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Chapter 1: Problem 47

Questions 45-48 refer to the following. Inside a calorimeter, 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M}\) hydrocyanic acid (HCN), a weak acid, and 100.0 \(\mathrm{mL}\) of 0.50 \(\mathrm{M}\) sodium hydroxide are mixed. The temperature of the mixture rises from \(21.5^{\circ} \mathrm{C}\) to \(28.5^{\circ} \mathrm{C}\) . The specific heat of the mixture is approximately \(4.2 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C},\) and the density is identical to that of water. As \(\Delta T\) increases, what happens to the equilibrium constant and why? (A) The equilibrium constant increases because more products are created. (B) The equilibrium constant increases because the rate of the forward reaction increases. (C) The equilibrium constant decreases because the equilibrium shifts to the left. (D) The value for the equilibrium constant is unaffected by temperature and will not change.

Short Answer

Expert verified
(C) The equilibrium constant decreases because the equilibrium shifts to the left.

Step by step solution

01

Identify the nature of the reaction

From the details given in the exercise, we can note that the temperature of the mixture has increased. This rise in temperature indicates that the reaction taking place is an exothermic reaction. In an exothermic reaction, heat is evolved. Therefore the reaction can be written as: \[ \mathrm{HCN + NaOH \rightarrow NaCN + H_2O + heat} \]
02

Apply Le Chatelier's principle

According to Le Chatelier's principle, when a reaction at equilibrium is subjected to a change in temperature, the equilibrium shifts to counteract the change. Basically, for a reaction at equilibrium, if we increase the temperature, the equilibrium will shift in the direction that consumes heat (endothermic direction) to counteract this change. Conversely, if the temperature is decreased, the equilibrium will shift in the direction that produces heat (exothermic direction) to compensate.
03

Analyze the effect of temperature change

Given that heat is a product in the reaction, an increase in temperature (\(\Delta T\)) is equivalent to increasing the product. Applying Le Chatelier's principle, the system will try to reduce the effect of this change by shifting the equilibrium to the left, i.e., in the direction of reactants. This is essentially an effort by the system to consume the excess heat and lower the product concentration, thereby striving to restore the equilibrium.
04

Draw conclusion about the equilibrium constant

When the equilibrium shifts to the left to counteract the effect of increasing temperature, the concentration of the products decreases and that of reactants increases. This reduces the value of the equilibrium constant, as the equilibrium constant is the ratio of the concentration of the products to reactants. Hence, the equilibrium constant decreases.

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Most popular questions from this chapter

When calcium chloride \(\left(\mathrm{CaCl}_{2}\right)\) dissolves in water, the temperature of the water increases dramatically. Which of the following must be true regarding the enthalpy of solution? (A) The lattice energy in \(\mathrm{CaCl}_{2}\) exceeds the bond energy within the water molecules. (B) The hydration energy between the water molecules and the solute ions exceeds the lattice energy within \(\mathrm{CaCl}_{2}\) . (C) The strength of the intermolecular forces between the solute ions and the dipoles on the water molecules must exceed the hydration energy. (D) The hydration energy must exceed the strength of the intermolecular forces between the water molecules.

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A strong acid/strong base titration is completed using an indicator which changes color at the exact equivalence point of the titration. The protonated form of the indicator is HIn, and the deprotonated form is In. At the equivalence point of the reaction: (A) \([\mathrm{HIn}]=\left[\mathrm{In}^{-}\right]\) (B) \([\mathrm{HIn}]=1 /\left[\mathrm{In}^{-}\right]\) (C) \([\mathrm{HIn}]=2\left[\mathrm{In}^{-}\right]\) (D) \([\mathrm{HIn}]=\left[\mathrm{In}^{-}\right]^{2}\)

Use the following information to answer questions 14-16 The radius of atoms and ions is typically measured in Angstroms \((A),\) which is equivalent to \(1 * 10^{-10} \mathrm{m} .\) Below is a table of information for three different elements. TABLE NOT AVAILABLE The phosphorus ion is larger than a neutral phosphorus atom, yet a zinc ion is smaller than a neutral zinc atom. Which of the following statements best explains why? (A) The zinc atom has more protons than the phosphorus atom. (B) The phosphorus atom is paramagnetic, but the zinc atom is diamagnetic. (C) Phosphorus gains electrons when forming an ion, but zinc loses them. (D) The valence electrons in zinc are further from the nucleus than those in phosphorus.

A sealed, rigid container contains three gases: 28.0 \(\mathrm{g}\) of nitrogen, 40.0 \(\mathrm{g}\) of argon, and 36.0 g of water vapor. If the total pressure exerted by the gases is \(2.0 \mathrm{atm},\) what is the partial pressure of the nitrogen? (A) 0.33 atm (B) 0.40 atm (C) 0.50 \(\mathrm{atm}\) (D) 2.0 \(\mathrm{atm}\)
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