Input interpretation
KOH potassium hydroxide + CrCl_3 chromic chloride + KClO ⟶ H_2O water + KCl potassium chloride + K_2CrO_4 potassium chromate
Balanced equation
Balance the chemical equation algebraically: KOH + CrCl_3 + KClO ⟶ H_2O + KCl + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 CrCl_3 + c_3 KClO ⟶ c_4 H_2O + c_5 KCl + c_6 K_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cl and Cr: H: | c_1 = 2 c_4 K: | c_1 + c_3 = c_5 + 2 c_6 O: | c_1 + c_3 = c_4 + 4 c_6 Cl: | 3 c_2 + c_3 = c_5 Cr: | c_2 = c_6 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 = 5 c_2 = 1 c_3 = 3/2 c_4 = 5/2 c_5 = 9/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 10 c_2 = 2 c_3 = 3 c_4 = 5 c_5 = 9 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 KOH + 2 CrCl_3 + 3 KClO ⟶ 5 H_2O + 9 KCl + 2 K_2CrO_4
Structures
+ + KClO ⟶ + +
Names
potassium hydroxide + chromic chloride + KClO ⟶ water + potassium chloride + potassium chromate
Equilibrium constant
Construct the equilibrium constant, K, expression for: KOH + CrCl_3 + KClO ⟶ H_2O + KCl + K_2CrO_4 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: 10 KOH + 2 CrCl_3 + 3 KClO ⟶ 5 H_2O + 9 KCl + 2 K_2CrO_4 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 | 10 | -10 CrCl_3 | 2 | -2 KClO | 3 | -3 H_2O | 5 | 5 KCl | 9 | 9 K_2CrO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 10 | -10 | ([KOH])^(-10) CrCl_3 | 2 | -2 | ([CrCl3])^(-2) KClO | 3 | -3 | ([KClO])^(-3) H_2O | 5 | 5 | ([H2O])^5 KCl | 9 | 9 | ([KCl])^9 K_2CrO_4 | 2 | 2 | ([K2CrO4])^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])^(-10) ([CrCl3])^(-2) ([KClO])^(-3) ([H2O])^5 ([KCl])^9 ([K2CrO4])^2 = (([H2O])^5 ([KCl])^9 ([K2CrO4])^2)/(([KOH])^10 ([CrCl3])^2 ([KClO])^3)
Rate of reaction
Construct the rate of reaction expression for: KOH + CrCl_3 + KClO ⟶ H_2O + KCl + K_2CrO_4 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: 10 KOH + 2 CrCl_3 + 3 KClO ⟶ 5 H_2O + 9 KCl + 2 K_2CrO_4 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 | 10 | -10 CrCl_3 | 2 | -2 KClO | 3 | -3 H_2O | 5 | 5 KCl | 9 | 9 K_2CrO_4 | 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 | 10 | -10 | -1/10 (Δ[KOH])/(Δt) CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) KClO | 3 | -3 | -1/3 (Δ[KClO])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) KCl | 9 | 9 | 1/9 (Δ[KCl])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(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 = -1/10 (Δ[KOH])/(Δt) = -1/2 (Δ[CrCl3])/(Δt) = -1/3 (Δ[KClO])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/9 (Δ[KCl])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| potassium hydroxide | chromic chloride | KClO | water | potassium chloride | potassium chromate formula | KOH | CrCl_3 | KClO | H_2O | KCl | K_2CrO_4 Hill formula | HKO | Cl_3Cr | ClKO | H_2O | ClK | CrK_2O_4 name | potassium hydroxide | chromic chloride | | water | potassium chloride | potassium chromate IUPAC name | potassium hydroxide | trichlorochromium | | water | potassium chloride | dipotassium dioxido-dioxochromium
Substance properties
| potassium hydroxide | chromic chloride | KClO | water | potassium chloride | potassium chromate molar mass | 56.105 g/mol | 158.3 g/mol | 90.55 g/mol | 18.015 g/mol | 74.55 g/mol | 194.19 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 1152 °C | | 0 °C | 770 °C | 971 °C boiling point | 1327 °C | | | 99.9839 °C | 1420 °C | density | 2.044 g/cm^3 | 2.87 g/cm^3 | | 1 g/cm^3 | 1.98 g/cm^3 | 2.73 g/cm^3 solubility in water | soluble | slightly soluble | | | 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