Input interpretation
NaHCO_3 sodium bicarbonate + Ca(H_2PO_4)_2·H_2O calcium dihydrogen phosphate monohydrate ⟶ H_2O water + CO_2 carbon dioxide + Na_2HPO_4 disodium hydrogen phosphate + CaHPO_4 calcium hydrogen phosphate
Balanced equation
Balance the chemical equation algebraically: NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ H_2O + CO_2 + Na_2HPO_4 + CaHPO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaHCO_3 + c_2 Ca(H_2PO_4)_2·H_2O ⟶ c_3 H_2O + c_4 CO_2 + c_5 Na_2HPO_4 + c_6 CaHPO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, Na, O, Ca and P: C: | c_1 = c_4 H: | c_1 + 4 c_2 = 2 c_3 + c_5 + c_6 Na: | c_1 = 2 c_5 O: | 3 c_1 + 8 c_2 = c_3 + 2 c_4 + 4 c_5 + 4 c_6 Ca: | c_2 = c_6 P: | 2 c_2 = c_5 + c_6 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 = 2 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ 2 H_2O + 2 CO_2 + Na_2HPO_4 + CaHPO_4
Structures
+ ⟶ + + +
Names
sodium bicarbonate + calcium dihydrogen phosphate monohydrate ⟶ water + carbon dioxide + disodium hydrogen phosphate + calcium hydrogen phosphate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ H_2O + CO_2 + Na_2HPO_4 + CaHPO_4 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 NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ 2 H_2O + 2 CO_2 + Na_2HPO_4 + CaHPO_4 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 NaHCO_3 | 2 | -2 Ca(H_2PO_4)_2·H_2O | 1 | -1 H_2O | 2 | 2 CO_2 | 2 | 2 Na_2HPO_4 | 1 | 1 CaHPO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaHCO_3 | 2 | -2 | ([NaHCO3])^(-2) Ca(H_2PO_4)_2·H_2O | 1 | -1 | ([Ca(H2PO4)2·H2O])^(-1) H_2O | 2 | 2 | ([H2O])^2 CO_2 | 2 | 2 | ([CO2])^2 Na_2HPO_4 | 1 | 1 | [Na2HPO4] CaHPO_4 | 1 | 1 | [CaHPO4] 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 = ([NaHCO3])^(-2) ([Ca(H2PO4)2·H2O])^(-1) ([H2O])^2 ([CO2])^2 [Na2HPO4] [CaHPO4] = (([H2O])^2 ([CO2])^2 [Na2HPO4] [CaHPO4])/(([NaHCO3])^2 [Ca(H2PO4)2·H2O])](../image_source/e238038a7386b4003162374027b7b325.png)
Construct the equilibrium constant, K, expression for: NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ H_2O + CO_2 + Na_2HPO_4 + CaHPO_4 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 NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ 2 H_2O + 2 CO_2 + Na_2HPO_4 + CaHPO_4 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 NaHCO_3 | 2 | -2 Ca(H_2PO_4)_2·H_2O | 1 | -1 H_2O | 2 | 2 CO_2 | 2 | 2 Na_2HPO_4 | 1 | 1 CaHPO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaHCO_3 | 2 | -2 | ([NaHCO3])^(-2) Ca(H_2PO_4)_2·H_2O | 1 | -1 | ([Ca(H2PO4)2·H2O])^(-1) H_2O | 2 | 2 | ([H2O])^2 CO_2 | 2 | 2 | ([CO2])^2 Na_2HPO_4 | 1 | 1 | [Na2HPO4] CaHPO_4 | 1 | 1 | [CaHPO4] 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 = ([NaHCO3])^(-2) ([Ca(H2PO4)2·H2O])^(-1) ([H2O])^2 ([CO2])^2 [Na2HPO4] [CaHPO4] = (([H2O])^2 ([CO2])^2 [Na2HPO4] [CaHPO4])/(([NaHCO3])^2 [Ca(H2PO4)2·H2O])
Rate of reaction
![Construct the rate of reaction expression for: NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ H_2O + CO_2 + Na_2HPO_4 + CaHPO_4 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 NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ 2 H_2O + 2 CO_2 + Na_2HPO_4 + CaHPO_4 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 NaHCO_3 | 2 | -2 Ca(H_2PO_4)_2·H_2O | 1 | -1 H_2O | 2 | 2 CO_2 | 2 | 2 Na_2HPO_4 | 1 | 1 CaHPO_4 | 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 NaHCO_3 | 2 | -2 | -1/2 (Δ[NaHCO3])/(Δt) Ca(H_2PO_4)_2·H_2O | 1 | -1 | -(Δ[Ca(H2PO4)2·H2O])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) Na_2HPO_4 | 1 | 1 | (Δ[Na2HPO4])/(Δt) CaHPO_4 | 1 | 1 | (Δ[CaHPO4])/(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[NaHCO3])/(Δt) = -(Δ[Ca(H2PO4)2·H2O])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[Na2HPO4])/(Δt) = (Δ[CaHPO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/c07f5b6707a58c63229903ad09564cb6.png)
Construct the rate of reaction expression for: NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ H_2O + CO_2 + Na_2HPO_4 + CaHPO_4 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 NaHCO_3 + Ca(H_2PO_4)_2·H_2O ⟶ 2 H_2O + 2 CO_2 + Na_2HPO_4 + CaHPO_4 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 NaHCO_3 | 2 | -2 Ca(H_2PO_4)_2·H_2O | 1 | -1 H_2O | 2 | 2 CO_2 | 2 | 2 Na_2HPO_4 | 1 | 1 CaHPO_4 | 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 NaHCO_3 | 2 | -2 | -1/2 (Δ[NaHCO3])/(Δt) Ca(H_2PO_4)_2·H_2O | 1 | -1 | -(Δ[Ca(H2PO4)2·H2O])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) Na_2HPO_4 | 1 | 1 | (Δ[Na2HPO4])/(Δt) CaHPO_4 | 1 | 1 | (Δ[CaHPO4])/(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[NaHCO3])/(Δt) = -(Δ[Ca(H2PO4)2·H2O])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[Na2HPO4])/(Δt) = (Δ[CaHPO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sodium bicarbonate | calcium dihydrogen phosphate monohydrate | water | carbon dioxide | disodium hydrogen phosphate | calcium hydrogen phosphate formula | NaHCO_3 | Ca(H_2PO_4)_2·H_2O | H_2O | CO_2 | Na_2HPO_4 | CaHPO_4 Hill formula | CHNaO_3 | CaH_4O_8P_2 | H_2O | CO_2 | HNa_2O_4P | CaHO_4P name | sodium bicarbonate | calcium dihydrogen phosphate monohydrate | water | carbon dioxide | disodium hydrogen phosphate | calcium hydrogen phosphate IUPAC name | sodium hydrogen carbonate | calcium dihydrogen phosphate | water | carbon dioxide | disodium hydrogen phosphate | calcium hydroxy-dioxido-oxo-phosphorane