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Chapter 15: Problem 59

The reaction \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}), \quad \Delta H^{\circ}=\) \(+181 \mathrm{kJ},\) occurs in high-temperature combustion processes carried out in air. Oxides of nitrogen produced from the nitrogen and oxygen in air are intimately involved in the production of photochemical smog. What effect does increasing the temperature have on (a) the equilibrium production of \(\mathrm{NO}(\mathrm{g})\) (b) the rate of this reaction?

Short Answer

Expert verified
(a) The equilibrium production of \(\mathrm{NO}(\mathrm{g})\) will increase. (b) The rate of reaction will also increase.

Step by step solution

01

Understanding Le Chatelier's Principle

Le Chatelier's Principle states that when a system at chemical equilibrium is disturbed by a change in temperature, pressure, or concentration of components, the system adjusts so as to reduce or counteract the effect of the change. This principle helps to predict how the position of equilibrium will shift.
02

Effect of temperature on equilibrium position

The reaction given is an endothermic reaction because its heat (delta H) is positive. This means heat is absorbed in the formation of products, causing the reaction to be favored in the direction where heat is consumed, that is, towards the products side. When the temperature increases in a reaction vessel, it means more 'heat' has been added to the system. In order to counter this change, the reaction shifts in the direction where that 'heat' will be absorbed, which in an endothermic reaction is towards the right or the product's side. Thus, increasing the temperature increases the equilibrium production of \(\mathrm{NO}(\mathrm{g})\).
03

Effect of temperature on reaction rate

The reaction rate generally increases with increase in temperature. In most cases, increasing the temperature increases the kinetic energy of the molecules, causing them to collide more frequently and with more energy which increases the probability of a successful reaction.

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Most popular questions from this chapter

Determine \(K_{c}\) for the reaction $$\frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{Br}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NOBr}(\mathrm{g})$$ from the following information (at \(298 \mathrm{K}\) ). $$\begin{aligned} 2 \mathrm{NO}(\mathrm{g}) & \rightleftharpoons \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) K_{\mathrm{c}}=2.1 \times 10^{30} \\ \mathrm{NO}(\mathrm{g})+\frac{1}{2} \mathrm{Br}_{2}(\mathrm{g}) & \rightleftharpoons \mathrm{NOBr}(\mathrm{g}) \quad K_{\mathrm{c}}=1.4 \end{aligned}$$

In the Ostwald process for oxidizing ammonia, a variety of products is possible- \(\mathrm{N}_{2}, \mathrm{N}_{2} \mathrm{O}, \mathrm{NO},\) and \(\mathrm{NO}_{2}-\) depending on the conditions. One possibility is $$\begin{aligned} \mathrm{NH}_{3}(\mathrm{g})+\frac{5}{4} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g}) &+\frac{3}{2} \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ K_{\mathrm{p}} &=2.11 \times 10^{19} \mathrm{at} 700 \mathrm{K} \end{aligned}$$ For the decomposition of \(\mathrm{NO}_{2}\) at \(700 \mathrm{K}\) $$\mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \quad K_{\mathrm{p}}=0.524$$ (a) Write a chemical equation for the oxidation of \(\mathrm{NH}_{3}(\mathrm{g})\) to \(\mathrm{NO}_{2}(\mathrm{g})\) (b) Determine \(K_{\mathrm{p}}\) for the chemical equation you have written.

A classic experiment in equilibrium studies dating from 1862 involved the reaction in solution of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) to produce ethyl acetate and water. $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\mathrm{CH}_{3} \mathrm{COOH} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O}$$ The reaction can be followed by analyzing the equilibrium mixture for its acetic acid content. $$\begin{array}{r} 2 \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq})+\mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq}) \rightleftharpoons \\ \mathrm{Ba}\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \end{array}$$ In one experiment, a mixture of 1.000 mol acetic acid and 0.5000 mol ethanol is brought to equilibrium. A sample containing exactly one-hundredth of the equilibrium mixture requires \(28.85 \mathrm{mL} 0.1000 \mathrm{M}\) \(\mathrm{Ba}(\mathrm{OH})_{2}\) for its titration. Calculate the equilibrium constant, \(K_{c}\), for the ethanol-acetic acid reaction based on this experiment.

The following two equilibrium reactions can be written for aqueous carbonic acid, \(\mathrm{H}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) $$ \begin{array}{ll} \mathrm{H}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{HCO}_{3}^{-}(\mathrm{aq}) & K_{1} \\ \mathrm{HCO}_{3}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{CO}_{3}^{2-}(\mathrm{aq}) & K_{2} \end{array} $$ For each reaction write the equilibrium constant expression. By using Le Châtelier's principle we may naively predict that by adding \(\mathrm{H}_{2} \mathrm{CO}_{3}\) to the system, the concentration of \(\mathrm{CO}_{3}^{2-}\) would increase. What we observe is that after adding \(\mathrm{H}_{2} \mathrm{CO}_{3}\) to the equilibrium mixture, an increase in the concentration of \(\mathrm{CO}_{3}^{2-}\) occurs when \(\left[\mathrm{CO}_{3}^{2-}\right] \ll \mathrm{K}_{2}\) however, the concentration of \(\mathrm{CO}_{3}^{2-}\) will decrease when \(\left[\mathrm{CO}_{3}^{2-}\right] \gg K_{2} .\) Show that this is true by considering the ratio of \(\left[\mathrm{H}^{+}\right] /\left[\mathrm{HCO}_{3}^{-}\right]\) before and after adding a small amount of \(\mathrm{H}_{2} \mathrm{CO}_{3}\) to the solution, and by using that ratio to calculate the \(\left[\mathrm{CO}_{3}^{2-}\right]\)

In organic synthesis many reactions produce very little yield, that is \(K \ll 1 .\) Consider the following hypothetical reaction: \(\mathrm{A}(\mathrm{aq})+\mathrm{B}(\mathrm{aq}) \longrightarrow \mathrm{C}(\mathrm{aq}), K=1 \times 10^{-2}\) We can extract product, \(\mathrm{C}\), from the aqueous layer by adding an organic layer in which \(\mathrm{C}(\mathrm{aq}) \longrightarrow \mathrm{C}(\mathrm{or})\), \(K=15 .\) Given initial concentrations of \([\mathrm{A}]=0.1 \mathrm{M}\) \([\mathrm{B}]=0.1,\) and \([\mathrm{C}]=0.1,\) calculate how much \(\mathrm{C}\) will be found in the organic layer. If the organic layer was not present, how much C would be produced?
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