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KOH + Cr2(SO4)3 + PbO2 = H2O + K2SO4 + K2CrO4 + K2PbO2

Input interpretation

KOH potassium hydroxide + Cr_2(SO_4)_3 chromium sulfate + PbO_2 lead dioxide ⟶ H_2O water + K_2SO_4 potassium sulfate + K_2CrO_4 potassium chromate + K2PbO2
KOH potassium hydroxide + Cr_2(SO_4)_3 chromium sulfate + PbO_2 lead dioxide ⟶ H_2O water + K_2SO_4 potassium sulfate + K_2CrO_4 potassium chromate + K2PbO2

Balanced equation

Balance the chemical equation algebraically: KOH + Cr_2(SO_4)_3 + PbO_2 ⟶ H_2O + K_2SO_4 + K_2CrO_4 + K2PbO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Cr_2(SO_4)_3 + c_3 PbO_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 K_2CrO_4 + c_7 K2PbO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cr, S and Pb: H: | c_1 = 2 c_4 K: | c_1 = 2 c_5 + 2 c_6 + 2 c_7 O: | c_1 + 12 c_2 + 2 c_3 = c_4 + 4 c_5 + 4 c_6 + 2 c_7 Cr: | 2 c_2 = c_6 S: | 3 c_2 = c_5 Pb: | c_3 = c_7 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 = 16 c_2 = 1 c_3 = 3 c_4 = 8 c_5 = 3 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 KOH + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 8 H_2O + 3 K_2SO_4 + 2 K_2CrO_4 + 3 K2PbO2
Balance the chemical equation algebraically: KOH + Cr_2(SO_4)_3 + PbO_2 ⟶ H_2O + K_2SO_4 + K_2CrO_4 + K2PbO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Cr_2(SO_4)_3 + c_3 PbO_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 K_2CrO_4 + c_7 K2PbO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cr, S and Pb: H: | c_1 = 2 c_4 K: | c_1 = 2 c_5 + 2 c_6 + 2 c_7 O: | c_1 + 12 c_2 + 2 c_3 = c_4 + 4 c_5 + 4 c_6 + 2 c_7 Cr: | 2 c_2 = c_6 S: | 3 c_2 = c_5 Pb: | c_3 = c_7 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 = 16 c_2 = 1 c_3 = 3 c_4 = 8 c_5 = 3 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 KOH + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 8 H_2O + 3 K_2SO_4 + 2 K_2CrO_4 + 3 K2PbO2

Structures

+ + ⟶ + + + K2PbO2
+ + ⟶ + + + K2PbO2

Names

potassium hydroxide + chromium sulfate + lead dioxide ⟶ water + potassium sulfate + potassium chromate + K2PbO2
potassium hydroxide + chromium sulfate + lead dioxide ⟶ water + potassium sulfate + potassium chromate + K2PbO2

Equilibrium constant

Construct the equilibrium constant, K, expression for: KOH + Cr_2(SO_4)_3 + PbO_2 ⟶ H_2O + K_2SO_4 + K_2CrO_4 + K2PbO2 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: 16 KOH + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 8 H_2O + 3 K_2SO_4 + 2 K_2CrO_4 + 3 K2PbO2 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 KOH | 16 | -16 Cr_2(SO_4)_3 | 1 | -1 PbO_2 | 3 | -3 H_2O | 8 | 8 K_2SO_4 | 3 | 3 K_2CrO_4 | 2 | 2 K2PbO2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 16 | -16 | ([KOH])^(-16) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) PbO_2 | 3 | -3 | ([PbO2])^(-3) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 3 | 3 | ([K2SO4])^3 K_2CrO_4 | 2 | 2 | ([K2CrO4])^2 K2PbO2 | 3 | 3 | ([K2PbO2])^3 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 = ([KOH])^(-16) ([Cr2(SO4)3])^(-1) ([PbO2])^(-3) ([H2O])^8 ([K2SO4])^3 ([K2CrO4])^2 ([K2PbO2])^3 = (([H2O])^8 ([K2SO4])^3 ([K2CrO4])^2 ([K2PbO2])^3)/(([KOH])^16 [Cr2(SO4)3] ([PbO2])^3)
Construct the equilibrium constant, K, expression for: KOH + Cr_2(SO_4)_3 + PbO_2 ⟶ H_2O + K_2SO_4 + K_2CrO_4 + K2PbO2 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: 16 KOH + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 8 H_2O + 3 K_2SO_4 + 2 K_2CrO_4 + 3 K2PbO2 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 KOH | 16 | -16 Cr_2(SO_4)_3 | 1 | -1 PbO_2 | 3 | -3 H_2O | 8 | 8 K_2SO_4 | 3 | 3 K_2CrO_4 | 2 | 2 K2PbO2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 16 | -16 | ([KOH])^(-16) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) PbO_2 | 3 | -3 | ([PbO2])^(-3) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 3 | 3 | ([K2SO4])^3 K_2CrO_4 | 2 | 2 | ([K2CrO4])^2 K2PbO2 | 3 | 3 | ([K2PbO2])^3 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 = ([KOH])^(-16) ([Cr2(SO4)3])^(-1) ([PbO2])^(-3) ([H2O])^8 ([K2SO4])^3 ([K2CrO4])^2 ([K2PbO2])^3 = (([H2O])^8 ([K2SO4])^3 ([K2CrO4])^2 ([K2PbO2])^3)/(([KOH])^16 [Cr2(SO4)3] ([PbO2])^3)

Rate of reaction

Construct the rate of reaction expression for: KOH + Cr_2(SO_4)_3 + PbO_2 ⟶ H_2O + K_2SO_4 + K_2CrO_4 + K2PbO2 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: 16 KOH + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 8 H_2O + 3 K_2SO_4 + 2 K_2CrO_4 + 3 K2PbO2 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 KOH | 16 | -16 Cr_2(SO_4)_3 | 1 | -1 PbO_2 | 3 | -3 H_2O | 8 | 8 K_2SO_4 | 3 | 3 K_2CrO_4 | 2 | 2 K2PbO2 | 3 | 3 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 KOH | 16 | -16 | -1/16 (Δ[KOH])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) PbO_2 | 3 | -3 | -1/3 (Δ[PbO2])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(Δt) K2PbO2 | 3 | 3 | 1/3 (Δ[K2PbO2])/(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 = -1/16 (Δ[KOH])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = -1/3 (Δ[PbO2])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) = 1/3 (Δ[K2PbO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: KOH + Cr_2(SO_4)_3 + PbO_2 ⟶ H_2O + K_2SO_4 + K_2CrO_4 + K2PbO2 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: 16 KOH + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 8 H_2O + 3 K_2SO_4 + 2 K_2CrO_4 + 3 K2PbO2 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 KOH | 16 | -16 Cr_2(SO_4)_3 | 1 | -1 PbO_2 | 3 | -3 H_2O | 8 | 8 K_2SO_4 | 3 | 3 K_2CrO_4 | 2 | 2 K2PbO2 | 3 | 3 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 KOH | 16 | -16 | -1/16 (Δ[KOH])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) PbO_2 | 3 | -3 | -1/3 (Δ[PbO2])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(Δt) K2PbO2 | 3 | 3 | 1/3 (Δ[K2PbO2])/(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 = -1/16 (Δ[KOH])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = -1/3 (Δ[PbO2])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) = 1/3 (Δ[K2PbO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium hydroxide | chromium sulfate | lead dioxide | water | potassium sulfate | potassium chromate | K2PbO2 formula | KOH | Cr_2(SO_4)_3 | PbO_2 | H_2O | K_2SO_4 | K_2CrO_4 | K2PbO2 Hill formula | HKO | Cr_2O_12S_3 | O_2Pb | H_2O | K_2O_4S | CrK_2O_4 | K2O2Pb name | potassium hydroxide | chromium sulfate | lead dioxide | water | potassium sulfate | potassium chromate | IUPAC name | potassium hydroxide | chromium(+3) cation trisulfate | | water | dipotassium sulfate | dipotassium dioxido-dioxochromium |
| potassium hydroxide | chromium sulfate | lead dioxide | water | potassium sulfate | potassium chromate | K2PbO2 formula | KOH | Cr_2(SO_4)_3 | PbO_2 | H_2O | K_2SO_4 | K_2CrO_4 | K2PbO2 Hill formula | HKO | Cr_2O_12S_3 | O_2Pb | H_2O | K_2O_4S | CrK_2O_4 | K2O2Pb name | potassium hydroxide | chromium sulfate | lead dioxide | water | potassium sulfate | potassium chromate | IUPAC name | potassium hydroxide | chromium(+3) cation trisulfate | | water | dipotassium sulfate | dipotassium dioxido-dioxochromium |

Substance properties

| potassium hydroxide | chromium sulfate | lead dioxide | water | potassium sulfate | potassium chromate | K2PbO2 molar mass | 56.105 g/mol | 392.2 g/mol | 239.2 g/mol | 18.015 g/mol | 174.25 g/mol | 194.19 g/mol | 317.4 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) | | solid (at STP) | melting point | 406 °C | | 290 °C | 0 °C | | 971 °C | boiling point | 1327 °C | 330 °C | | 99.9839 °C | | | density | 2.044 g/cm^3 | 1.84 g/cm^3 | 9.58 g/cm^3 | 1 g/cm^3 | | 2.73 g/cm^3 | solubility in water | soluble | | insoluble | | soluble | soluble | surface tension | | | | 0.0728 N/m | | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | odorless | | odorless | | odorless |
| potassium hydroxide | chromium sulfate | lead dioxide | water | potassium sulfate | potassium chromate | K2PbO2 molar mass | 56.105 g/mol | 392.2 g/mol | 239.2 g/mol | 18.015 g/mol | 174.25 g/mol | 194.19 g/mol | 317.4 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) | | solid (at STP) | melting point | 406 °C | | 290 °C | 0 °C | | 971 °C | boiling point | 1327 °C | 330 °C | | 99.9839 °C | | | density | 2.044 g/cm^3 | 1.84 g/cm^3 | 9.58 g/cm^3 | 1 g/cm^3 | | 2.73 g/cm^3 | solubility in water | soluble | | insoluble | | soluble | soluble | surface tension | | | | 0.0728 N/m | | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | odorless | | odorless | | odorless |

Units

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