HNO3 + ZnSO4 = H2SO4 + Zn(NO3)2

HNO_3 nitric acid + ZnSO_4 zinc sulfate ⟶ H_2SO_4 sulfuric acid + Zn(NO3)2

Balance the chemical equation algebraically: HNO_3 + ZnSO_4 ⟶ H_2SO_4 + Zn(NO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 ZnSO_4 ⟶ c_3 H_2SO_4 + c_4 Zn(NO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, S and Zn: H: | c_1 = 2 c_3 N: | c_1 = 2 c_4 O: | 3 c_1 + 4 c_2 = 4 c_3 + 6 c_4 S: | c_2 = c_3 Zn: | c_2 = c_4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + ZnSO_4 ⟶ H_2SO_4 + Zn(NO3)2

+ ⟶ + Zn(NO3)2

nitric acid + zinc sulfate ⟶ sulfuric acid + Zn(NO3)2

Construct the equilibrium constant, K, expression for: HNO_3 + ZnSO_4 ⟶ H_2SO_4 + Zn(NO3)2 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: 2 HNO_3 + ZnSO_4 ⟶ H_2SO_4 + Zn(NO3)2 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 HNO_3 | 2 | -2 ZnSO_4 | 1 | -1 H_2SO_4 | 1 | 1 Zn(NO3)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 2 | -2 | ([HNO3])^(-2) ZnSO_4 | 1 | -1 | ([ZnSO4])^(-1) H_2SO_4 | 1 | 1 | [H2SO4] Zn(NO3)2 | 1 | 1 | [Zn(NO3)2] 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 = ([HNO3])^(-2) ([ZnSO4])^(-1) [H2SO4] [Zn(NO3)2] = ([H2SO4] [Zn(NO3)2])/(([HNO3])^2 [ZnSO4])

Construct the rate of reaction expression for: HNO_3 + ZnSO_4 ⟶ H_2SO_4 + Zn(NO3)2 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: 2 HNO_3 + ZnSO_4 ⟶ H_2SO_4 + Zn(NO3)2 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 HNO_3 | 2 | -2 ZnSO_4 | 1 | -1 H_2SO_4 | 1 | 1 Zn(NO3)2 | 1 | 1 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 HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) ZnSO_4 | 1 | -1 | -(Δ[ZnSO4])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) Zn(NO3)2 | 1 | 1 | (Δ[Zn(NO3)2])/(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 = -1/2 (Δ[HNO3])/(Δt) = -(Δ[ZnSO4])/(Δt) = (Δ[H2SO4])/(Δt) = (Δ[Zn(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | zinc sulfate | sulfuric acid | Zn(NO3)2 formula | HNO_3 | ZnSO_4 | H_2SO_4 | Zn(NO3)2 Hill formula | HNO_3 | O_4SZn | H_2O_4S | N2O6Zn name | nitric acid | zinc sulfate | sulfuric acid |

| nitric acid | zinc sulfate | sulfuric acid | Zn(NO3)2 molar mass | 63.012 g/mol | 161.4 g/mol | 98.07 g/mol | 189.4 g/mol phase | liquid (at STP) | | liquid (at STP) | melting point | -41.6 °C | | 10.371 °C | boiling point | 83 °C | | 279.6 °C | density | 1.5129 g/cm^3 | 1.005 g/cm^3 | 1.8305 g/cm^3 | solubility in water | miscible | soluble | very soluble | surface tension | | | 0.0735 N/m | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 0.021 Pa s (at 25 °C) | odor | | odorless | odorless |