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H2O + HCl + KCrO2 = KCl + Cr(OH)3

Input interpretation

H_2O water + HCl hydrogen chloride + KCrO2 ⟶ KCl potassium chloride + Cr(OH)3
H_2O water + HCl hydrogen chloride + KCrO2 ⟶ KCl potassium chloride + Cr(OH)3

Balanced equation

Balance the chemical equation algebraically: H_2O + HCl + KCrO2 ⟶ KCl + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HCl + c_3 KCrO2 ⟶ c_4 KCl + c_5 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, K and Cr: H: | 2 c_1 + c_2 = 3 c_5 O: | c_1 + 2 c_3 = 3 c_5 Cl: | c_2 = c_4 K: | c_3 = c_4 Cr: | c_3 = c_5 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 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + HCl + KCrO2 ⟶ KCl + Cr(OH)3
Balance the chemical equation algebraically: H_2O + HCl + KCrO2 ⟶ KCl + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HCl + c_3 KCrO2 ⟶ c_4 KCl + c_5 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, K and Cr: H: | 2 c_1 + c_2 = 3 c_5 O: | c_1 + 2 c_3 = 3 c_5 Cl: | c_2 = c_4 K: | c_3 = c_4 Cr: | c_3 = c_5 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 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + HCl + KCrO2 ⟶ KCl + Cr(OH)3

Structures

+ + KCrO2 ⟶ + Cr(OH)3
+ + KCrO2 ⟶ + Cr(OH)3

Names

water + hydrogen chloride + KCrO2 ⟶ potassium chloride + Cr(OH)3
water + hydrogen chloride + KCrO2 ⟶ potassium chloride + Cr(OH)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + HCl + KCrO2 ⟶ KCl + 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: H_2O + HCl + KCrO2 ⟶ KCl + 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 H_2O | 1 | -1 HCl | 1 | -1 KCrO2 | 1 | -1 KCl | 1 | 1 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 H_2O | 1 | -1 | ([H2O])^(-1) HCl | 1 | -1 | ([HCl])^(-1) KCrO2 | 1 | -1 | ([KCrO2])^(-1) KCl | 1 | 1 | [KCl] 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 = ([H2O])^(-1) ([HCl])^(-1) ([KCrO2])^(-1) [KCl] [Cr(OH)3] = ([KCl] [Cr(OH)3])/([H2O] [HCl] [KCrO2])
Construct the equilibrium constant, K, expression for: H_2O + HCl + KCrO2 ⟶ KCl + 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: H_2O + HCl + KCrO2 ⟶ KCl + 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 H_2O | 1 | -1 HCl | 1 | -1 KCrO2 | 1 | -1 KCl | 1 | 1 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 H_2O | 1 | -1 | ([H2O])^(-1) HCl | 1 | -1 | ([HCl])^(-1) KCrO2 | 1 | -1 | ([KCrO2])^(-1) KCl | 1 | 1 | [KCl] 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 = ([H2O])^(-1) ([HCl])^(-1) ([KCrO2])^(-1) [KCl] [Cr(OH)3] = ([KCl] [Cr(OH)3])/([H2O] [HCl] [KCrO2])

Rate of reaction

Construct the rate of reaction expression for: H_2O + HCl + KCrO2 ⟶ KCl + 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: H_2O + HCl + KCrO2 ⟶ KCl + 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 H_2O | 1 | -1 HCl | 1 | -1 KCrO2 | 1 | -1 KCl | 1 | 1 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) HCl | 1 | -1 | -(Δ[HCl])/(Δt) KCrO2 | 1 | -1 | -(Δ[KCrO2])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(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 = -(Δ[H2O])/(Δt) = -(Δ[HCl])/(Δt) = -(Δ[KCrO2])/(Δt) = (Δ[KCl])/(Δt) = (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + HCl + KCrO2 ⟶ KCl + 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: H_2O + HCl + KCrO2 ⟶ KCl + 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 H_2O | 1 | -1 HCl | 1 | -1 KCrO2 | 1 | -1 KCl | 1 | 1 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) HCl | 1 | -1 | -(Δ[HCl])/(Δt) KCrO2 | 1 | -1 | -(Δ[KCrO2])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(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 = -(Δ[H2O])/(Δt) = -(Δ[HCl])/(Δt) = -(Δ[KCrO2])/(Δt) = (Δ[KCl])/(Δt) = (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | hydrogen chloride | KCrO2 | potassium chloride | Cr(OH)3 formula | H_2O | HCl | KCrO2 | KCl | Cr(OH)3 Hill formula | H_2O | ClH | CrKO2 | ClK | H3CrO3 name | water | hydrogen chloride | | potassium chloride |
| water | hydrogen chloride | KCrO2 | potassium chloride | Cr(OH)3 formula | H_2O | HCl | KCrO2 | KCl | Cr(OH)3 Hill formula | H_2O | ClH | CrKO2 | ClK | H3CrO3 name | water | hydrogen chloride | | potassium chloride |

Substance properties

| water | hydrogen chloride | KCrO2 | potassium chloride | Cr(OH)3 molar mass | 18.015 g/mol | 36.46 g/mol | 123.09 g/mol | 74.55 g/mol | 103.02 g/mol phase | liquid (at STP) | gas (at STP) | | solid (at STP) | melting point | 0 °C | -114.17 °C | | 770 °C | boiling point | 99.9839 °C | -85 °C | | 1420 °C | density | 1 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | | 1.98 g/cm^3 | solubility in water | | miscible | | soluble | surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | odor | odorless | | | odorless |
| water | hydrogen chloride | KCrO2 | potassium chloride | Cr(OH)3 molar mass | 18.015 g/mol | 36.46 g/mol | 123.09 g/mol | 74.55 g/mol | 103.02 g/mol phase | liquid (at STP) | gas (at STP) | | solid (at STP) | melting point | 0 °C | -114.17 °C | | 770 °C | boiling point | 99.9839 °C | -85 °C | | 1420 °C | density | 1 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | | 1.98 g/cm^3 | solubility in water | | miscible | | soluble | surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | odor | odorless | | | odorless |

Units

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