HNO3 + CrO = H2O + N2 + Cr2O3

HNO_3 nitric acid + CrO ⟶ H_2O water + N_2 nitrogen + Cr_2O_3 chromium(III) oxide

Balance the chemical equation algebraically: HNO_3 + CrO ⟶ H_2O + N_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CrO ⟶ c_3 H_2O + c_4 N_2 + c_5 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Cr: H: | c_1 = 2 c_3 N: | c_1 = 2 c_4 O: | 3 c_1 + c_2 = c_3 + 3 c_5 Cr: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 10 c_3 = 1 c_4 = 1 c_5 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + 10 CrO ⟶ H_2O + N_2 + 5 Cr_2O_3

+ CrO ⟶ + +

nitric acid + CrO ⟶ water + nitrogen + chromium(III) oxide

Construct the equilibrium constant, K, expression for: HNO_3 + CrO ⟶ H_2O + N_2 + Cr_2O_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: 2 HNO_3 + 10 CrO ⟶ H_2O + N_2 + 5 Cr_2O_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 HNO_3 | 2 | -2 CrO | 10 | -10 H_2O | 1 | 1 N_2 | 1 | 1 Cr_2O_3 | 5 | 5 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) CrO | 10 | -10 | ([CrO])^(-10) H_2O | 1 | 1 | [H2O] N_2 | 1 | 1 | [N2] Cr_2O_3 | 5 | 5 | ([Cr2O3])^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 = ([HNO3])^(-2) ([CrO])^(-10) [H2O] [N2] ([Cr2O3])^5 = ([H2O] [N2] ([Cr2O3])^5)/(([HNO3])^2 ([CrO])^10)

Construct the rate of reaction expression for: HNO_3 + CrO ⟶ H_2O + N_2 + Cr_2O_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: 2 HNO_3 + 10 CrO ⟶ H_2O + N_2 + 5 Cr_2O_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 HNO_3 | 2 | -2 CrO | 10 | -10 H_2O | 1 | 1 N_2 | 1 | 1 Cr_2O_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 HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) CrO | 10 | -10 | -1/10 (Δ[CrO])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) Cr_2O_3 | 5 | 5 | 1/5 (Δ[Cr2O3])/(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) = -1/10 (Δ[CrO])/(Δt) = (Δ[H2O])/(Δt) = (Δ[N2])/(Δt) = 1/5 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | CrO | water | nitrogen | chromium(III) oxide formula | HNO_3 | CrO | H_2O | N_2 | Cr_2O_3 name | nitric acid | | water | nitrogen | chromium(III) oxide IUPAC name | nitric acid | | water | molecular nitrogen |

| nitric acid | CrO | water | nitrogen | chromium(III) oxide molar mass | 63.012 g/mol | 67.995 g/mol | 18.015 g/mol | 28.014 g/mol | 151.99 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -41.6 °C | | 0 °C | -210 °C | 2435 °C boiling point | 83 °C | | 99.9839 °C | -195.79 °C | 4000 °C density | 1.5129 g/cm^3 | | 1 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | 4.8 g/cm^3 solubility in water | miscible | | | insoluble | insoluble surface tension | | | 0.0728 N/m | 0.0066 N/m | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless |