NaOH + NaNO3 + Cr = H2O + Na2CrO4 + NaNO2

Input interpretation

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NaOH sodium hydroxide + NaNO_3 sodium nitrate + Cr chromium ⟶ H_2O water + Na_2CrO_4 sodium chromate + NaNO_2 sodium nitrite

Balanced equation

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Balance the chemical equation algebraically: NaOH + NaNO_3 + Cr ⟶ H_2O + Na_2CrO_4 + NaNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 NaNO_3 + c_3 Cr ⟶ c_4 H_2O + c_5 Na_2CrO_4 + c_6 NaNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, N and Cr: H: | c_1 = 2 c_4 Na: | c_1 + c_2 = 2 c_5 + c_6 O: | c_1 + 3 c_2 = c_4 + 4 c_5 + 2 c_6 N: | c_2 = c_6 Cr: | c_3 = 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 = 3 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + 3 NaNO_3 + Cr ⟶ H_2O + Na_2CrO_4 + 3 NaNO_2

+ + ⟶ + +

Names

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sodium hydroxide + sodium nitrate + chromium ⟶ water + sodium chromate + sodium nitrite

Equilibrium constant

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Construct the equilibrium constant, K, expression for: NaOH + NaNO_3 + Cr ⟶ H_2O + Na_2CrO_4 + NaNO_2 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 NaOH + 3 NaNO_3 + Cr ⟶ H_2O + Na_2CrO_4 + 3 NaNO_2 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 NaOH | 2 | -2 NaNO_3 | 3 | -3 Cr | 1 | -1 H_2O | 1 | 1 Na_2CrO_4 | 1 | 1 NaNO_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) NaNO_3 | 3 | -3 | ([NaNO3])^(-3) Cr | 1 | -1 | ([Cr])^(-1) H_2O | 1 | 1 | [H2O] Na_2CrO_4 | 1 | 1 | [Na2CrO4] NaNO_2 | 3 | 3 | ([NaNO2])^3 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 = ([NaOH])^(-2) ([NaNO3])^(-3) ([Cr])^(-1) [H2O] [Na2CrO4] ([NaNO2])^3 = ([H2O] [Na2CrO4] ([NaNO2])^3)/(([NaOH])^2 ([NaNO3])^3 [Cr])

Rate of reaction

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Construct the rate of reaction expression for: NaOH + NaNO_3 + Cr ⟶ H_2O + Na_2CrO_4 + NaNO_2 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 NaOH + 3 NaNO_3 + Cr ⟶ H_2O + Na_2CrO_4 + 3 NaNO_2 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 NaOH | 2 | -2 NaNO_3 | 3 | -3 Cr | 1 | -1 H_2O | 1 | 1 Na_2CrO_4 | 1 | 1 NaNO_2 | 3 | 3 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) NaNO_3 | 3 | -3 | -1/3 (Δ[NaNO3])/(Δt) Cr | 1 | -1 | -(Δ[Cr])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Na_2CrO_4 | 1 | 1 | (Δ[Na2CrO4])/(Δt) NaNO_2 | 3 | 3 | 1/3 (Δ[NaNO2])/(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[NaOH])/(Δt) = -1/3 (Δ[NaNO3])/(Δt) = -(Δ[Cr])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2CrO4])/(Δt) = 1/3 (Δ[NaNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)