Calculating the Equilibrium Constant - AP Chemistry

1. What is $\Delta n_{\text{gas}}$ for $2\text{SO}_2(g)+\text{O}_2(g)\rightleftharpoons^2\text{SO}_3(g)$?

   $\Delta n_{\text{gas}}=-1$. $2$ moles gas products minus $3$ moles gas reactants equals $-1$.

2. What is $K_p$ from $K_c=0.50$ at $T=300\,K$ for $N_2O_4(g)\rightleftharpoons 2NO_2(g)$? Use $R=0.0821$.

   $K_p=0.50\,(0.0821\cdot 300)^1=12$. $\Delta n=2-1=1$; multiply $K_c$ by $(RT)^1$.

3. Calculate $K_p$ for $2A(g)\rightleftharpoons B(g)$ if $P_A=0.50\,\text{atm}$ and $P_B=2.0\,\text{atm}$ at equilibrium.

   $K_p=8.0$. $K_p = P_B/(P_A)^2 = 2.0/(0.50)^2 = 2.0/0.25 = 8.0$

4. What is $K$ for the reverse reaction if $K=4.0\times10^{-3}$ for the forward reaction?

   $K_{\text{reverse}}=2.5\times10^2$. $K_{reverse} = 1 ÷ (4.0×10^{-3}) = 2.5×10^2$

5. State the relationship between $K_p$ and $K_c$ using $\Delta n_{\text{gas}}$.

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

6. What is the relationship between $\Delta G^\circ$, $K$, $R$, and $T$?

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

7. Identify the correct $K_c$ for $\text{N}_2(g)+3\text{H}_2(g)\rightleftharpoons^2\text{NH}_3(g)$.

   $K_c=\frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}$. Products over reactants with coefficients: $2$ for NH₃, $3$ for H₂.

8. What is $K$ for the reaction if the given reaction has $K=3.0$ and all coefficients are doubled?

   $K_{\text{new}}=9.0$. Doubling coefficients squares $K$: $3.0^2 = 9.0$

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

   $\Delta n_{\text{gas}}=\sum \nu_{\text{prod,gas}}-\sum \nu_{\text{react,gas}}$. Change in moles of gas: product coefficients minus reactant coefficients.

10. What is the numerical value of $K$ when $\Delta G^\circ=0$ at that temperature?

    $K=1$. At equilibrium, forward and reverse rates are equal.

11. What is the value of $K$ for any reaction written as $X\rightleftharpoons X$?

    $K=1$. Same species on both sides cancel out, leaving unity.

12. What is the equilibrium constant expression $K_c$ for $2NO_2(g)\rightleftharpoons N_2O_4(g)$?

    $K_c=\frac{[N_2O_4]}{[NO_2]^2}$. Products over reactants with stoichiometric exponents.

13. Which species are omitted from $K$ expressions: pure solids, pure liquids, gases, or aqueous solutes?

    Pure solids and pure liquids are omitted. Their activities equal 1, so they don't affect the equilibrium constant.

14. What is the relationship between $K_c$ and $K_p$ using $\Delta n$ and $R,T$?

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

15. Which temperature unit must be used in $K_p=K_c(RT)^{\Delta n}$ calculations?

    $T$ must be in kelvin $(\text{K})$. Absolute temperature required for ideal gas calculations.

16. What is $K_c$ for $CaCO_3(s)\rightleftharpoons CaO(s)+CO_2(g)$?

    $K_c=[CO_2]$. Solids omitted; only gas concentration appears.

17. Find $K_c$ if $K_p=2.0$, $\Delta n_{\text{gas}}=-2$, $T=400\,\text{K}$, and $R=0.0821$.

    $K_c=2.15\times10^3$. $K_c = 2.0 ÷ (0.0821 × 400)^{-2} = 2.0 × 1079 = 2.15×10^3$

18. Identify the correct $K_c$ for $\text{CaCO}_3(s)\rightleftharpoons\text{CaO}(s)+\text{CO}_2(g)$.

    $K_c=[\text{CO}_2]$. Solids omitted; only gaseous CO₂ appears in the expression.

19. What is the general expression for $K_p$ 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 gas-phase equilibria.

20. Find $K_p$ if $K_c=0.50$, $\Delta n_{\text{gas}}=1$, $T=300\,\text{K}$, and $R=0.0821$.

    $K_p=12.3$. $K_p = 0.50 × (0.0821 × 300)^1 = 0.50 × 24.63 = 12.3$

21. Which species are omitted from $K$ for a heterogeneous equilibrium involving pure solids and liquids?

    Pure solids and pure liquids are omitted (activity $=1$). Their concentrations remain constant during reaction.

22. What is $K_c$ for $CH_3COOH(aq)\rightleftharpoons H^+(aq)+CH_3COO^-(aq)$?

    $K_c=\frac{[H^+][CH_3COO^-]}{[CH_3COOH]}$. Weak acid dissociation with products over reactant.

23. Find $K_\text{overall}$ if reaction 2 is the reverse of a step with constant $K_2$ and reactions are added.

    $K_\text{overall}=K_1\left(\frac{1}{K_2}\right)$. Reversing step 2 inverts its $K$ before multiplying.

24. What happens to $K$ when all coefficients in the reaction are multiplied by $n$?

    $K_{\text{new}}=K^n$. Each concentration term gets raised to $n$, so $K$ is raised to $n$.

25. What is the general expression for $K_p$ for $aA+bB\rightleftharpoons cC+dD$?

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

26. Identify $K_c$ for $2SO_2(g)+O_2(g)\rightleftharpoons 2SO_3(g)$.

    $K_c=\frac{[SO_3]^2}{[SO_2]^2[O_2]}$. Products over reactants with stoichiometric powers.

27. What is $\Delta n$ (used in $K_p=K_c(RT)^{\Delta n}$) for gas-phase equilibria?

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

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

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

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

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

30. What is the equilibrium constant expression $K_p$ for $N_2(g)+3H_2(g)\rightleftharpoons 2NH_3(g)$?

    $K_p=\frac{(P_{NH_3})^2}{P_{N_2}(P_{H_2})^3}$. Partial pressures raised to stoichiometric coefficients.

31. What is $K_p$ for $CaCO_3(s)\rightleftharpoons CaO(s)+CO_2(g)$?

    $K_p=P_{CO_2}$. Solids omitted; only gas pressure appears.

32. What is $K$ for an overall reaction made by adding reactions with constants $K_1$ and $K_2$?

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

33. Calculate $K_c$ if at equilibrium $[A]=0.20\,M$, $[B]=0.30\,M$, $[C]=0.40\,M$ for $A+B\rightleftharpoons C$.

    $K_c=\frac{0.40}{(0.20)(0.30)}=6.7$. Substitute equilibrium concentrations into $K_c$ expression.

34. Calculate $K_p$ if $P_{CO}=2.0\,atm$, $P_{H_2}=3.0\,atm$, $P_{CH_3OH}=1.5\,atm$ for $CO+2H_2\rightleftharpoons CH_3OH$.

    $K_p=\frac{1.5}{(2.0)(3.0)^2}=0.083$. Substitute equilibrium pressures into $K_p$ expression.

35. What is the effect on $K$ when a reaction is reversed?

    $K_\text{rev}=\frac{1}{K}$. Reversing flips the fraction, giving the reciprocal.

36. What happens to $K$ when the reaction is reversed?

    $K_{\text{reverse}}=\frac{1}{K_{\text{forward}}}$. Reversing swaps products and reactants, inverting the fraction.

37. What is the effect on $K$ when all coefficients are multiplied by $n$?

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

38. Identify the correct $K_c$ for $\text{CH}_3\text{COOH}(aq)\rightleftharpoons\text{H}^+(aq)+\text{CH}_3\text{COO}^-(aq)$.

    $K_c=\frac{[\text{H}^+][\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]}$. Weak acid dissociation: products over undissociated acid.

39. Calculate $K_c$ for $A\rightleftharpoons^2B$ if $[A]=0.50\,\text{M}$ and $[B]=0.20\,\text{M}$ at equilibrium.

    $K_c=0.080$. $K_c = [B]^2/[A] = (0.20)^2/0.50 = 0.040/0.50 = 0.080$

40. What is $K$ for the overall reaction if two steps have constants $K_1$ and $K_2$ and are added?

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

Study these flashcards