H2SO4 + KCrO7 + KN2 = H2O + K2SO4 + Cr2(SO4)3 + KN3

H_2SO_4 sulfuric acid + KCrO7 + KN2 ⟶ H_2O water + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + KN3

Balance the chemical equation algebraically: H_2SO_4 + KCrO7 + KN2 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + KN3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KCrO7 + c_3 KN2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 KN3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Cr and N: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_2 = c_4 + 4 c_5 + 12 c_6 S: | c_1 = c_5 + 3 c_6 K: | c_2 + c_3 = 2 c_5 + c_7 Cr: | c_2 = 2 c_6 N: | 2 c_3 = 3 c_7 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 = 14 c_2 = 2 c_3 = 60 c_4 = 14 c_5 = 11 c_6 = 1 c_7 = 40 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 H_2SO_4 + 2 KCrO7 + 60 KN2 ⟶ 14 H_2O + 11 K_2SO_4 + Cr_2(SO_4)_3 + 40 KN3

+ KCrO7 + KN2 ⟶ + + + KN3

sulfuric acid + KCrO7 + KN2 ⟶ water + potassium sulfate + chromium sulfate + KN3

Construct the equilibrium constant, K, expression for: H_2SO_4 + KCrO7 + KN2 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + KN3 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: 14 H_2SO_4 + 2 KCrO7 + 60 KN2 ⟶ 14 H_2O + 11 K_2SO_4 + Cr_2(SO_4)_3 + 40 KN3 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 | 14 | -14 KCrO7 | 2 | -2 KN2 | 60 | -60 H_2O | 14 | 14 K_2SO_4 | 11 | 11 Cr_2(SO_4)_3 | 1 | 1 KN3 | 40 | 40 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 14 | -14 | ([H2SO4])^(-14) KCrO7 | 2 | -2 | ([KCrO7])^(-2) KN2 | 60 | -60 | ([KN2])^(-60) H_2O | 14 | 14 | ([H2O])^14 K_2SO_4 | 11 | 11 | ([K2SO4])^11 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] KN3 | 40 | 40 | ([KN3])^40 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])^(-14) ([KCrO7])^(-2) ([KN2])^(-60) ([H2O])^14 ([K2SO4])^11 [Cr2(SO4)3] ([KN3])^40 = (([H2O])^14 ([K2SO4])^11 [Cr2(SO4)3] ([KN3])^40)/(([H2SO4])^14 ([KCrO7])^2 ([KN2])^60)

Construct the rate of reaction expression for: H_2SO_4 + KCrO7 + KN2 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + KN3 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: 14 H_2SO_4 + 2 KCrO7 + 60 KN2 ⟶ 14 H_2O + 11 K_2SO_4 + Cr_2(SO_4)_3 + 40 KN3 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 | 14 | -14 KCrO7 | 2 | -2 KN2 | 60 | -60 H_2O | 14 | 14 K_2SO_4 | 11 | 11 Cr_2(SO_4)_3 | 1 | 1 KN3 | 40 | 40 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 | 14 | -14 | -1/14 (Δ[H2SO4])/(Δt) KCrO7 | 2 | -2 | -1/2 (Δ[KCrO7])/(Δt) KN2 | 60 | -60 | -1/60 (Δ[KN2])/(Δt) H_2O | 14 | 14 | 1/14 (Δ[H2O])/(Δt) K_2SO_4 | 11 | 11 | 1/11 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) KN3 | 40 | 40 | 1/40 (Δ[KN3])/(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 = -1/14 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KCrO7])/(Δt) = -1/60 (Δ[KN2])/(Δt) = 1/14 (Δ[H2O])/(Δt) = 1/11 (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/40 (Δ[KN3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | KCrO7 | KN2 | water | potassium sulfate | chromium sulfate | KN3 formula | H_2SO_4 | KCrO7 | KN2 | H_2O | K_2SO_4 | Cr_2(SO_4)_3 | KN3 Hill formula | H_2O_4S | CrKO7 | KN2 | H_2O | K_2O_4S | Cr_2O_12S_3 | KN3 name | sulfuric acid | | | water | potassium sulfate | chromium sulfate | IUPAC name | sulfuric acid | | | water | dipotassium sulfate | chromium(+3) cation trisulfate |

| sulfuric acid | KCrO7 | KN2 | water | potassium sulfate | chromium sulfate | KN3 molar mass | 98.07 g/mol | 203.09 g/mol | 67.112 g/mol | 18.015 g/mol | 174.25 g/mol | 392.2 g/mol | 81.119 g/mol phase | liquid (at STP) | | | liquid (at STP) | | liquid (at STP) | melting point | 10.371 °C | | | 0 °C | | | boiling point | 279.6 °C | | | 99.9839 °C | | 330 °C | density | 1.8305 g/cm^3 | | | 1 g/cm^3 | | 1.84 g/cm^3 | solubility in water | very 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 |