H2SO4 + K2CrO4 = H2O + K2SO4 + K2Cr2O7

H_2SO_4 (sulfuric acid) + K_2CrO_4 (potassium chromate) ⟶ H_2O (water) + K_2SO_4 (potassium sulfate) + K_2Cr_2O_7 (potassium dichromate)

Balance the chemical equation algebraically: H_2SO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + K_2Cr_2O_7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2CrO_4 ⟶ c_3 H_2O + c_4 K_2SO_4 + c_5 K_2Cr_2O_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr and K: H: | 2 c_1 = 2 c_3 O: | 4 c_1 + 4 c_2 = c_3 + 4 c_4 + 7 c_5 S: | c_1 = c_4 Cr: | c_2 = 2 c_5 K: | 2 c_2 = 2 c_4 + 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 = 2 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 2 K_2CrO_4 ⟶ H_2O + K_2SO_4 + K_2Cr_2O_7

+ ⟶ + +

sulfuric acid + potassium chromate ⟶ water + potassium sulfate + potassium dichromate

Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + K_2Cr_2O_7 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 + 2 K_2CrO_4 ⟶ H_2O + K_2SO_4 + K_2Cr_2O_7 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 K_2CrO_4 | 2 | -2 H_2O | 1 | 1 K_2SO_4 | 1 | 1 K_2Cr_2O_7 | 1 | 1 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) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) H_2O | 1 | 1 | [H2O] K_2SO_4 | 1 | 1 | [K2SO4] K_2Cr_2O_7 | 1 | 1 | [K2Cr2O7] 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) ([K2CrO4])^(-2) [H2O] [K2SO4] [K2Cr2O7] = ([H2O] [K2SO4] [K2Cr2O7])/([H2SO4] ([K2CrO4])^2)

Construct the rate of reaction expression for: H_2SO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + K_2Cr_2O_7 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 + 2 K_2CrO_4 ⟶ H_2O + K_2SO_4 + K_2Cr_2O_7 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 K_2CrO_4 | 2 | -2 H_2O | 1 | 1 K_2SO_4 | 1 | 1 K_2Cr_2O_7 | 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 H_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) K_2Cr_2O_7 | 1 | 1 | (Δ[K2Cr2O7])/(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) = -1/2 (Δ[K2CrO4])/(Δt) = (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[K2Cr2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium chromate | water | potassium sulfate | potassium dichromate formula | H_2SO_4 | K_2CrO_4 | H_2O | K_2SO_4 | K_2Cr_2O_7 Hill formula | H_2O_4S | CrK_2O_4 | H_2O | K_2O_4S | Cr_2K_2O_7 name | sulfuric acid | potassium chromate | water | potassium sulfate | potassium dichromate IUPAC name | sulfuric acid | dipotassium dioxido-dioxochromium | water | dipotassium sulfate | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium

| sulfuric acid | potassium chromate | water | potassium sulfate | potassium dichromate molar mass | 98.07 g/mol | 194.19 g/mol | 18.015 g/mol | 174.25 g/mol | 294.18 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | | solid (at STP) melting point | 10.371 °C | 971 °C | 0 °C | | 398 °C boiling point | 279.6 °C | | 99.9839 °C | | density | 1.8305 g/cm^3 | 2.73 g/cm^3 | 1 g/cm^3 | | 2.67 g/cm^3 solubility in water | very soluble | soluble | | soluble | surface tension | 0.0735 N/m | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | odorless | odorless | | odorless