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- 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
- 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
- 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
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?
- 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
- 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
Problem 61f
Consider the following equilibrium, for which Δ𝐻<0
2 SO2(𝑔) + O2(𝑔) ⇌ 2 SO3(𝑔)
(f) How will each of the following changes affect an equilibrium mixture of the three gases: SO3(𝑔) is removed from the system?
Problem 62a,b,c
Consider the reaction 4 NH3(𝑔) + 5 O2(𝑔) ⇌ 4 NO(𝑔) + 6 H2O(𝑔), Δ𝐻 = −904.4 kJ Does each of the following increase, decrease, or leave unchanged the yield of NO at equilibrium? (a) increase [NH3] (b) increase [H2O] (c) decrease [O2]
Problem 62d
Consider the reaction 4 NH3(𝑔) + 5 O2(𝑔) ⇌ 4 NO(𝑔) + 6 H2O(𝑔), Δ𝐻 = −904.4 kJ Does each of the following increase, decrease, or leave unchanged the yield of NO at equilibrium? (d) decrease the volume of the container in which the reaction occurs
Problem 62e
Consider the reaction 4 NH3(𝑔) + 5 O2(𝑔) ⇌ 4 NO(𝑔) + 6 H2O(𝑔), Δ𝐻 = −904.4 kJ Does each of the following increase, decrease, or leave unchanged the yield of NO at equilibrium? (e) add a catalyst
Problem 62f
Consider the reaction 4 NH3(𝑔) + 5 O2(𝑔) ⇌ 4 NO(𝑔) + 6 H2O(𝑔), Δ𝐻 = −904.4 kJ Does each of the following increase, decrease, or leave unchanged the yield of NO at equilibrium? (f) increase temperature.
- How do the following changes affect the value of the equilibrium constant for a gas-phase exothermic reaction: (a) removal of a reactant, (b) removal of a product?
Problem 63
- For a certain gas-phase reaction, the fraction of products in an equilibrium mixture is increased by either increasing the temperature or by increasing the volume of the reaction vessel. Does the balanced chemical equation have more molecules on the reactant side or product side?
Problem 64
Problem 65a
Consider the following equilibrium between oxides of nitrogen 3 NO(g) ⇌ NO2(g) + N2O(g) (a) At constant temperature, would a change in the volume of the container affect the fraction of products in the equilibrium mixture?
Problem 66a
Methanol (CH3OH) can be made by the reaction of CO with H2: CO(𝑔) + 2 H2(𝑔) ⇌ CH3OH(𝑔) (a) Use thermochemical data in Appendix C to calculate ΔH° for this reaction.
Problem 66b
Methanol (CH3OH) can be made by the reaction of CO with H2: CO(𝑔) + 2 H2(𝑔) ⇌ CH3OH(𝑔) (b) To maximize the equilibrium yield of methanol, would you use a high or low temperature?
Problem 67
Ozone, O3, decomposes to molecular oxygen in the stratosphere according to the reaction 2 O3(𝑔) ⟶ 3 O2(𝑔). Would increasing the pressure by decreasing the size of the reaction vessel favor the formation of ozone or of oxygen?
Problem 69a
(a) Is the dissociation of fluorine molecules into atomic fluorine, F2(𝑔) ⇌ 2 F(𝑔), an exothermic or endothermic process?