Input interpretation
![CaCO_3 calcium carbonate + H_2CO_3 carbonic acid ⟶ Ca(HCO3)2](../image_source/0559baa42a190a38bcbaac4bd51bf506.png)
CaCO_3 calcium carbonate + H_2CO_3 carbonic acid ⟶ Ca(HCO3)2
Balanced equation
![Balance the chemical equation algebraically: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCO_3 + c_2 H_2CO_3 ⟶ c_3 Ca(HCO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ca, O and H: C: | c_1 + c_2 = 2 c_3 Ca: | c_1 = c_3 O: | 3 c_1 + 3 c_2 = 6 c_3 H: | 2 c_2 = 2 c_3 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 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)2](../image_source/aa627c66efe842efd0f77526621cead9.png)
Balance the chemical equation algebraically: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCO_3 + c_2 H_2CO_3 ⟶ c_3 Ca(HCO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ca, O and H: C: | c_1 + c_2 = 2 c_3 Ca: | c_1 = c_3 O: | 3 c_1 + 3 c_2 = 6 c_3 H: | 2 c_2 = 2 c_3 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 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)2
Structures
![+ ⟶ Ca(HCO3)2](../image_source/3dc1f2a3715fe02ca86b3d5c429a9be8.png)
+ ⟶ Ca(HCO3)2
Names
![calcium carbonate + carbonic acid ⟶ Ca(HCO3)2](../image_source/bb25f9c7746738c947015e41c4e46dd2.png)
calcium carbonate + carbonic acid ⟶ Ca(HCO3)2
Equilibrium constant
![Construct the equilibrium constant, K, expression for: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)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: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)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 CaCO_3 | 1 | -1 H_2CO_3 | 1 | -1 Ca(HCO3)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaCO_3 | 1 | -1 | ([CaCO3])^(-1) H_2CO_3 | 1 | -1 | ([H2CO3])^(-1) Ca(HCO3)2 | 1 | 1 | [Ca(HCO3)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 = ([CaCO3])^(-1) ([H2CO3])^(-1) [Ca(HCO3)2] = ([Ca(HCO3)2])/([CaCO3] [H2CO3])](../image_source/70e8abedb68afe5fdbc7145c2cf0952d.png)
Construct the equilibrium constant, K, expression for: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)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: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)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 CaCO_3 | 1 | -1 H_2CO_3 | 1 | -1 Ca(HCO3)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaCO_3 | 1 | -1 | ([CaCO3])^(-1) H_2CO_3 | 1 | -1 | ([H2CO3])^(-1) Ca(HCO3)2 | 1 | 1 | [Ca(HCO3)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 = ([CaCO3])^(-1) ([H2CO3])^(-1) [Ca(HCO3)2] = ([Ca(HCO3)2])/([CaCO3] [H2CO3])
Rate of reaction
![Construct the rate of reaction expression for: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)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: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)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 CaCO_3 | 1 | -1 H_2CO_3 | 1 | -1 Ca(HCO3)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 CaCO_3 | 1 | -1 | -(Δ[CaCO3])/(Δt) H_2CO_3 | 1 | -1 | -(Δ[H2CO3])/(Δt) Ca(HCO3)2 | 1 | 1 | (Δ[Ca(HCO3)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 = -(Δ[CaCO3])/(Δt) = -(Δ[H2CO3])/(Δt) = (Δ[Ca(HCO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/1307a344013218756ca30c666a446def.png)
Construct the rate of reaction expression for: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)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: CaCO_3 + H_2CO_3 ⟶ Ca(HCO3)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 CaCO_3 | 1 | -1 H_2CO_3 | 1 | -1 Ca(HCO3)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 CaCO_3 | 1 | -1 | -(Δ[CaCO3])/(Δt) H_2CO_3 | 1 | -1 | -(Δ[H2CO3])/(Δt) Ca(HCO3)2 | 1 | 1 | (Δ[Ca(HCO3)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 = -(Δ[CaCO3])/(Δt) = -(Δ[H2CO3])/(Δt) = (Δ[Ca(HCO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| calcium carbonate | carbonic acid | Ca(HCO3)2 formula | CaCO_3 | H_2CO_3 | Ca(HCO3)2 Hill formula | CCaO_3 | CH_2O_3 | C2H2CaO6 name | calcium carbonate | carbonic acid |](../image_source/b575585b7ca461f75f35ab434c89cc5b.png)
| calcium carbonate | carbonic acid | Ca(HCO3)2 formula | CaCO_3 | H_2CO_3 | Ca(HCO3)2 Hill formula | CCaO_3 | CH_2O_3 | C2H2CaO6 name | calcium carbonate | carbonic acid |
Substance properties
![| calcium carbonate | carbonic acid | Ca(HCO3)2 molar mass | 100.09 g/mol | 62.024 g/mol | 162.11 g/mol phase | solid (at STP) | | melting point | 1340 °C | | density | 2.71 g/cm^3 | | solubility in water | insoluble | |](../image_source/67268adc78edbb8e6314b0031c053ad8.png)
| calcium carbonate | carbonic acid | Ca(HCO3)2 molar mass | 100.09 g/mol | 62.024 g/mol | 162.11 g/mol phase | solid (at STP) | | melting point | 1340 °C | | density | 2.71 g/cm^3 | | solubility in water | insoluble | |
Units