H2SO4 + NaNO2 + KIO3 = H2O + K2SO4 + I2 + NaNO3

H_2SO_4 sulfuric acid + NaNO_2 sodium nitrite + KIO_3 potassium iodate ⟶ H_2O water + K_2SO_4 potassium sulfate + I_2 iodine + NaNO_3 sodium nitrate

Balance the chemical equation algebraically: H_2SO_4 + NaNO_2 + KIO_3 ⟶ H_2O + K_2SO_4 + I_2 + NaNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 NaNO_2 + c_3 KIO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 I_2 + c_7 NaNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, N, Na, I and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_2 + 3 c_3 = c_4 + 4 c_5 + 3 c_7 S: | c_1 = c_5 N: | c_2 = c_7 Na: | c_2 = c_7 I: | c_3 = 2 c_6 K: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 5 c_3 = 2 c_4 = 1 c_5 = 1 c_6 = 1 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 5 NaNO_2 + 2 KIO_3 ⟶ H_2O + K_2SO_4 + I_2 + 5 NaNO_3

+ + ⟶ + + +

sulfuric acid + sodium nitrite + potassium iodate ⟶ water + potassium sulfate + iodine + sodium nitrate

Construct the equilibrium constant, K, expression for: H_2SO_4 + NaNO_2 + KIO_3 ⟶ H_2O + K_2SO_4 + I_2 + NaNO_3 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: H_2SO_4 + 5 NaNO_2 + 2 KIO_3 ⟶ H_2O + K_2SO_4 + I_2 + 5 NaNO_3 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 | 1 | -1 NaNO_2 | 5 | -5 KIO_3 | 2 | -2 H_2O | 1 | 1 K_2SO_4 | 1 | 1 I_2 | 1 | 1 NaNO_3 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) NaNO_2 | 5 | -5 | ([NaNO2])^(-5) KIO_3 | 2 | -2 | ([KIO3])^(-2) H_2O | 1 | 1 | [H2O] K_2SO_4 | 1 | 1 | [K2SO4] I_2 | 1 | 1 | [I2] NaNO_3 | 5 | 5 | ([NaNO3])^5 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])^(-1) ([NaNO2])^(-5) ([KIO3])^(-2) [H2O] [K2SO4] [I2] ([NaNO3])^5 = ([H2O] [K2SO4] [I2] ([NaNO3])^5)/([H2SO4] ([NaNO2])^5 ([KIO3])^2)

Construct the rate of reaction expression for: H_2SO_4 + NaNO_2 + KIO_3 ⟶ H_2O + K_2SO_4 + I_2 + NaNO_3 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: H_2SO_4 + 5 NaNO_2 + 2 KIO_3 ⟶ H_2O + K_2SO_4 + I_2 + 5 NaNO_3 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 | 1 | -1 NaNO_2 | 5 | -5 KIO_3 | 2 | -2 H_2O | 1 | 1 K_2SO_4 | 1 | 1 I_2 | 1 | 1 NaNO_3 | 5 | 5 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 | 1 | -1 | -(Δ[H2SO4])/(Δt) NaNO_2 | 5 | -5 | -1/5 (Δ[NaNO2])/(Δt) KIO_3 | 2 | -2 | -1/2 (Δ[KIO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) I_2 | 1 | 1 | (Δ[I2])/(Δt) NaNO_3 | 5 | 5 | 1/5 (Δ[NaNO3])/(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 = -(Δ[H2SO4])/(Δt) = -1/5 (Δ[NaNO2])/(Δt) = -1/2 (Δ[KIO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[I2])/(Δt) = 1/5 (Δ[NaNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | sodium nitrite | potassium iodate | water | potassium sulfate | iodine | sodium nitrate formula | H_2SO_4 | NaNO_2 | KIO_3 | H_2O | K_2SO_4 | I_2 | NaNO_3 Hill formula | H_2O_4S | NNaO_2 | IKO_3 | H_2O | K_2O_4S | I_2 | NNaO_3 name | sulfuric acid | sodium nitrite | potassium iodate | water | potassium sulfate | iodine | sodium nitrate IUPAC name | sulfuric acid | sodium nitrite | potassium iodate | water | dipotassium sulfate | molecular iodine | sodium nitrate