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NaOH + Cr2O3 + Ca(ClO)Cl = H2O + CaCl2 + Na2CrO4

Input interpretation

NaOH sodium hydroxide + Cr_2O_3 chromium(III) oxide + CaClOCl ⟶ H_2O water + CaCl_2 calcium chloride + Na_2CrO_4 sodium chromate
NaOH sodium hydroxide + Cr_2O_3 chromium(III) oxide + CaClOCl ⟶ H_2O water + CaCl_2 calcium chloride + Na_2CrO_4 sodium chromate

Balanced equation

Balance the chemical equation algebraically: NaOH + Cr_2O_3 + CaClOCl ⟶ H_2O + CaCl_2 + Na_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Cr_2O_3 + c_3 CaClOCl ⟶ c_4 H_2O + c_5 CaCl_2 + c_6 Na_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Cr, Ca and Cl: H: | c_1 = 2 c_4 Na: | c_1 = 2 c_6 O: | c_1 + 3 c_2 + c_3 = c_4 + 4 c_6 Cr: | 2 c_2 = c_6 Ca: | c_3 = c_5 Cl: | 2 c_3 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 3 c_4 = 2 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 NaOH + Cr_2O_3 + 3 CaClOCl ⟶ 2 H_2O + 3 CaCl_2 + 2 Na_2CrO_4
Balance the chemical equation algebraically: NaOH + Cr_2O_3 + CaClOCl ⟶ H_2O + CaCl_2 + Na_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Cr_2O_3 + c_3 CaClOCl ⟶ c_4 H_2O + c_5 CaCl_2 + c_6 Na_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Cr, Ca and Cl: H: | c_1 = 2 c_4 Na: | c_1 = 2 c_6 O: | c_1 + 3 c_2 + c_3 = c_4 + 4 c_6 Cr: | 2 c_2 = c_6 Ca: | c_3 = c_5 Cl: | 2 c_3 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 3 c_4 = 2 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 NaOH + Cr_2O_3 + 3 CaClOCl ⟶ 2 H_2O + 3 CaCl_2 + 2 Na_2CrO_4

Structures

+ + CaClOCl ⟶ + +
+ + CaClOCl ⟶ + +

Names

sodium hydroxide + chromium(III) oxide + CaClOCl ⟶ water + calcium chloride + sodium chromate
sodium hydroxide + chromium(III) oxide + CaClOCl ⟶ water + calcium chloride + sodium chromate

Equilibrium constant

Construct the equilibrium constant, K, expression for: NaOH + Cr_2O_3 + CaClOCl ⟶ H_2O + CaCl_2 + Na_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: 4 NaOH + Cr_2O_3 + 3 CaClOCl ⟶ 2 H_2O + 3 CaCl_2 + 2 Na_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 NaOH | 4 | -4 Cr_2O_3 | 1 | -1 CaClOCl | 3 | -3 H_2O | 2 | 2 CaCl_2 | 3 | 3 Na_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 NaOH | 4 | -4 | ([NaOH])^(-4) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) CaClOCl | 3 | -3 | ([CaClOCl])^(-3) H_2O | 2 | 2 | ([H2O])^2 CaCl_2 | 3 | 3 | ([CaCl2])^3 Na_2CrO_4 | 2 | 2 | ([Na2CrO4])^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 = ([NaOH])^(-4) ([Cr2O3])^(-1) ([CaClOCl])^(-3) ([H2O])^2 ([CaCl2])^3 ([Na2CrO4])^2 = (([H2O])^2 ([CaCl2])^3 ([Na2CrO4])^2)/(([NaOH])^4 [Cr2O3] ([CaClOCl])^3)
Construct the equilibrium constant, K, expression for: NaOH + Cr_2O_3 + CaClOCl ⟶ H_2O + CaCl_2 + Na_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: 4 NaOH + Cr_2O_3 + 3 CaClOCl ⟶ 2 H_2O + 3 CaCl_2 + 2 Na_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 NaOH | 4 | -4 Cr_2O_3 | 1 | -1 CaClOCl | 3 | -3 H_2O | 2 | 2 CaCl_2 | 3 | 3 Na_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 NaOH | 4 | -4 | ([NaOH])^(-4) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) CaClOCl | 3 | -3 | ([CaClOCl])^(-3) H_2O | 2 | 2 | ([H2O])^2 CaCl_2 | 3 | 3 | ([CaCl2])^3 Na_2CrO_4 | 2 | 2 | ([Na2CrO4])^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 = ([NaOH])^(-4) ([Cr2O3])^(-1) ([CaClOCl])^(-3) ([H2O])^2 ([CaCl2])^3 ([Na2CrO4])^2 = (([H2O])^2 ([CaCl2])^3 ([Na2CrO4])^2)/(([NaOH])^4 [Cr2O3] ([CaClOCl])^3)

Rate of reaction

Construct the rate of reaction expression for: NaOH + Cr_2O_3 + CaClOCl ⟶ H_2O + CaCl_2 + Na_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: 4 NaOH + Cr_2O_3 + 3 CaClOCl ⟶ 2 H_2O + 3 CaCl_2 + 2 Na_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 NaOH | 4 | -4 Cr_2O_3 | 1 | -1 CaClOCl | 3 | -3 H_2O | 2 | 2 CaCl_2 | 3 | 3 Na_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 NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) CaClOCl | 3 | -3 | -1/3 (Δ[CaClOCl])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CaCl_2 | 3 | 3 | 1/3 (Δ[CaCl2])/(Δt) Na_2CrO_4 | 2 | 2 | 1/2 (Δ[Na2CrO4])/(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 = -1/4 (Δ[NaOH])/(Δt) = -(Δ[Cr2O3])/(Δt) = -1/3 (Δ[CaClOCl])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/3 (Δ[CaCl2])/(Δt) = 1/2 (Δ[Na2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: NaOH + Cr_2O_3 + CaClOCl ⟶ H_2O + CaCl_2 + Na_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: 4 NaOH + Cr_2O_3 + 3 CaClOCl ⟶ 2 H_2O + 3 CaCl_2 + 2 Na_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 NaOH | 4 | -4 Cr_2O_3 | 1 | -1 CaClOCl | 3 | -3 H_2O | 2 | 2 CaCl_2 | 3 | 3 Na_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 NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) CaClOCl | 3 | -3 | -1/3 (Δ[CaClOCl])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CaCl_2 | 3 | 3 | 1/3 (Δ[CaCl2])/(Δt) Na_2CrO_4 | 2 | 2 | 1/2 (Δ[Na2CrO4])/(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 = -1/4 (Δ[NaOH])/(Δt) = -(Δ[Cr2O3])/(Δt) = -1/3 (Δ[CaClOCl])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/3 (Δ[CaCl2])/(Δt) = 1/2 (Δ[Na2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sodium hydroxide | chromium(III) oxide | CaClOCl | water | calcium chloride | sodium chromate formula | NaOH | Cr_2O_3 | CaClOCl | H_2O | CaCl_2 | Na_2CrO_4 Hill formula | HNaO | Cr_2O_3 | CaCl2O | H_2O | CaCl_2 | CrNa_2O_4 name | sodium hydroxide | chromium(III) oxide | | water | calcium chloride | sodium chromate IUPAC name | sodium hydroxide | | | water | calcium dichloride | disodium dioxido(dioxo)chromium
| sodium hydroxide | chromium(III) oxide | CaClOCl | water | calcium chloride | sodium chromate formula | NaOH | Cr_2O_3 | CaClOCl | H_2O | CaCl_2 | Na_2CrO_4 Hill formula | HNaO | Cr_2O_3 | CaCl2O | H_2O | CaCl_2 | CrNa_2O_4 name | sodium hydroxide | chromium(III) oxide | | water | calcium chloride | sodium chromate IUPAC name | sodium hydroxide | | | water | calcium dichloride | disodium dioxido(dioxo)chromium

Substance properties

| sodium hydroxide | chromium(III) oxide | CaClOCl | water | calcium chloride | sodium chromate molar mass | 39.997 g/mol | 151.99 g/mol | 127 g/mol | 18.015 g/mol | 111 g/mol | 161.97 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 323 °C | 2435 °C | | 0 °C | 772 °C | 780 °C boiling point | 1390 °C | 4000 °C | | 99.9839 °C | | density | 2.13 g/cm^3 | 4.8 g/cm^3 | | 1 g/cm^3 | 2.15 g/cm^3 | 2.698 g/cm^3 solubility in water | soluble | insoluble | | | soluble | surface tension | 0.07435 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | |
| sodium hydroxide | chromium(III) oxide | CaClOCl | water | calcium chloride | sodium chromate molar mass | 39.997 g/mol | 151.99 g/mol | 127 g/mol | 18.015 g/mol | 111 g/mol | 161.97 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 323 °C | 2435 °C | | 0 °C | 772 °C | 780 °C boiling point | 1390 °C | 4000 °C | | 99.9839 °C | | density | 2.13 g/cm^3 | 4.8 g/cm^3 | | 1 g/cm^3 | 2.15 g/cm^3 | 2.698 g/cm^3 solubility in water | soluble | insoluble | | | soluble | surface tension | 0.07435 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | |

Units

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