HNO3 + CaSO3 = H2O + SO2 + Ca(NO3)2

HNO_3 nitric acid + CaSO3 ⟶ H_2O water + SO_2 sulfur dioxide + Ca(NO_3)_2 calcium nitrate

Balance the chemical equation algebraically: HNO_3 + CaSO3 ⟶ H_2O + SO_2 + Ca(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CaSO3 ⟶ c_3 H_2O + c_4 SO_2 + c_5 Ca(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Ca and S: H: | c_1 = 2 c_3 N: | c_1 = 2 c_5 O: | 3 c_1 + 3 c_2 = c_3 + 2 c_4 + 6 c_5 Ca: | c_2 = c_5 S: | c_2 = c_4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + CaSO3 ⟶ H_2O + SO_2 + Ca(NO_3)_2

+ CaSO3 ⟶ + +

nitric acid + CaSO3 ⟶ water + sulfur dioxide + calcium nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + CaSO3 ⟶ H_2O + SO_2 + Ca(NO_3)_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 HNO_3 + CaSO3 ⟶ H_2O + SO_2 + Ca(NO_3)_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 HNO_3 | 2 | -2 CaSO3 | 1 | -1 H_2O | 1 | 1 SO_2 | 1 | 1 Ca(NO_3)_2 | 1 | 1 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) CaSO3 | 1 | -1 | ([CaSO3])^(-1) H_2O | 1 | 1 | [H2O] SO_2 | 1 | 1 | [SO2] Ca(NO_3)_2 | 1 | 1 | [Ca(NO3)2] 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) ([CaSO3])^(-1) [H2O] [SO2] [Ca(NO3)2] = ([H2O] [SO2] [Ca(NO3)2])/(([HNO3])^2 [CaSO3])

Construct the rate of reaction expression for: HNO_3 + CaSO3 ⟶ H_2O + SO_2 + Ca(NO_3)_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 HNO_3 + CaSO3 ⟶ H_2O + SO_2 + Ca(NO_3)_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 HNO_3 | 2 | -2 CaSO3 | 1 | -1 H_2O | 1 | 1 SO_2 | 1 | 1 Ca(NO_3)_2 | 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 HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) CaSO3 | 1 | -1 | -(Δ[CaSO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) Ca(NO_3)_2 | 1 | 1 | (Δ[Ca(NO3)2])/(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) = -(Δ[CaSO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[SO2])/(Δt) = (Δ[Ca(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | CaSO3 | water | sulfur dioxide | calcium nitrate formula | HNO_3 | CaSO3 | H_2O | SO_2 | Ca(NO_3)_2 Hill formula | HNO_3 | CaO3S | H_2O | O_2S | CaN_2O_6 name | nitric acid | | water | sulfur dioxide | calcium nitrate IUPAC name | nitric acid | | water | sulfur dioxide | calcium dinitrate

| nitric acid | CaSO3 | water | sulfur dioxide | calcium nitrate molar mass | 63.012 g/mol | 120.1 g/mol | 18.015 g/mol | 64.06 g/mol | 164.09 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -41.6 °C | | 0 °C | -73 °C | 562 °C boiling point | 83 °C | | 99.9839 °C | -10 °C | density | 1.5129 g/cm^3 | | 1 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 2.5 g/cm^3 solubility in water | miscible | | | | soluble surface tension | | | 0.0728 N/m | 0.02859 N/m | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.282×10^-5 Pa s (at 25 °C) | odor | | | odorless | |