NaOH + Ca(NO3)2 = Ca(OH)2 + NaNO3

NaOH sodium hydroxide + Ca(NO_3)_2 calcium nitrate ⟶ Ca(OH)_2 calcium hydroxide + NaNO_3 sodium nitrate

Balance the chemical equation algebraically: NaOH + Ca(NO_3)_2 ⟶ Ca(OH)_2 + NaNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Ca(NO_3)_2 ⟶ c_3 Ca(OH)_2 + c_4 NaNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Ca and N: H: | c_1 = 2 c_3 Na: | c_1 = c_4 O: | c_1 + 6 c_2 = 2 c_3 + 3 c_4 Ca: | c_2 = c_3 N: | 2 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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + Ca(NO_3)_2 ⟶ Ca(OH)_2 + 2 NaNO_3

+ ⟶ +

sodium hydroxide + calcium nitrate ⟶ calcium hydroxide + sodium nitrate

| sodium hydroxide | calcium nitrate | calcium hydroxide | sodium nitrate molecular enthalpy | -425.8 kJ/mol | -938.2 kJ/mol | -985.2 kJ/mol | -467.9 kJ/mol total enthalpy | -851.6 kJ/mol | -938.2 kJ/mol | -985.2 kJ/mol | -935.8 kJ/mol | H_initial = -1790 kJ/mol | | H_final = -1921 kJ/mol | ΔH_rxn^0 | -1921 kJ/mol - -1790 kJ/mol = -131.2 kJ/mol (exothermic) | | |

| sodium hydroxide | calcium nitrate | calcium hydroxide | sodium nitrate molecular free energy | -379.7 kJ/mol | -742.8 kJ/mol | -897.5 kJ/mol | -366 kJ/mol total free energy | -759.4 kJ/mol | -742.8 kJ/mol | -897.5 kJ/mol | -732 kJ/mol | G_initial = -1502 kJ/mol | | G_final = -1630 kJ/mol | ΔG_rxn^0 | -1630 kJ/mol - -1502 kJ/mol = -127.3 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: NaOH + Ca(NO_3)_2 ⟶ Ca(OH)_2 + NaNO_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 NaOH + Ca(NO_3)_2 ⟶ Ca(OH)_2 + 2 NaNO_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 NaOH | 2 | -2 Ca(NO_3)_2 | 1 | -1 Ca(OH)_2 | 1 | 1 NaNO_3 | 2 | 2 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) Ca(NO_3)_2 | 1 | -1 | ([Ca(NO3)2])^(-1) Ca(OH)_2 | 1 | 1 | [Ca(OH)2] NaNO_3 | 2 | 2 | ([NaNO3])^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 = ([NaOH])^(-2) ([Ca(NO3)2])^(-1) [Ca(OH)2] ([NaNO3])^2 = ([Ca(OH)2] ([NaNO3])^2)/(([NaOH])^2 [Ca(NO3)2])

Construct the rate of reaction expression for: NaOH + Ca(NO_3)_2 ⟶ Ca(OH)_2 + NaNO_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 NaOH + Ca(NO_3)_2 ⟶ Ca(OH)_2 + 2 NaNO_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 NaOH | 2 | -2 Ca(NO_3)_2 | 1 | -1 Ca(OH)_2 | 1 | 1 NaNO_3 | 2 | 2 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) Ca(NO_3)_2 | 1 | -1 | -(Δ[Ca(NO3)2])/(Δt) Ca(OH)_2 | 1 | 1 | (Δ[Ca(OH)2])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(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) = -(Δ[Ca(NO3)2])/(Δt) = (Δ[Ca(OH)2])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | calcium nitrate | calcium hydroxide | sodium nitrate formula | NaOH | Ca(NO_3)_2 | Ca(OH)_2 | NaNO_3 Hill formula | HNaO | CaN_2O_6 | CaH_2O_2 | NNaO_3 name | sodium hydroxide | calcium nitrate | calcium hydroxide | sodium nitrate IUPAC name | sodium hydroxide | calcium dinitrate | calcium dihydroxide | sodium nitrate

| sodium hydroxide | calcium nitrate | calcium hydroxide | sodium nitrate molar mass | 39.997 g/mol | 164.09 g/mol | 74.092 g/mol | 84.994 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 323 °C | 562 °C | 550 °C | 306 °C boiling point | 1390 °C | | | density | 2.13 g/cm^3 | 2.5 g/cm^3 | 2.24 g/cm^3 | 2.26 g/cm^3 solubility in water | soluble | soluble | slightly soluble | soluble surface tension | 0.07435 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | | 0.003 Pa s (at 250 °C) odor | | | odorless |