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KOH + Cr2(SO4)3 = K2SO4 + Cr(OH)3

Input interpretation

KOH potassium hydroxide + Cr_2(SO_4)_3 chromium sulfate ⟶ K_2SO_4 potassium sulfate + Cr(OH)3
KOH potassium hydroxide + Cr_2(SO_4)_3 chromium sulfate ⟶ K_2SO_4 potassium sulfate + Cr(OH)3

Balanced equation

Balance the chemical equation algebraically: KOH + Cr_2(SO_4)_3 ⟶ K_2SO_4 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Cr_2(SO_4)_3 ⟶ c_3 K_2SO_4 + c_4 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cr and S: H: | c_1 = 3 c_4 K: | c_1 = 2 c_3 O: | c_1 + 12 c_2 = 4 c_3 + 3 c_4 Cr: | 2 c_2 = c_4 S: | 3 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 KOH + Cr_2(SO_4)_3 ⟶ 3 K_2SO_4 + 2 Cr(OH)3
Balance the chemical equation algebraically: KOH + Cr_2(SO_4)_3 ⟶ K_2SO_4 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Cr_2(SO_4)_3 ⟶ c_3 K_2SO_4 + c_4 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cr and S: H: | c_1 = 3 c_4 K: | c_1 = 2 c_3 O: | c_1 + 12 c_2 = 4 c_3 + 3 c_4 Cr: | 2 c_2 = c_4 S: | 3 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 KOH + Cr_2(SO_4)_3 ⟶ 3 K_2SO_4 + 2 Cr(OH)3

Structures

+ ⟶ + Cr(OH)3
+ ⟶ + Cr(OH)3

Names

potassium hydroxide + chromium sulfate ⟶ potassium sulfate + Cr(OH)3
potassium hydroxide + chromium sulfate ⟶ potassium sulfate + Cr(OH)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: KOH + Cr_2(SO_4)_3 ⟶ K_2SO_4 + Cr(OH)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: 6 KOH + Cr_2(SO_4)_3 ⟶ 3 K_2SO_4 + 2 Cr(OH)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 KOH | 6 | -6 Cr_2(SO_4)_3 | 1 | -1 K_2SO_4 | 3 | 3 Cr(OH)3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 6 | -6 | ([KOH])^(-6) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) K_2SO_4 | 3 | 3 | ([K2SO4])^3 Cr(OH)3 | 2 | 2 | ([Cr(OH)3])^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 = ([KOH])^(-6) ([Cr2(SO4)3])^(-1) ([K2SO4])^3 ([Cr(OH)3])^2 = (([K2SO4])^3 ([Cr(OH)3])^2)/(([KOH])^6 [Cr2(SO4)3])
Construct the equilibrium constant, K, expression for: KOH + Cr_2(SO_4)_3 ⟶ K_2SO_4 + Cr(OH)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: 6 KOH + Cr_2(SO_4)_3 ⟶ 3 K_2SO_4 + 2 Cr(OH)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 KOH | 6 | -6 Cr_2(SO_4)_3 | 1 | -1 K_2SO_4 | 3 | 3 Cr(OH)3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 6 | -6 | ([KOH])^(-6) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) K_2SO_4 | 3 | 3 | ([K2SO4])^3 Cr(OH)3 | 2 | 2 | ([Cr(OH)3])^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 = ([KOH])^(-6) ([Cr2(SO4)3])^(-1) ([K2SO4])^3 ([Cr(OH)3])^2 = (([K2SO4])^3 ([Cr(OH)3])^2)/(([KOH])^6 [Cr2(SO4)3])

Rate of reaction

Construct the rate of reaction expression for: KOH + Cr_2(SO_4)_3 ⟶ K_2SO_4 + Cr(OH)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: 6 KOH + Cr_2(SO_4)_3 ⟶ 3 K_2SO_4 + 2 Cr(OH)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 KOH | 6 | -6 Cr_2(SO_4)_3 | 1 | -1 K_2SO_4 | 3 | 3 Cr(OH)3 | 2 | 2 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 | 6 | -6 | -1/6 (Δ[KOH])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) Cr(OH)3 | 2 | 2 | 1/2 (Δ[Cr(OH)3])/(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 = -1/6 (Δ[KOH])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[Cr(OH)3])/(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 ⟶ K_2SO_4 + Cr(OH)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: 6 KOH + Cr_2(SO_4)_3 ⟶ 3 K_2SO_4 + 2 Cr(OH)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 KOH | 6 | -6 Cr_2(SO_4)_3 | 1 | -1 K_2SO_4 | 3 | 3 Cr(OH)3 | 2 | 2 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 | 6 | -6 | -1/6 (Δ[KOH])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) Cr(OH)3 | 2 | 2 | 1/2 (Δ[Cr(OH)3])/(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 = -1/6 (Δ[KOH])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium hydroxide | chromium sulfate | potassium sulfate | Cr(OH)3 formula | KOH | Cr_2(SO_4)_3 | K_2SO_4 | Cr(OH)3 Hill formula | HKO | Cr_2O_12S_3 | K_2O_4S | H3CrO3 name | potassium hydroxide | chromium sulfate | potassium sulfate | IUPAC name | potassium hydroxide | chromium(+3) cation trisulfate | dipotassium sulfate |
| potassium hydroxide | chromium sulfate | potassium sulfate | Cr(OH)3 formula | KOH | Cr_2(SO_4)_3 | K_2SO_4 | Cr(OH)3 Hill formula | HKO | Cr_2O_12S_3 | K_2O_4S | H3CrO3 name | potassium hydroxide | chromium sulfate | potassium sulfate | IUPAC name | potassium hydroxide | chromium(+3) cation trisulfate | dipotassium sulfate |

Substance properties

| potassium hydroxide | chromium sulfate | potassium sulfate | Cr(OH)3 molar mass | 56.105 g/mol | 392.2 g/mol | 174.25 g/mol | 103.02 g/mol phase | solid (at STP) | liquid (at STP) | | melting point | 406 °C | | | boiling point | 1327 °C | 330 °C | | density | 2.044 g/cm^3 | 1.84 g/cm^3 | | solubility in water | soluble | | soluble | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | odor | | odorless | |
| potassium hydroxide | chromium sulfate | potassium sulfate | Cr(OH)3 molar mass | 56.105 g/mol | 392.2 g/mol | 174.25 g/mol | 103.02 g/mol phase | solid (at STP) | liquid (at STP) | | melting point | 406 °C | | | boiling point | 1327 °C | 330 °C | | density | 2.044 g/cm^3 | 1.84 g/cm^3 | | solubility in water | soluble | | soluble | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | odor | | odorless | |

Units

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