HCl + K2CrO4 = H2O + KCl + K2Cr2O7

HCl hydrogen chloride + K_2CrO_4 potassium chromate ⟶ H_2O water + KCl potassium chloride + K_2Cr_2O_7 potassium dichromate

Balance the chemical equation algebraically: HCl + K_2CrO_4 ⟶ H_2O + KCl + K_2Cr_2O_7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2CrO_4 ⟶ c_3 H_2O + c_4 KCl + c_5 K_2Cr_2O_7 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr, K and O: Cl: | c_1 = c_4 H: | c_1 = 2 c_3 Cr: | c_2 = 2 c_5 K: | 2 c_2 = c_4 + 2 c_5 O: | 4 c_2 = c_3 + 7 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + 2 K_2CrO_4 ⟶ H_2O + 2 KCl + K_2Cr_2O_7

+ ⟶ + +

hydrogen chloride + potassium chromate ⟶ water + potassium chloride + potassium dichromate

Construct the equilibrium constant, K, expression for: HCl + K_2CrO_4 ⟶ H_2O + KCl + 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: 2 HCl + 2 K_2CrO_4 ⟶ H_2O + 2 KCl + 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 HCl | 2 | -2 K_2CrO_4 | 2 | -2 H_2O | 1 | 1 KCl | 2 | 2 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 HCl | 2 | -2 | ([HCl])^(-2) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) H_2O | 1 | 1 | [H2O] KCl | 2 | 2 | ([KCl])^2 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 = ([HCl])^(-2) ([K2CrO4])^(-2) [H2O] ([KCl])^2 [K2Cr2O7] = ([H2O] ([KCl])^2 [K2Cr2O7])/(([HCl])^2 ([K2CrO4])^2)

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

| hydrogen chloride | potassium chromate | water | potassium chloride | potassium dichromate formula | HCl | K_2CrO_4 | H_2O | KCl | K_2Cr_2O_7 Hill formula | ClH | CrK_2O_4 | H_2O | ClK | Cr_2K_2O_7 name | hydrogen chloride | potassium chromate | water | potassium chloride | potassium dichromate IUPAC name | hydrogen chloride | dipotassium dioxido-dioxochromium | water | potassium chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium

| hydrogen chloride | potassium chromate | water | potassium chloride | potassium dichromate molar mass | 36.46 g/mol | 194.19 g/mol | 18.015 g/mol | 74.55 g/mol | 294.18 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | 971 °C | 0 °C | 770 °C | 398 °C boiling point | -85 °C | | 99.9839 °C | 1420 °C | density | 0.00149 g/cm^3 (at 25 °C) | 2.73 g/cm^3 | 1 g/cm^3 | 1.98 g/cm^3 | 2.67 g/cm^3 solubility in water | miscible | soluble | | soluble | surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | odorless | odorless | odorless