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9.E: Fundamental Equlibrium Concepts - Homework

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    Chemical Equilibria

    1. Is a system at equilibrium if the rate constants of the forward and reverse reactions are equal?
      Answer
      yes
    2. If the concentrations of products and reactants are equal, is the system at equilibrium?
      Answer
      no

    Equilibrium Constants

    1. Explain why there may be an infinite number of values for the reaction quotient of a reaction at a given temperature but there can be only one value for the equilibrium constant at that temperature.
      Answer
      the reaction quotient depends upon the concentration of the products and reactants, which can have an infinate number of values. The equilibrium constant is a constant - so it only has one value
    2. Explain why an equilibrium between Br2(l) and Br2(g) would not be established if the container were not a closed vessel shown in Figure 7.1.4.
      Answer
      in an open vessel the bromine gas can escape and is not able to condense back into a liquid - so the system can not go in both directions
    3. If you observe the following reaction at equilibrium, is it possible to tell whether the reaction started with pure NO2 or with pure N2O4? \( \mathrm{2 NO_2} \rightleftharpoons \mathrm{N_2O_4} \)
      Answer
      no
    4. Write the mathematical expression for the reaction quotient, Qc, for the following reaction: \( \mathrm{CH_4}(g) + \mathrm{Cl_2}(g) \rightleftharpoons \mathrm{CH_3Cl}(g) + \mathrm{HCl}(g) \)
      Answer
      \[ Q=\frac{[\mathrm{CH_3Cl}][\mathrm{HCl}]}{[\mathrm{CH_4}][\mathrm{Cl_2}]} \]
    5. Determine if the following system is at equilibrium. If not, in which direction will the system need to shift to reach equilibrium? \( \mathrm{SO_2Cl_2}(g) \rightleftharpoons \mathrm{SO_2}(g) + \mathrm{Cl_2}(g) \) ; [SO2Cl2] = 0.12 M, [Cl2] = 0.16 M and [SO2] = 0.050 M. Kc for the reaction is 0.078.
      Answer
      Q=0.66, Q is less than K so the reaction will go forward, increasing the concentration of products and reducing the concentration of reactants.

    Shifting Equilibria: Le Châtelier’s Principle

     

    1. Methanol can be prepared from carbon monoxide and hydrogen at high temperature and pressure in the presence of a suitable catalyst. \[ \mathrm{H_2}(g) + \mathrm{CO}(g) \rightleftharpoons \mathrm{CH_3OH}(g)\]
      1. (a) Write the expression for the equilibrium constant (K) for the reversible reaction
        Answer
        \[ Q=\frac{[\mathrm{CH_3OH}]} {[\mathrm{H_2}][\mathrm{CO}]} \]
      2. (b) What will happen to the concentrations of H2, CO, and CH3OH at equilibrium if more H2 is added?
        Answer
        H2 and CO will decrease, CH3OH will increase
      3. (c) What will happen to the concentrations of H2, CO, and CH3OH at equilibrium if CO is removed?
        Answer
        H2 and CO will increase, CH3OH will decrease
      4. (d) What will happen to the concentrations of H2, CO, and CH3OH at equilibrium if CH3OH is added?
        Answer
        H2 and CO will increase, CH3OH will decrease
      5. (e) What will happen to the concentrations of H2, CO, and CH3OH at equilibrium if the temperature of the system is increased (Δ H = -90.2 kJ)?
        Answer
        H2 and CO will increase, CH3OH will decrease
      6. (f) What will happen to the concentrations of H2, CO, and CH3OH at equilibrium if more catalyst is added?
        Answer
        no change
    2. Water gas, a mixture of H2 and CO, is an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon. \[ \mathrm{C}(s) + \mathrm{H_2O}(g) \rightleftharpoons \mathrm{CO}(g) + \mathrm{H_2}(g) \]  
      1. (a) Write the expression for the equilibrium constant for the reversible reaction
        Answer
        \[ Q=\frac{[\mathrm{CO}][\mathrm{H_2}]} {[\mathrm{H_2O}]} \]
      2. (b) What will happen to the concentration of each reactant and product at equilibrium if more C is added?
        Answer
        no change, since C is a solid and is not in the equlibrium constant expression
      3. (c) What will happen to the concentration of each reactant and product at equilibrium if H2O is removed?
        Answer
        amount of C will increase, concentration of H2O will increase, CO and H2 will decrease
      4. (d) What will happen to the concentration of each reactant and product at equilibrium if CO is added?
        Answer
        amount of C will increase, concentration of H2O will increase, CO and H2 will decrease
      5. (e) What will happen to the concentration of each reactant and product at equilibrium if the temperature of the system is increased? Δ H = 131.30 kJ
        Answer
        amount of C will decrease, concentration of H2O will decrease, CO and H2 will increase

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