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K2Cr2O7 + Pb(CH3COO)2 = KCH3COO + PbCr2O7

Input interpretation

K_2Cr_2O_7 potassium dichromate + Pb(CH_3CO_2)_2 lead(II) acetate ⟶ CH_3COOK potassium acetate + PbCr2O7
K_2Cr_2O_7 potassium dichromate + Pb(CH_3CO_2)_2 lead(II) acetate ⟶ CH_3COOK potassium acetate + PbCr2O7

Balanced equation

Balance the chemical equation algebraically: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ CH_3COOK + PbCr2O7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2Cr_2O_7 + c_2 Pb(CH_3CO_2)_2 ⟶ c_3 CH_3COOK + c_4 PbCr2O7 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, K, O, C, H and Pb: Cr: | 2 c_1 = 2 c_4 K: | 2 c_1 = c_3 O: | 7 c_1 + 4 c_2 = 2 c_3 + 7 c_4 C: | 4 c_2 = 2 c_3 H: | 6 c_2 = 3 c_3 Pb: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ 2 CH_3COOK + PbCr2O7
Balance the chemical equation algebraically: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ CH_3COOK + PbCr2O7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2Cr_2O_7 + c_2 Pb(CH_3CO_2)_2 ⟶ c_3 CH_3COOK + c_4 PbCr2O7 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, K, O, C, H and Pb: Cr: | 2 c_1 = 2 c_4 K: | 2 c_1 = c_3 O: | 7 c_1 + 4 c_2 = 2 c_3 + 7 c_4 C: | 4 c_2 = 2 c_3 H: | 6 c_2 = 3 c_3 Pb: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ 2 CH_3COOK + PbCr2O7

Structures

+ ⟶ + PbCr2O7
+ ⟶ + PbCr2O7

Names

potassium dichromate + lead(II) acetate ⟶ potassium acetate + PbCr2O7
potassium dichromate + lead(II) acetate ⟶ potassium acetate + PbCr2O7

Equilibrium constant

Construct the equilibrium constant, K, expression for: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ CH_3COOK + PbCr2O7 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: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ 2 CH_3COOK + PbCr2O7 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 K_2Cr_2O_7 | 1 | -1 Pb(CH_3CO_2)_2 | 1 | -1 CH_3COOK | 2 | 2 PbCr2O7 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) Pb(CH_3CO_2)_2 | 1 | -1 | ([Pb(CH3CO2)2])^(-1) CH_3COOK | 2 | 2 | ([CH3COOK])^2 PbCr2O7 | 1 | 1 | [PbCr2O7] 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 = ([K2Cr2O7])^(-1) ([Pb(CH3CO2)2])^(-1) ([CH3COOK])^2 [PbCr2O7] = (([CH3COOK])^2 [PbCr2O7])/([K2Cr2O7] [Pb(CH3CO2)2])
Construct the equilibrium constant, K, expression for: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ CH_3COOK + PbCr2O7 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: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ 2 CH_3COOK + PbCr2O7 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 K_2Cr_2O_7 | 1 | -1 Pb(CH_3CO_2)_2 | 1 | -1 CH_3COOK | 2 | 2 PbCr2O7 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) Pb(CH_3CO_2)_2 | 1 | -1 | ([Pb(CH3CO2)2])^(-1) CH_3COOK | 2 | 2 | ([CH3COOK])^2 PbCr2O7 | 1 | 1 | [PbCr2O7] 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 = ([K2Cr2O7])^(-1) ([Pb(CH3CO2)2])^(-1) ([CH3COOK])^2 [PbCr2O7] = (([CH3COOK])^2 [PbCr2O7])/([K2Cr2O7] [Pb(CH3CO2)2])

Rate of reaction

Construct the rate of reaction expression for: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ CH_3COOK + PbCr2O7 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: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ 2 CH_3COOK + PbCr2O7 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 K_2Cr_2O_7 | 1 | -1 Pb(CH_3CO_2)_2 | 1 | -1 CH_3COOK | 2 | 2 PbCr2O7 | 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 K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) Pb(CH_3CO_2)_2 | 1 | -1 | -(Δ[Pb(CH3CO2)2])/(Δt) CH_3COOK | 2 | 2 | 1/2 (Δ[CH3COOK])/(Δt) PbCr2O7 | 1 | 1 | (Δ[PbCr2O7])/(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[K2Cr2O7])/(Δt) = -(Δ[Pb(CH3CO2)2])/(Δt) = 1/2 (Δ[CH3COOK])/(Δt) = (Δ[PbCr2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ CH_3COOK + PbCr2O7 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: K_2Cr_2O_7 + Pb(CH_3CO_2)_2 ⟶ 2 CH_3COOK + PbCr2O7 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 K_2Cr_2O_7 | 1 | -1 Pb(CH_3CO_2)_2 | 1 | -1 CH_3COOK | 2 | 2 PbCr2O7 | 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 K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) Pb(CH_3CO_2)_2 | 1 | -1 | -(Δ[Pb(CH3CO2)2])/(Δt) CH_3COOK | 2 | 2 | 1/2 (Δ[CH3COOK])/(Δt) PbCr2O7 | 1 | 1 | (Δ[PbCr2O7])/(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[K2Cr2O7])/(Δt) = -(Δ[Pb(CH3CO2)2])/(Δt) = 1/2 (Δ[CH3COOK])/(Δt) = (Δ[PbCr2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium dichromate | lead(II) acetate | potassium acetate | PbCr2O7 formula | K_2Cr_2O_7 | Pb(CH_3CO_2)_2 | CH_3COOK | PbCr2O7 Hill formula | Cr_2K_2O_7 | C_4H_6O_4Pb | C_2H_3KO_2 | Cr2O7Pb name | potassium dichromate | lead(II) acetate | potassium acetate | IUPAC name | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | lead(2+) diacetate | potassium acetate |
| potassium dichromate | lead(II) acetate | potassium acetate | PbCr2O7 formula | K_2Cr_2O_7 | Pb(CH_3CO_2)_2 | CH_3COOK | PbCr2O7 Hill formula | Cr_2K_2O_7 | C_4H_6O_4Pb | C_2H_3KO_2 | Cr2O7Pb name | potassium dichromate | lead(II) acetate | potassium acetate | IUPAC name | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | lead(2+) diacetate | potassium acetate |

Substance properties

| potassium dichromate | lead(II) acetate | potassium acetate | PbCr2O7 molar mass | 294.18 g/mol | 325.3 g/mol | 98.142 g/mol | 423.2 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 398 °C | 280 °C | 304 °C | density | 2.67 g/cm^3 | 3.25 g/cm^3 | 1.57 g/cm^3 | surface tension | | | 0.0256 N/m | odor | odorless | | |
| potassium dichromate | lead(II) acetate | potassium acetate | PbCr2O7 molar mass | 294.18 g/mol | 325.3 g/mol | 98.142 g/mol | 423.2 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 398 °C | 280 °C | 304 °C | density | 2.67 g/cm^3 | 3.25 g/cm^3 | 1.57 g/cm^3 | surface tension | | | 0.0256 N/m | odor | odorless | | |

Units

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