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Chapter 12: Problem 75

Consider the statement "The equilibrium constant for a reaction at \(400 \mathrm{~K}\) is 792 . It must be a very fast reaction." What is wrong with the statement?

Short Answer

Expert verified
Answer: The flaw in the statement is the incorrect assumption that a high equilibrium constant indicates a very fast reaction. The equilibrium constant reflects the position of equilibrium and has no direct relation to the reaction rate or speed.

Step by step solution

01

Understanding the Equilibrium Constant

The equilibrium constant (K) is a measure of the relative amounts of reactants and products present at equilibrium. It indicates the position of equilibrium but does not provide any information about the rate (speed) at which the reaction takes place.
02

Distinguishing between Equilibrium Constant and Reaction Rate

It's important to differentiate between equilibrium constant (K) and reaction rate. A high equilibrium constant means that the reaction reaches an equilibrium state where the concentration of products is higher compared to the reactants. On the other hand, reaction rate relates to how fast the reaction reaches the equilibrium.
03

Assessing the Given Statement

The given statement claims that because the equilibrium constant for the reaction is 792 at 400 K, it must be a very fast reaction. But as discussed earlier, the equilibrium constant merely indicates the position of equilibrium and does not provide any information about the rate or speed of the reaction. Therefore, the statement is incorrect in making the assumption that a high equilibrium constant translates into a fast reaction rate.
04

Conclusion

The flaw in the statement is the assumption that a high equilibrium constant (792 in this case) indicates a very fast reaction. The equilibrium constant reflects the position of equilibrium, and it has no direct relation to the reaction rate or speed.

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Most popular questions from this chapter

Ammonium carbamate solid \(\left(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\right)\) decomposes at \(313 \mathrm{~K}\) into ammonia and carbon dioxide gases. At equilibrium, analysis shows that there are \(0.0451\) atm of \(\mathrm{CO}_{2}, 0.0961\) atm of ammonia, and \(0.159 \mathrm{~g}\) of ammonium carbamate. (a) Write a balanced equation for the decomposition of one mole of \(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\) (b) Calculate \(K\) at \(313 \mathrm{~K}\).

For the system $$\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$ \(K\) is 26 at \(300^{\circ} \mathrm{C}\). In a 5.0-L flask, a gaseous mixture consists of all three gases with partial pressures as follows: \(P_{\mathrm{PCl}_{5}}=0.012 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.45 \mathrm{~atm}\), \(P_{\mathrm{PCl}_{3}}=0.90 \mathrm{~atm} .\) (a) Is the mixture at equilibrium? Explain. (b) If it is not at equilibrium, which way will the system shift to establish equilibrium?

WEB Write equilibrium constant \((K)\) expressions for the following reactions: (a) \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g})\) (b) \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{BaCO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)\) (d) \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(s)\)

A 1.0-L reaction vessel at \(90^{\circ} \mathrm{C}\) contains \(8.00 \mathrm{~g}\) of sulfur, hydrogen, and hydrogen sulfide gases with partial pressures of \(6.0 \mathrm{~atm}\) and \(0.40 \mathrm{~atm}\), respectively, at equilibrium: $$\mathrm{H}_{2}(g)+\mathrm{S}(s) \rightleftharpoons \mathrm{H}_{2} \mathrm{~S}(g)$$ (a) Calculate \(K\) for the reaction at equilibrium. (b) The mass of sulfur is increased to \(10.0\) grams. What are the partial pressures of \(\mathrm{H}_{2}\) and \(\mathrm{H}_{2} \mathrm{~S}\) when equilibrium is reestablished? (c) The pressure of \(\mathrm{H}_{2} \mathrm{~S}\) is increased to \(1.0 \mathrm{~atm}\). What are the partial pressures of \(\mathrm{H}_{2}\) and \(\mathrm{H}_{2} \mathrm{~S}\) when equilibrium is reestablished?

Consider the following reaction at a certain temperature: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ A reaction mixture contains \(0.70 \mathrm{~atm}\) of \(\mathrm{O}_{2}\) and \(0.81\) atm of NO. When equilibrium is established, the total pressure in the reaction vessel is \(1.20 \mathrm{~atm}\). Find \(K\)
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