Properties of the Equilibrium Constant - AP Chemistry

1. What does $Q<K$ indicate about the direction the system will shift to reach equilibrium?

   Shifts right (toward products). System needs more products to reach equilibrium.

2. What is $\Delta n$ in the formula $K_p=K_c(RT)^{\Delta n}$ for a gas-phase reaction?

   $\Delta n=\text{mol gas products}-\text{mol gas reactants}$. Counts net change in moles of gas from reactants to products.

3. What is the general equilibrium constant expression $K_p$ for $aA+bB\rightleftharpoons cC+dD$ (gases)?

   $K_p=\frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$. Uses partial pressures instead of concentrations for gases.

4. Which species are omitted from $K$ expressions for heterogeneous equilibria: pure solids, pure liquids, or both?

   Both pure solids and pure liquids are omitted. Their activities are constant at 1, so they don't affect K.

5. If $\Delta n_{\text{gas}}=0$, what is the relationship between $K_p$ and $K_c$?

   $K_p=K_c$. When gas moles don't change, $(RT)^0=1$.

6. What is the general rule for how $K$ changes when a reaction is reversed?

   $K_{\text{rev}}=\frac{1}{K}$. Reversing flips products and reactants, so K becomes its reciprocal.

7. What is the equilibrium-constant expression for $aA+bB\rightleftharpoons cC+dD$ using partial pressures?

   $K_p=\frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$. Same form as $K_c$ but uses partial pressures instead of concentrations.

8. What is the general rule for how $K$ changes when all coefficients are multiplied by $n$?

   $K_{\text{new}}=K^n$. Multiplying coefficients by n raises K to the nth power.

9. What is the general rule for how $K$ changes when two reactions are added to give an overall reaction?

   $K_{\text{overall}}=K_1K_2$. When reactions add, their equilibrium constants multiply.

10. What is the general equilibrium constant expression $K_c$ for $aA+bB\rightleftharpoons cC+dD$?

    $K_c=\frac{[C]^c[D]^d}{[A]^a[B]^b}$. Products raised to stoichiometric coefficients over reactants.

11. Identify the correct $K$ when $K=3.0$ and the balanced equation coefficients are doubled.

    $9.0$. $K_{\text{new}} = 3.0^2 = 9.0$ when coefficients are doubled.

12. What happens to $K$ when the initial concentrations or partial pressures are changed at constant temperature?

    $K$ is unchanged. K depends only on temperature, not on initial conditions.

13. Find $K$ for $2\times$ the reaction if the original reaction has $K=3.0\times10^2$.

    $K_{\text{new}}=9.0\times10^4$. $K_{\text{new}}=(3.0\times10^2)^2=9.0\times10^4$.

14. How are equilibrium constants combined when reactions are added to give an overall reaction?

    $K_{\text{overall}}=K_1\times K_2\times\cdots$. Adding reactions multiplies their equilibrium constants.

15. What is the activity value used for any pure solid or pure liquid in an equilibrium expression?

    $1$. Pure solids and liquids have unit activity by definition.

16. Identify the equilibrium direction if $K=2.0\times10^3$ for a reaction written as products over reactants.

    Product-favored (equilibrium lies to the right). $K>>1$ means products predominate at equilibrium.

17. What is the relationship between $K_p$ and $K_c$ for gases using $\Delta n_{\text{gas}}$?

    $K_p=K_c(RT)^{\Delta n_{\text{gas}}}$. Relates pressure and concentration constants via ideal gas law.

18. How does $K$ change if all coefficients in the balanced reaction are multiplied by $n$?

    $K_{\text{new}}=K^n$. Each species' exponent multiplies by $n$, so $K$ raises to $n$.

19. Which species are omitted from $K$ for a heterogeneous equilibrium: pure solids, pure liquids, or aqueous solutes?

    Pure solids and pure liquids are omitted. Their activities equal 1, so they don't affect $K$.

20. Identify the correct $K_p$ if $K_c=0.50$, $\Delta n=2$, and $RT=25$ for an ideal-gas reaction.

    $312.5$. $K_p = 0.50 × 25^2 = 312.5$ using $K_p = K_c(RT)^{\Delta n}$

21. Identify the correct $K$ when $K=4.0$ for $A\rightleftharpoons B$ and the reaction is reversed.

    $0.25$. $K_{\text{rev}} = \frac{1}{4.0} = 0.25$ by the reversal rule.

22. What is $\Delta n_{\text{gas}}$ for $K_p=K_c(RT)^{\Delta n_{\text{gas}}}$?

    $\Delta n_{\text{gas}}=\sum\nu_{\text{prod,gas}}-\sum\nu_{\text{react,gas}}$. Moles of gas products minus moles of gas reactants.

23. What is the sign of $\Delta G^\circ$ when $K<1$ at a given temperature?

    $\Delta G^\circ>0$. Since $\ln K < 0$ when $K < 1$, $\Delta G^\circ$ must be positive.

24. What happens to $K$ when a catalyst is added to a system at constant temperature?

    $K$ is unchanged. Catalysts speed up both forward and reverse reactions equally.

25. Find $K_{\text{rev}}$ if $K=5.0\times10^{-4}$ for the forward reaction.

    $K_{\text{rev}}=2.0\times10^3$. $K_{\text{rev}}=\frac{1}{5.0\times10^{-4}}=2.0\times10^3$.

26. What is the sign of $\Delta G^\circ$ when $K>1$ at a given temperature?

    $\Delta G^\circ<0$. Since $\ln K > 0$ when $K > 1$, $\Delta G^\circ$ must be negative.

27. Identify the correct $K$ for the overall reaction if $K_1=2.0\times10^3$ and $K_2=5.0\times10^{-2}$ are added.

    $1.0\times10^2$. $K_{\text{overall}} = (2.0×10^3)(5.0×10^{-2}) = 1.0×10^2$

28. How does $K$ change if the balanced reaction is reversed?

    $K_{\text{rev}}=\frac{1}{K}$. Reversing swaps products and reactants, inverting $K$.

29. Identify the equilibrium direction if $K=4.0\times10^{-6}$ for a reaction written as products over reactants.

    Reactant-favored (equilibrium lies to the left). $K<<1$ means reactants predominate at equilibrium.

30. What is the only common experimental change that can change $K$ for a given reaction?

    Changing temperature. K is a function of temperature only for a given reaction.

31. What does $Q>K$ indicate about the direction the system will shift to reach equilibrium?

    Shifts left (toward reactants). System has too many products, needs more reactants.

32. Find $K$ for $\frac{1}{2}\times$ the reaction if the original reaction has $K=1.6\times10^{-5}$.

    $K_{\text{new}}=4.0\times10^{-3}$. $K_{\text{new}}=(1.6\times10^{-5})^{1/2}=4.0\times10^{-3}$.

33. What is the relationship between $K_p$ and $K_c$ for ideal gases in terms of $\Delta n$?

    $K_p=K_c(RT)^{\Delta n}$. Relates pressure and concentration equilibrium constants via ideal gas law.

34. How does $K$ change if all coefficients in the balanced reaction are divided by $n$?

    $K_{\text{new}}=K^{\frac{1}{n}}$. Each exponent divides by $n$, so $K$ raises to $\frac{1}{n}$.

35. What is the relationship between $K$ and $\Delta G^\circ$ at a given temperature?

    $\Delta G^\circ=-RT\ln K$. Links thermodynamic favorability to equilibrium position.

36. What does $Q=K$ indicate about the system?

    The system is at equilibrium. No net change; forward and reverse rates are equal.

37. What is the reaction quotient expression $Q_c$ for $aA+bB\rightleftharpoons cC+dD$?

    $Q_c=\frac{[C]^c[D]^d}{[A]^a[B]^b}$. Same form as $K_c$ but uses actual concentrations.

38. What is the equilibrium-constant expression for $aA+bB\rightleftharpoons cC+dD$ using concentrations?

    $K_c=\frac{[C]^c[D]^d}{[A]^a[B]^b}$. Products over reactants, each raised to its stoichiometric coefficient.

39. What is the value of the activity used for any pure solid or pure liquid in an equilibrium expression?

    $a=1$. By definition, pure solids/liquids have unit activity.

40. Identify the correct $K$ if $\Delta G^\circ=0$ at a given temperature.

    $1$. When $\Delta G^\circ = 0$, then $\ln K = 0$, so $K = 1$.

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