Q: If the half-life of a first-order reaction is 55 days, what is the rate constant $$k$$?

$$k = \frac{0.693}{55}$$ \text{ days}^{-1}$

Question 1

Dichlorodiphenyltrichloroethane (DDT) is a pesticide that degrades in the environment with a half-life of 55 days. If the initial concentration of DDT in soil is $$1.0 	imes 10$$^{-4}$$ M, what will its concentration be after 165 days? Assume first-order kinetics.

Accepted Answer

$$1.25 	imes 10$$^{-6}$$ M

Question 2

Which of the following best describes the effect of lowering the pH on the solubility of calcium oxalate ($$CaC_2O_4) in $$water?

Accepted Answer

The solubility increases because $$C_2O_4$$^{2-}$$ is protonated to HC_2O$$_$$4^{-}$$, reducing the concentration of $$C_2O_4$$^{2-}$$.

Question 3

Formaldehyde ($$H_2CO) is $$synthesized by the reaction: $$H_2CO + H_2O \rightleftharpoons H_2CO_2 + H_2$. If the reaction mixture at 600 K has P$$_{H_2CO} = 1.1$$ atm, P$$_{H_2O} = 1.0$$ atm, P$$_{H_2CO_2} = 0.01$$ atm, and P$$_{$$H_2$$} = $$10^{-4}$$ atm, what is the equilibrium constant $$K_p$$ for this reaction?

Accepted Answer

$$9.09 	imes 10$$^{-3}$$

Question 4

Nickel is refined by the Mond process, which involves the reaction $$Ni(s) + 4CO(g) \rightleftharpoons Ni(CO)_4(g). At $$equilibrium, the mole fraction of $$Ni(CO)_4 is$$ $$0.5$$ and $$CO is$$ $$0.5. $$What is the total pressure at equilibrium if the mole fraction of $$Ni(CO)_4 is$$ $$0.9$$ and $$CO is$$ $$0.1 at $$the same temperature?

Accepted Answer

The total pressure cannot be determined without knowing the equilibrium constant.

Question 5

Which of the following is the correct integrated rate law for a first-order reaction?

Accepted Answer

$$\ln([A]) = -kt + \ln([A]_0)$$

Question 6

Dimethylnitrosamine (Me$$_2SO$_4) $$reacts with DNA and is a known carcinogen. If the rate law for its reaction with DNA is $$	ext{rate} = k[Me_2SO_4][DNA]$$, what is the order of the reaction?

Accepted Answer

Second order

Question 7

Which of the following statements about the entropy change ($$\Delta S) $$for the reaction $$H_2CO + H_2O \rightarrow H_2CO_2 + H_2$ is correct?

Accepted Answer

$$\Delta S is $$positive because the number of gas molecules increases.

Question 8

Which equation correctly relates the equilibrium constant $$K to $$the standard Gibbs free energy change $$\Delta G^\circ$$?

Accepted Answer

$$\Delta G^\circ = -RT \ln K$$

Question 9

If the half-life of a first-order reaction is 55 days, what is the rate constant $$k$$?

Accepted Answer

$$k = \frac{0.693}{55}$$ 	ext{ days}^{-1}$

Question 10

Which of the following best explains why oxalic acid ($$H_2C_2O_4) is $$more soluble at low pH?

Accepted Answer

At low pH, $$C_2O_4$$^{2-}$$ is protonated, reducing its concentration and shifting the equilibrium to dissolve more $$CaC_2O_4$$.

Question 11

Which of the following is the correct expression for the equilibrium constant $$K_p$$ for the reaction $$H_2CO + H_2O \rightleftharpoons H_2CO_2 + H_2$?

Accepted Answer

$$K_p = \frac{P_{H_2CO_2} P_{H_2$}}{P_{H_2CO} P_{H_2O}}$$

Question 12

Which of the following is true about the principal form of oxalic acid at pH 2?

Accepted Answer

$$H_2C_2O_4 is $$the principal form because the pH is below both $$pK_a$$ values.

Question 13

Which of the following is the correct differential rate law for a reaction that is first order in $$Me_2SO_4$$ and zero order in DNA?

Accepted Answer

$$	ext{rate} = k[Me_2SO_4]$$

Question 14

Which of the following is the correct relationship for the change in Gibbs free energy ($$\Delta G) at $$non-standard conditions?

Accepted Answer

$$\Delta G = \Delta G^\circ + RT \ln Q$$

Question 15

Which of the following is the correct expression for the solubility product constant $$K_{sp}$$ for calcium oxalate ($$CaC_2O_4$$)?

Accepted Answer

$$K_{sp} = [Ca$$^{2+}$$][C_2O_4$$^{2-}$$]$$

Question 16

Which of the following best describes the effect of increasing temperature on the equilibrium constant $$K$$ for an endothermic reaction?

Accepted Answer

$$K$$ increases because the reaction absorbs heat.

Question 17

Which of the following is the correct formula for calculating the entropy change ($$\Delta S) $$for a process?

Accepted Answer

$$\Delta S = \frac{q_{rev}}{T}$$

Question 18

Which of the following is the correct relationship for the equilibrium constant $$K in $$terms of partial pressures for the reaction $$Ni(s) + 4CO(g) \rightleftharpoons Ni(CO)_4(g)$$?

Accepted Answer

$$K = \frac{P_{Ni(CO)_4}}{P_{CO}^4}$$

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