Input interpretation
![KOH potassium hydroxide + CrKO_8S_2 chrome potash alum ⟶ K_2SO_4 potassium sulfate + Cr(OH)3](../image_source/028f4971497ed32ee19d89c2b7d53135.png)
KOH potassium hydroxide + CrKO_8S_2 chrome potash alum ⟶ K_2SO_4 potassium sulfate + Cr(OH)3
Balanced equation
![Balance the chemical equation algebraically: KOH + CrKO_8S_2 ⟶ K_2SO_4 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 CrKO_8S_2 ⟶ 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 + c_2 = 2 c_3 O: | c_1 + 8 c_2 = 4 c_3 + 3 c_4 Cr: | c_2 = c_4 S: | 2 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 = 3 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 KOH + CrKO_8S_2 ⟶ 2 K_2SO_4 + Cr(OH)3](../image_source/35c3fdd2ca6012c97525a8fcb18f6700.png)
Balance the chemical equation algebraically: KOH + CrKO_8S_2 ⟶ K_2SO_4 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 CrKO_8S_2 ⟶ 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 + c_2 = 2 c_3 O: | c_1 + 8 c_2 = 4 c_3 + 3 c_4 Cr: | c_2 = c_4 S: | 2 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 = 3 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 KOH + CrKO_8S_2 ⟶ 2 K_2SO_4 + Cr(OH)3
Structures
![+ ⟶ + Cr(OH)3](../image_source/efc2f4be4dc5f99bd24ef97bfc0b52fe.png)
+ ⟶ + Cr(OH)3
Names
![potassium hydroxide + chrome potash alum ⟶ potassium sulfate + Cr(OH)3](../image_source/05bc7007c6906b148e2f0534e6452613.png)
potassium hydroxide + chrome potash alum ⟶ potassium sulfate + Cr(OH)3
Equilibrium constant
![Construct the equilibrium constant, K, expression for: KOH + CrKO_8S_2 ⟶ 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: 3 KOH + CrKO_8S_2 ⟶ 2 K_2SO_4 + 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 | 3 | -3 CrKO_8S_2 | 1 | -1 K_2SO_4 | 2 | 2 Cr(OH)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 3 | -3 | ([KOH])^(-3) CrKO_8S_2 | 1 | -1 | ([CrKO8S2])^(-1) K_2SO_4 | 2 | 2 | ([K2SO4])^2 Cr(OH)3 | 1 | 1 | [Cr(OH)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])^(-3) ([CrKO8S2])^(-1) ([K2SO4])^2 [Cr(OH)3] = (([K2SO4])^2 [Cr(OH)3])/(([KOH])^3 [CrKO8S2])](../image_source/3d102da78d990ae74d610a1ab7569c2d.png)
Construct the equilibrium constant, K, expression for: KOH + CrKO_8S_2 ⟶ 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: 3 KOH + CrKO_8S_2 ⟶ 2 K_2SO_4 + 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 | 3 | -3 CrKO_8S_2 | 1 | -1 K_2SO_4 | 2 | 2 Cr(OH)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 3 | -3 | ([KOH])^(-3) CrKO_8S_2 | 1 | -1 | ([CrKO8S2])^(-1) K_2SO_4 | 2 | 2 | ([K2SO4])^2 Cr(OH)3 | 1 | 1 | [Cr(OH)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])^(-3) ([CrKO8S2])^(-1) ([K2SO4])^2 [Cr(OH)3] = (([K2SO4])^2 [Cr(OH)3])/(([KOH])^3 [CrKO8S2])
Rate of reaction
![Construct the rate of reaction expression for: KOH + CrKO_8S_2 ⟶ 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: 3 KOH + CrKO_8S_2 ⟶ 2 K_2SO_4 + 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 | 3 | -3 CrKO_8S_2 | 1 | -1 K_2SO_4 | 2 | 2 Cr(OH)3 | 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 KOH | 3 | -3 | -1/3 (Δ[KOH])/(Δt) CrKO_8S_2 | 1 | -1 | -(Δ[CrKO8S2])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) Cr(OH)3 | 1 | 1 | (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 = -1/3 (Δ[KOH])/(Δt) = -(Δ[CrKO8S2])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/0e351f574f06e0b271c051308a4eee11.png)
Construct the rate of reaction expression for: KOH + CrKO_8S_2 ⟶ 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: 3 KOH + CrKO_8S_2 ⟶ 2 K_2SO_4 + 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 | 3 | -3 CrKO_8S_2 | 1 | -1 K_2SO_4 | 2 | 2 Cr(OH)3 | 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 KOH | 3 | -3 | -1/3 (Δ[KOH])/(Δt) CrKO_8S_2 | 1 | -1 | -(Δ[CrKO8S2])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) Cr(OH)3 | 1 | 1 | (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 = -1/3 (Δ[KOH])/(Δt) = -(Δ[CrKO8S2])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| potassium hydroxide | chrome potash alum | potassium sulfate | Cr(OH)3 formula | KOH | CrKO_8S_2 | K_2SO_4 | Cr(OH)3 Hill formula | HKO | CrKO_8S_2 | K_2O_4S | H3CrO3 name | potassium hydroxide | chrome potash alum | potassium sulfate | IUPAC name | potassium hydroxide | potassium chromium(+3) cation disulfate | dipotassium sulfate |](../image_source/83dada94defc2be9b644e0c8d8f1ef61.png)
| potassium hydroxide | chrome potash alum | potassium sulfate | Cr(OH)3 formula | KOH | CrKO_8S_2 | K_2SO_4 | Cr(OH)3 Hill formula | HKO | CrKO_8S_2 | K_2O_4S | H3CrO3 name | potassium hydroxide | chrome potash alum | potassium sulfate | IUPAC name | potassium hydroxide | potassium chromium(+3) cation disulfate | dipotassium sulfate |
Substance properties
![| potassium hydroxide | chrome potash alum | potassium sulfate | Cr(OH)3 molar mass | 56.105 g/mol | 283.21 g/mol | 174.25 g/mol | 103.02 g/mol phase | solid (at STP) | solid (at STP) | | melting point | 406 °C | 89 °C | | boiling point | 1327 °C | 400 °C | | density | 2.044 g/cm^3 | 2.548 g/cm^3 | | solubility in water | soluble | insoluble | soluble | dynamic viscosity | 0.001 Pa s (at 550 °C) | | |](../image_source/42499f39268dd51386cd41342294c6ff.png)
| potassium hydroxide | chrome potash alum | potassium sulfate | Cr(OH)3 molar mass | 56.105 g/mol | 283.21 g/mol | 174.25 g/mol | 103.02 g/mol phase | solid (at STP) | solid (at STP) | | melting point | 406 °C | 89 °C | | boiling point | 1327 °C | 400 °C | | density | 2.044 g/cm^3 | 2.548 g/cm^3 | | solubility in water | soluble | insoluble | soluble | dynamic viscosity | 0.001 Pa s (at 550 °C) | | |
Units