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- Mercury(I) oxide decomposes into elemental mercury and elemental oxygen: 2 Hg2O(s) ⇌ 4 Hg(l) + O2(g). (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures. (b) Suppose you run this reaction in a solvent that dissolves elemental mercury and elemental oxygen. Rewrite the equilibrium-constant expression in terms of molarities for the reaction, using (solv) to indicate solvation.
Problem 29
- Methanol (CH3OH) is produced commercially by the catalyzed reaction of carbon monoxide and hydrogen: CO(g) + 2 H2(g) ⇌ CH3OH(g). An equilibrium mixture in a 2.00-L vessel is found to contain 0.0406 mol CH3OH, 0.170 mol CO, and 0.302 mol H2 at 500 K. Calculate Kc at this temperature.
Problem 31
- Gaseous hydrogen iodide is placed in a closed container at 425 °C, where it partially decomposes to hydrogen and iodine: 2 HI(g) ⇌ H2(g) + I2(g). At equilibrium, it is found that [HI] = 3.53 × 10⁻³ M, [H2] = 4.79 × 10⁻⁴ M, and [I2] = 4.79 × 10⁻⁴ M. What is the value of Kc at this temperature?
Problem 32
Problem 33a
The equilibrium 2 NO(𝑔) + Cl2(𝑔) ⇌ 2 NOCl(𝑔) is established at 500.0 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl2, and NOCl, respectively. (a) Calculate 𝐾𝑝 for this reaction at 500.0 K.
Problem 33b
The equilibrium 2 NO(𝑔) + Cl2(𝑔) ⇌ 2 NOCl(𝑔) is established at 500.0 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl2, and NOCl, respectively. (b) If the vessel has a volume of 5.00 L, calculate Kc at this temperature.
Problem 34a
Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: PCl3(𝑔) + Cl2(𝑔) ⇌ PCl5(𝑔). A 7.5-L gas vessel is charged with a mixture of PCl3(𝑔) and Cl2(𝑔), which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are 𝑃PCl3 = 0.124 atm, 𝑃Cl2 = 0.157 atm, and 𝑃PCl5 = 1.30 atm. (a) What is the value of 𝐾𝑝 at this temperature?
- A mixture of 0.10 mol of NO, 0.050 mol of H2, and 0.10 mol of H2O is placed in a 1.0-L vessel at 300 K. The following equilibrium is established: 2 NO(g) + 2 H2(g) ⇌ N2(g) + 2 H2O(g). At equilibrium [NO] = 0.062 M. (a) Calculate the equilibrium concentrations of H2, N2, and H2O.
Problem 35
- A mixture of 1.374 g of H2 and 70.31 g of Br2 is heated in a 2.00-L vessel at 700 K. These substances react according to H2(g) + Br2(g) ⇌ 2 HBr(g). At equilibrium, the vessel is found to contain 0.566 g of H2. (a) Calculate the equilibrium concentrations of H2, Br2, and HBr.
Problem 36
Problem 37d
A mixture of 0.2000 mol of CO2, 0.1000 mol of H2, and 0.1600 mol of H2O is placed in a 2.000-L vessel. The following equilibrium is established at 500 K: CO2(g) + H2(g) ⇌ CO(g) + H2O(g) (d) Calculate Kc for the reaction.
- A flask is charged with 1.500 atm of N2O4 and 1.00 atm NO2 at 25 _x001F_C, and the following equilibrium is achieved: N2O4(g) ⇌ 2 NO2(g). After equilibrium is reached, the partial pressure of NO2 is 0.512 atm. (b) Calculate the value of Kp for the reaction. (c) Calculate Kc for the reaction.
Problem 38
- Two different proteins X and Y are dissolved in aqueous solution at 37 _x001F_C. The proteins bind in a 1:1 ratio to form XY. A solution that is initially 1.00 mM in each protein is allowed to reach equilibrium. At equilibrium, 0.20 mM of free X and 0.20 mM of free Y remain. What is Kc for the reaction?
Problem 39
Problem 41a
Indicate whether each of the following statements about the reaction quotient Q is true or false: (a) The expression for 𝑄𝑐 looks the same as the expression for 𝐾𝑐.
Problem 41b
Indicate whether each of the following statements about the reaction quotient Q is true or false: (b) If 𝑄𝑐 < 𝐾𝑐, the reaction needs to proceed to the right to reach equilibrium.
Problem 43
At 100°C, the equilibrium constant for the reaction COCl2(𝑔) ⇌ CO(𝑔) + Cl2(𝑔) has the value 𝐾𝑐 = 2.19×10−10. Are the following mixtures of COCl2, CO, and Cl2 at 100°C at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium.
(a) [COCl2] = 2.00×10−3 M, [CO] = 3.3×10−6 M, [Cl2] = 6.62×10−6 M
(b) [COCl2] = 4.50×10−2 M, [CO] = 1.1×10−7 M, [Cl2] = 2.25×10−6 M
(c) [COCl2] = 0.0100 M, [CO] = [Cl2] = 1.48×10−6 M
- As shown in Table 15.2, Kp for the equilibrium N2(g) + 3 H2(g) ⇌ 2 NH3(g) is 4.51 * 10^-5 at 450 _x001F_C. For each of the mixtures listed here, indicate whether the mixture is at equilibrium at 450 _x001F_C. If it is not at equilibrium, indicate the direction (toward product or toward reactants) in which the mixture must shift to achieve equilibrium. (a) 98 atm NH3, 45 atm N2, 55 atm H2. (b) 57 atm NH3, 143 atm N2, no H2. (c) 13 atm NH3, 27 atm N2, 82 atm H2.
Problem 44
- At 100 _x001F_C, Kc = 0.078 for the reaction SO2Cl2(g) ⇌ SO2(g) + Cl2(g). In an equilibrium mixture of the three gases, the concentrations of SO2Cl2 and SO2 are 0.108 M and 0.052 M, respectively. What is the partial pressure of Cl2 in the equilibrium mixture?
Problem 45
Problem 46
At 900 K, the following reaction has 𝐾𝑝 = 0.345: 2 SO2(𝑔) + O2(𝑔) ⇌ 2 SO3(𝑔) In an equilibrium mixture the partial pressures of SO2 and O2 are 0.135 atm and 0.455 atm, respectively. What is the equilibrium partial pressure of SO3 in the mixture?
- At 1285 _x001F_C, the equilibrium constant for the reaction Br2(g) ⇌ 2 Br(g) is Kc = 1.04 * 10^-3. A 0.200-L vessel containing an equilibrium mixture of the gases has 0.245 g of Br2(g) in it. What is the mass of Br(g) in the vessel?
Problem 47
- For the reaction H2(g) + I2(g) ⇌ 2 HI(g), Kc = 55.3 at 700 K. In a 2.00-L flask containing an equilibrium mixture of the three gases, there are 0.056 g H2 and 4.36 g I2. What is the mass of HI in the flask?
Problem 48
- At 800 K, the equilibrium constant for the reaction I2(g) ⇌ 2 I(g) is Kc = 3.1 * 10^-5. If an equilibrium mixture in a 10.0-L vessel contains 2.67 * 10^-2 g of I(g), how many grams of I2 are in the mixture?
Problem 49
Problem 51a
At 218°C, 𝐾𝑐 = 1.2×10−4 for the equilibrium NH4SH(𝑠) ⇌ NH3(𝑔) + H2S(𝑔) (a) Calculate the equilibrium concentrations of NH3 and H2S if a sample of solid NH4SH is placed in a closed vessel at 218°C and decomposes until equilibrium is reached.
Problem 52a
At 80°C, 𝐾𝑐 = 1.87×10−3 for the reaction PH3BCl3(𝑠) ⇌ PH3(𝑔) + BCl3(𝑔) (a) Calculate the equilibrium concentrations of PH3 and BCl3 if a solid sample of PH3BCl3 is placed in a closed vessel at 80°C and decomposes until equilibrium is reached.
Problem 52b
At 80°C, 𝐾𝑐 = 1.87×10−3 for the reaction PH3BCl3(𝑠) ⇌ PH3(𝑔) + BCl3(𝑔) (a) Calculate the equilibrium concentrations of PH3 and BCl3 if a solid sample of PH3BCl3 is placed in a closed vessel at 80°C and decomposes until equilibrium is reached. (b) If the flask has a volume of 0.250 L, what is the minimum mass of PH3BCl3(𝑠) that must be added to the flask to achieve equilibrium?
Problem 53
At 25°C, the reaction CaCrO4(𝑠) ⇌ Ca2+(𝑎𝑞) + CrO42−(𝑎𝑞) has an equilibrium constant 𝐾𝑐 = 7.1×10−4. What are the equilibrium concentrations of Ca2+ and CrO42− in a saturated solution of CaCrO4?
- Consider the reaction \( \text{CaSO}_4(\text{s}) \rightleftharpoons \text{Ca}^{2+}(\text{aq}) + \text{SO}_4^{2-}(\text{aq}) \) At 25 °C, the equilibrium constant is \( K_c = 2.4 \times 10^{-5} \) for this reaction. (a) If excess \( \text{CaSO}_4(\text{s}) \) is mixed with water at 25 °C to produce a saturated solution of \( \text{CaSO}_4 \), what are the equilibrium concentrations of \( \text{Ca}^{2+} \) and \( \text{SO}_4^{2-} \)? (b) If the resulting solution has a volume of 1.4 L, what is the minimum mass of \( \text{CaSO}_4(\text{s}) \) needed to achieve equilibrium?
Problem 54
Problem 55
At 2000°C, the equilibrium constant for the reaction 2 NO(𝑔) ⇌ N2(𝑔) + O2(𝑔) is 𝐾𝑐 = 2.4×103. If the initial concentration of NO is 0.175 M, what are the equilibrium concentrations of NO, N2, and O2?
- For the reaction I2(g) + Br2(g) ⇌ 2 IBr(g), Kc = 280 at 150 _x001F_C. Suppose that 0.500 mol IBr in a 2.00-L flask is allowed to reach equilibrium at 150 _x001F_C. What are the equilibrium concentrations of IBr, I2, and Br2?
Problem 56
Problem 57
For the equilibrium Br2(𝑔) + Cl2(𝑔) ⇌ 2 BrCl(𝑔) at 400 K, 𝐾𝑐 = 7.0. If 0.25 mol of Br2 and 0.55 mol of Cl2 are introduced into a 3.0-L container at 400 K, what will be the equilibrium concentrations of Br2, Cl2, and BrCl?
Problem 58
At 373 K, 𝐾𝑝 = 0.416 for the equilibrium 2 NOBr(𝑔) ⇌ 2 NO(𝑔) + Br2(𝑔) If the equilibrium partial pressures of NOBr(𝑔) and Br2(𝑔) are both 0.100 atm at 373 K, what is the equilibrium partial pressure of NO(𝑔)?
- Methane, CH4, reacts with I2 according to the reaction CH4(g) + I2(g) ⇌ CH3I(g) + HI(g). At 630 K, Kp for this reaction is 2.26 × 10^-4. A reaction was set up at 630 K with initial partial pressures of methane at 105.1 torr and I2 at 7.96 torr. Calculate the pressures, in torr, of all reactants and products at equilibrium.
Problem 59