Input interpretation
![CaSO_4 calcium sulfate + Ba(NO_3)_2 barium nitrate ⟶ BaSO_4 barium sulfate + Ca(NO_3)_2 calcium nitrate](../image_source/70b29fe713bf1a60daabce2229deefdc.png)
CaSO_4 calcium sulfate + Ba(NO_3)_2 barium nitrate ⟶ BaSO_4 barium sulfate + Ca(NO_3)_2 calcium nitrate
Balanced equation
![Balance the chemical equation algebraically: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + Ca(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaSO_4 + c_2 Ba(NO_3)_2 ⟶ c_3 BaSO_4 + c_4 Ca(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, O, S, Ba and N: Ca: | c_1 = c_4 O: | 4 c_1 + 6 c_2 = 4 c_3 + 6 c_4 S: | c_1 = c_3 Ba: | c_2 = c_3 N: | 2 c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + Ca(NO_3)_2](../image_source/3bd0bcbd85faeadb9cb7a31497fa2238.png)
Balance the chemical equation algebraically: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + Ca(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaSO_4 + c_2 Ba(NO_3)_2 ⟶ c_3 BaSO_4 + c_4 Ca(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, O, S, Ba and N: Ca: | c_1 = c_4 O: | 4 c_1 + 6 c_2 = 4 c_3 + 6 c_4 S: | c_1 = c_3 Ba: | c_2 = c_3 N: | 2 c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + Ca(NO_3)_2
Structures
![+ ⟶ +](../image_source/5b89d0575196b73a0aa43c8dd845a37b.png)
+ ⟶ +
Names
![calcium sulfate + barium nitrate ⟶ barium sulfate + calcium nitrate](../image_source/31178382ebe50ea8a9157eb5d140b517.png)
calcium sulfate + barium nitrate ⟶ barium sulfate + calcium nitrate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + 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: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + 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 CaSO_4 | 1 | -1 Ba(NO_3)_2 | 1 | -1 BaSO_4 | 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 CaSO_4 | 1 | -1 | ([CaSO4])^(-1) Ba(NO_3)_2 | 1 | -1 | ([Ba(NO3)2])^(-1) BaSO_4 | 1 | 1 | [BaSO4] 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 = ([CaSO4])^(-1) ([Ba(NO3)2])^(-1) [BaSO4] [Ca(NO3)2] = ([BaSO4] [Ca(NO3)2])/([CaSO4] [Ba(NO3)2])](../image_source/c044f552451ba114e49823cdf34e71d4.png)
Construct the equilibrium constant, K, expression for: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + 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: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + 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 CaSO_4 | 1 | -1 Ba(NO_3)_2 | 1 | -1 BaSO_4 | 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 CaSO_4 | 1 | -1 | ([CaSO4])^(-1) Ba(NO_3)_2 | 1 | -1 | ([Ba(NO3)2])^(-1) BaSO_4 | 1 | 1 | [BaSO4] 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 = ([CaSO4])^(-1) ([Ba(NO3)2])^(-1) [BaSO4] [Ca(NO3)2] = ([BaSO4] [Ca(NO3)2])/([CaSO4] [Ba(NO3)2])
Rate of reaction
![Construct the rate of reaction expression for: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + 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: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + 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 CaSO_4 | 1 | -1 Ba(NO_3)_2 | 1 | -1 BaSO_4 | 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 CaSO_4 | 1 | -1 | -(Δ[CaSO4])/(Δt) Ba(NO_3)_2 | 1 | -1 | -(Δ[Ba(NO3)2])/(Δt) BaSO_4 | 1 | 1 | (Δ[BaSO4])/(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 = -(Δ[CaSO4])/(Δt) = -(Δ[Ba(NO3)2])/(Δt) = (Δ[BaSO4])/(Δt) = (Δ[Ca(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/b901d09ca5e97165558ea37b07961222.png)
Construct the rate of reaction expression for: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + 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: CaSO_4 + Ba(NO_3)_2 ⟶ BaSO_4 + 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 CaSO_4 | 1 | -1 Ba(NO_3)_2 | 1 | -1 BaSO_4 | 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 CaSO_4 | 1 | -1 | -(Δ[CaSO4])/(Δt) Ba(NO_3)_2 | 1 | -1 | -(Δ[Ba(NO3)2])/(Δt) BaSO_4 | 1 | 1 | (Δ[BaSO4])/(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 = -(Δ[CaSO4])/(Δt) = -(Δ[Ba(NO3)2])/(Δt) = (Δ[BaSO4])/(Δt) = (Δ[Ca(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| calcium sulfate | barium nitrate | barium sulfate | calcium nitrate formula | CaSO_4 | Ba(NO_3)_2 | BaSO_4 | Ca(NO_3)_2 Hill formula | CaO_4S | BaN_2O_6 | BaO_4S | CaN_2O_6 name | calcium sulfate | barium nitrate | barium sulfate | calcium nitrate IUPAC name | calcium sulfate | barium(+2) cation dinitrate | barium(+2) cation sulfate | calcium dinitrate](../image_source/c9df918e87a3dd2934446632a5efc59e.png)
| calcium sulfate | barium nitrate | barium sulfate | calcium nitrate formula | CaSO_4 | Ba(NO_3)_2 | BaSO_4 | Ca(NO_3)_2 Hill formula | CaO_4S | BaN_2O_6 | BaO_4S | CaN_2O_6 name | calcium sulfate | barium nitrate | barium sulfate | calcium nitrate IUPAC name | calcium sulfate | barium(+2) cation dinitrate | barium(+2) cation sulfate | calcium dinitrate
Substance properties
![| calcium sulfate | barium nitrate | barium sulfate | calcium nitrate molar mass | 136.13 g/mol | 261.34 g/mol | 233.38 g/mol | 164.09 g/mol phase | | solid (at STP) | solid (at STP) | solid (at STP) melting point | | 592 °C | 1345 °C | 562 °C density | | 3.23 g/cm^3 | 4.5 g/cm^3 | 2.5 g/cm^3 solubility in water | slightly soluble | | insoluble | soluble odor | odorless | | |](../image_source/675deeffb45b8c5ebad23abe3764b015.png)
| calcium sulfate | barium nitrate | barium sulfate | calcium nitrate molar mass | 136.13 g/mol | 261.34 g/mol | 233.38 g/mol | 164.09 g/mol phase | | solid (at STP) | solid (at STP) | solid (at STP) melting point | | 592 °C | 1345 °C | 562 °C density | | 3.23 g/cm^3 | 4.5 g/cm^3 | 2.5 g/cm^3 solubility in water | slightly soluble | | insoluble | soluble odor | odorless | | |
Units