temperature will shift the equilibrium to the left, increasing the concentration of \( \text{N}_{2}\text{O}_{4} \) and decreasing the concentration of \( \text{NO}_{2} \).
This shift happens because the system compensates for the reduced temperature by favoring the reaction that absorbs heat. Thus, understanding endothermic reactions is essential for predicting how temperature changes impact equilibrium states in chemical reactions.

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Most popular questions from this chapter

Even at high \(T,\) the formation of \(\mathrm{NO}\) is not favored: $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad K_{\mathrm{c}}=4.10 \times 10^{-4} \text {at } 2000^{\circ} \mathrm{C} $$ What is [NO] when a mixture of \(0.20 \mathrm{~mol}\) of \(\mathrm{N}_{2}(g)\) and \(0.15 \mathrm{~mol}\) of \(\mathrm{O}_{2}(g)\) reaches equilibrium in a \(1.0-\mathrm{L}\) container at \(2000^{\circ} \mathrm{C} ?\)

For the equilibrium $$ \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \quad K_{\mathrm{c}}=9.0 \times 10^{-8} \text {at } 700^{\circ} \mathrm{C} $$ the initial concentrations of the three gases are \(0.300 \mathrm{M} \mathrm{H}_{2} \mathrm{~S}\), \(0.300 M \mathrm{H}_{2}\), and \(0.150 \mathrm{M} \mathrm{S}_{2}\). Determine the equilibrium concentrations of the gases.

Isolation of Group \(8 \mathrm{~B}(10)\) elements, used as industrial catalysts, involves a series of steps. For nickel, the sulfide ore is roasted in air: \(\mathrm{Ni}_{3} \mathrm{~S}_{2}(s)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{NiO}(s)+\mathrm{SO}_{2}(g) .\) The metal oxide is reduced by the \(\mathrm{H}_{2}\) in water gas \(\left(\mathrm{CO}+\mathrm{H}_{2}\right)\) to impure \(\mathrm{Ni}: \mathrm{NiO}(s)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{Ni}(s)+\mathrm{H}_{2} \mathrm{O}(g) .\) The \(\mathrm{CO}\) in water gas then reacts with the metal in the Mond process to form gaseous nickel carbonyl, \(\mathrm{Ni}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g),\) which is sub- sequently decomposed to the metal. (a) Balance each of the three steps, and obtain an overall balanced equation for the conversion of \(\mathrm{Ni}_{3} \mathrm{~S}_{2}\) to \(\mathrm{Ni}(\mathrm{CO})_{4}\). (b) Show that the overall \(Q_{\mathrm{c}}\) is the product of the \(Q_{c}\) 's for the individual reactions.

A sealed 2.0 -L container initially contains 0.12 mol each of \(\mathrm{H}_{2} \mathrm{O}(g), \mathrm{Cl}_{2} \mathrm{O}(g),\) and \(\mathrm{HClO}(g) ;\) the reaction mixture is allowed to come to equilibrium according to the reaction $$ \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HClO}(g) \quad K_{\mathrm{c}}=0.090 $$ Calculate the equilibrium concentrations of all three compounds.

A change in reaction conditions increases the rate of a certain forward reaction more than that of the reverse reaction. What is the effect on the equilibrium constant and on the concentrations of reactants and products at equilibrium?
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