Input interpretation
H_2SO_4 sulfuric acid + Zn zinc + K_2CrO_4 potassium chromate ⟶ H_2O water + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + ZnSO_4 zinc sulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + Zn + K_2CrO_4 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + ZnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Zn + c_3 K_2CrO_4 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 ZnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Zn, Cr and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_3 = c_4 + 4 c_5 + 12 c_6 + 4 c_7 S: | c_1 = c_5 + 3 c_6 + c_7 Zn: | c_2 = c_7 Cr: | c_3 = 2 c_6 K: | 2 c_3 = 2 c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 3 c_3 = 2 c_4 = 8 c_5 = 2 c_6 = 1 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2SO_4 + 3 Zn + 2 K_2CrO_4 ⟶ 8 H_2O + 2 K_2SO_4 + Cr_2(SO_4)_3 + 3 ZnSO_4
Structures
+ + ⟶ + + +
Names
sulfuric acid + zinc + potassium chromate ⟶ water + potassium sulfate + chromium sulfate + zinc sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + Zn + K_2CrO_4 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + ZnSO_4 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 8 H_2SO_4 + 3 Zn + 2 K_2CrO_4 ⟶ 8 H_2O + 2 K_2SO_4 + Cr_2(SO_4)_3 + 3 ZnSO_4 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 8 | -8 Zn | 3 | -3 K_2CrO_4 | 2 | -2 H_2O | 8 | 8 K_2SO_4 | 2 | 2 Cr_2(SO_4)_3 | 1 | 1 ZnSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 8 | -8 | ([H2SO4])^(-8) Zn | 3 | -3 | ([Zn])^(-3) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 2 | 2 | ([K2SO4])^2 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] ZnSO_4 | 3 | 3 | ([ZnSO4])^3 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2SO4])^(-8) ([Zn])^(-3) ([K2CrO4])^(-2) ([H2O])^8 ([K2SO4])^2 [Cr2(SO4)3] ([ZnSO4])^3 = (([H2O])^8 ([K2SO4])^2 [Cr2(SO4)3] ([ZnSO4])^3)/(([H2SO4])^8 ([Zn])^3 ([K2CrO4])^2)](../image_source/4c4ed749e25e98608646509439121c90.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + Zn + K_2CrO_4 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + ZnSO_4 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 8 H_2SO_4 + 3 Zn + 2 K_2CrO_4 ⟶ 8 H_2O + 2 K_2SO_4 + Cr_2(SO_4)_3 + 3 ZnSO_4 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 8 | -8 Zn | 3 | -3 K_2CrO_4 | 2 | -2 H_2O | 8 | 8 K_2SO_4 | 2 | 2 Cr_2(SO_4)_3 | 1 | 1 ZnSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 8 | -8 | ([H2SO4])^(-8) Zn | 3 | -3 | ([Zn])^(-3) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 2 | 2 | ([K2SO4])^2 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] ZnSO_4 | 3 | 3 | ([ZnSO4])^3 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2SO4])^(-8) ([Zn])^(-3) ([K2CrO4])^(-2) ([H2O])^8 ([K2SO4])^2 [Cr2(SO4)3] ([ZnSO4])^3 = (([H2O])^8 ([K2SO4])^2 [Cr2(SO4)3] ([ZnSO4])^3)/(([H2SO4])^8 ([Zn])^3 ([K2CrO4])^2)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + Zn + K_2CrO_4 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + ZnSO_4 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 8 H_2SO_4 + 3 Zn + 2 K_2CrO_4 ⟶ 8 H_2O + 2 K_2SO_4 + Cr_2(SO_4)_3 + 3 ZnSO_4 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 8 | -8 Zn | 3 | -3 K_2CrO_4 | 2 | -2 H_2O | 8 | 8 K_2SO_4 | 2 | 2 Cr_2(SO_4)_3 | 1 | 1 ZnSO_4 | 3 | 3 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2SO_4 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) ZnSO_4 | 3 | 3 | 1/3 (Δ[ZnSO4])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/8 (Δ[H2SO4])/(Δt) = -1/3 (Δ[Zn])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[ZnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/4eb80cccc4bc005be8a1ef090305071f.png)
Construct the rate of reaction expression for: H_2SO_4 + Zn + K_2CrO_4 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + ZnSO_4 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 8 H_2SO_4 + 3 Zn + 2 K_2CrO_4 ⟶ 8 H_2O + 2 K_2SO_4 + Cr_2(SO_4)_3 + 3 ZnSO_4 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 8 | -8 Zn | 3 | -3 K_2CrO_4 | 2 | -2 H_2O | 8 | 8 K_2SO_4 | 2 | 2 Cr_2(SO_4)_3 | 1 | 1 ZnSO_4 | 3 | 3 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2SO_4 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) ZnSO_4 | 3 | 3 | 1/3 (Δ[ZnSO4])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/8 (Δ[H2SO4])/(Δt) = -1/3 (Δ[Zn])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[ZnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | zinc | potassium chromate | water | potassium sulfate | chromium sulfate | zinc sulfate formula | H_2SO_4 | Zn | K_2CrO_4 | H_2O | K_2SO_4 | Cr_2(SO_4)_3 | ZnSO_4 Hill formula | H_2O_4S | Zn | CrK_2O_4 | H_2O | K_2O_4S | Cr_2O_12S_3 | O_4SZn name | sulfuric acid | zinc | potassium chromate | water | potassium sulfate | chromium sulfate | zinc sulfate IUPAC name | sulfuric acid | zinc | dipotassium dioxido-dioxochromium | water | dipotassium sulfate | chromium(+3) cation trisulfate | zinc sulfate