Input interpretation
Pb(NO_3)_2 lead(II) nitrate + NaHCO_3 sodium bicarbonate ⟶ H_2O water + CO_2 carbon dioxide + NaNO_3 sodium nitrate + PbCO_3 cerussete
Balanced equation
Balance the chemical equation algebraically: Pb(NO_3)_2 + NaHCO_3 ⟶ H_2O + CO_2 + NaNO_3 + PbCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Pb(NO_3)_2 + c_2 NaHCO_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 NaNO_3 + c_6 PbCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for N, O, Pb, C, H and Na: N: | 2 c_1 = c_5 O: | 6 c_1 + 3 c_2 = c_3 + 2 c_4 + 3 c_5 + 3 c_6 Pb: | c_1 = c_6 C: | c_2 = c_4 + c_6 H: | c_2 = 2 c_3 Na: | c_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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Pb(NO_3)_2 + 2 NaHCO_3 ⟶ H_2O + CO_2 + 2 NaNO_3 + PbCO_3
Structures
+ ⟶ + + +
Names
lead(II) nitrate + sodium bicarbonate ⟶ water + carbon dioxide + sodium nitrate + cerussete
Equilibrium constant
![Construct the equilibrium constant, K, expression for: Pb(NO_3)_2 + NaHCO_3 ⟶ H_2O + CO_2 + NaNO_3 + PbCO_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: Pb(NO_3)_2 + 2 NaHCO_3 ⟶ H_2O + CO_2 + 2 NaNO_3 + PbCO_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 Pb(NO_3)_2 | 1 | -1 NaHCO_3 | 2 | -2 H_2O | 1 | 1 CO_2 | 1 | 1 NaNO_3 | 2 | 2 PbCO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Pb(NO_3)_2 | 1 | -1 | ([Pb(NO3)2])^(-1) NaHCO_3 | 2 | -2 | ([NaHCO3])^(-2) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] NaNO_3 | 2 | 2 | ([NaNO3])^2 PbCO_3 | 1 | 1 | [PbCO3] 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 = ([Pb(NO3)2])^(-1) ([NaHCO3])^(-2) [H2O] [CO2] ([NaNO3])^2 [PbCO3] = ([H2O] [CO2] ([NaNO3])^2 [PbCO3])/([Pb(NO3)2] ([NaHCO3])^2)](../image_source/512f058ae29ad2ea9a055a003d39ad1e.png)
Construct the equilibrium constant, K, expression for: Pb(NO_3)_2 + NaHCO_3 ⟶ H_2O + CO_2 + NaNO_3 + PbCO_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: Pb(NO_3)_2 + 2 NaHCO_3 ⟶ H_2O + CO_2 + 2 NaNO_3 + PbCO_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 Pb(NO_3)_2 | 1 | -1 NaHCO_3 | 2 | -2 H_2O | 1 | 1 CO_2 | 1 | 1 NaNO_3 | 2 | 2 PbCO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Pb(NO_3)_2 | 1 | -1 | ([Pb(NO3)2])^(-1) NaHCO_3 | 2 | -2 | ([NaHCO3])^(-2) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] NaNO_3 | 2 | 2 | ([NaNO3])^2 PbCO_3 | 1 | 1 | [PbCO3] 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 = ([Pb(NO3)2])^(-1) ([NaHCO3])^(-2) [H2O] [CO2] ([NaNO3])^2 [PbCO3] = ([H2O] [CO2] ([NaNO3])^2 [PbCO3])/([Pb(NO3)2] ([NaHCO3])^2)
Rate of reaction
![Construct the rate of reaction expression for: Pb(NO_3)_2 + NaHCO_3 ⟶ H_2O + CO_2 + NaNO_3 + PbCO_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: Pb(NO_3)_2 + 2 NaHCO_3 ⟶ H_2O + CO_2 + 2 NaNO_3 + PbCO_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 Pb(NO_3)_2 | 1 | -1 NaHCO_3 | 2 | -2 H_2O | 1 | 1 CO_2 | 1 | 1 NaNO_3 | 2 | 2 PbCO_3 | 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 Pb(NO_3)_2 | 1 | -1 | -(Δ[Pb(NO3)2])/(Δt) NaHCO_3 | 2 | -2 | -1/2 (Δ[NaHCO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(Δt) PbCO_3 | 1 | 1 | (Δ[PbCO3])/(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 = -(Δ[Pb(NO3)2])/(Δt) = -1/2 (Δ[NaHCO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) = (Δ[PbCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/42cd5e66faefa6e6d1ea71638f0eb3e9.png)
Construct the rate of reaction expression for: Pb(NO_3)_2 + NaHCO_3 ⟶ H_2O + CO_2 + NaNO_3 + PbCO_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: Pb(NO_3)_2 + 2 NaHCO_3 ⟶ H_2O + CO_2 + 2 NaNO_3 + PbCO_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 Pb(NO_3)_2 | 1 | -1 NaHCO_3 | 2 | -2 H_2O | 1 | 1 CO_2 | 1 | 1 NaNO_3 | 2 | 2 PbCO_3 | 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 Pb(NO_3)_2 | 1 | -1 | -(Δ[Pb(NO3)2])/(Δt) NaHCO_3 | 2 | -2 | -1/2 (Δ[NaHCO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(Δt) PbCO_3 | 1 | 1 | (Δ[PbCO3])/(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 = -(Δ[Pb(NO3)2])/(Δt) = -1/2 (Δ[NaHCO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) = (Δ[PbCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| lead(II) nitrate | sodium bicarbonate | water | carbon dioxide | sodium nitrate | cerussete formula | Pb(NO_3)_2 | NaHCO_3 | H_2O | CO_2 | NaNO_3 | PbCO_3 Hill formula | N_2O_6Pb | CHNaO_3 | H_2O | CO_2 | NNaO_3 | CO_3Pb name | lead(II) nitrate | sodium bicarbonate | water | carbon dioxide | sodium nitrate | cerussete IUPAC name | plumbous dinitrate | sodium hydrogen carbonate | water | carbon dioxide | sodium nitrate | lead(+2) cation carbonate