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O2 + Cr + HCe2 = H2O + CrCe2

Input interpretation

O_2 oxygen + Cr chromium + HCe2 ⟶ H_2O water + CrCe2
O_2 oxygen + Cr chromium + HCe2 ⟶ H_2O water + CrCe2

Balanced equation

Balance the chemical equation algebraically: O_2 + Cr + HCe2 ⟶ H_2O + CrCe2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 Cr + c_3 HCe2 ⟶ c_4 H_2O + c_5 CrCe2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Cr, H and Ce: O: | 2 c_1 = c_4 Cr: | c_2 = c_5 H: | c_3 = 2 c_4 Ce: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 4 c_4 = 2 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + 4 Cr + 4 HCe2 ⟶ 2 H_2O + 4 CrCe2
Balance the chemical equation algebraically: O_2 + Cr + HCe2 ⟶ H_2O + CrCe2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 Cr + c_3 HCe2 ⟶ c_4 H_2O + c_5 CrCe2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Cr, H and Ce: O: | 2 c_1 = c_4 Cr: | c_2 = c_5 H: | c_3 = 2 c_4 Ce: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 4 c_4 = 2 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + 4 Cr + 4 HCe2 ⟶ 2 H_2O + 4 CrCe2

Structures

+ + HCe2 ⟶ + CrCe2
+ + HCe2 ⟶ + CrCe2

Names

oxygen + chromium + HCe2 ⟶ water + CrCe2
oxygen + chromium + HCe2 ⟶ water + CrCe2

Equilibrium constant

Construct the equilibrium constant, K, expression for: O_2 + Cr + HCe2 ⟶ H_2O + CrCe2 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: O_2 + 4 Cr + 4 HCe2 ⟶ 2 H_2O + 4 CrCe2 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 O_2 | 1 | -1 Cr | 4 | -4 HCe2 | 4 | -4 H_2O | 2 | 2 CrCe2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 1 | -1 | ([O2])^(-1) Cr | 4 | -4 | ([Cr])^(-4) HCe2 | 4 | -4 | ([HCe2])^(-4) H_2O | 2 | 2 | ([H2O])^2 CrCe2 | 4 | 4 | ([CrCe2])^4 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 = ([O2])^(-1) ([Cr])^(-4) ([HCe2])^(-4) ([H2O])^2 ([CrCe2])^4 = (([H2O])^2 ([CrCe2])^4)/([O2] ([Cr])^4 ([HCe2])^4)
Construct the equilibrium constant, K, expression for: O_2 + Cr + HCe2 ⟶ H_2O + CrCe2 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: O_2 + 4 Cr + 4 HCe2 ⟶ 2 H_2O + 4 CrCe2 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 O_2 | 1 | -1 Cr | 4 | -4 HCe2 | 4 | -4 H_2O | 2 | 2 CrCe2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 1 | -1 | ([O2])^(-1) Cr | 4 | -4 | ([Cr])^(-4) HCe2 | 4 | -4 | ([HCe2])^(-4) H_2O | 2 | 2 | ([H2O])^2 CrCe2 | 4 | 4 | ([CrCe2])^4 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 = ([O2])^(-1) ([Cr])^(-4) ([HCe2])^(-4) ([H2O])^2 ([CrCe2])^4 = (([H2O])^2 ([CrCe2])^4)/([O2] ([Cr])^4 ([HCe2])^4)

Rate of reaction

Construct the rate of reaction expression for: O_2 + Cr + HCe2 ⟶ H_2O + CrCe2 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: O_2 + 4 Cr + 4 HCe2 ⟶ 2 H_2O + 4 CrCe2 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 O_2 | 1 | -1 Cr | 4 | -4 HCe2 | 4 | -4 H_2O | 2 | 2 CrCe2 | 4 | 4 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 O_2 | 1 | -1 | -(Δ[O2])/(Δt) Cr | 4 | -4 | -1/4 (Δ[Cr])/(Δt) HCe2 | 4 | -4 | -1/4 (Δ[HCe2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CrCe2 | 4 | 4 | 1/4 (Δ[CrCe2])/(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[O2])/(Δt) = -1/4 (Δ[Cr])/(Δt) = -1/4 (Δ[HCe2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/4 (Δ[CrCe2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: O_2 + Cr + HCe2 ⟶ H_2O + CrCe2 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: O_2 + 4 Cr + 4 HCe2 ⟶ 2 H_2O + 4 CrCe2 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 O_2 | 1 | -1 Cr | 4 | -4 HCe2 | 4 | -4 H_2O | 2 | 2 CrCe2 | 4 | 4 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 O_2 | 1 | -1 | -(Δ[O2])/(Δt) Cr | 4 | -4 | -1/4 (Δ[Cr])/(Δt) HCe2 | 4 | -4 | -1/4 (Δ[HCe2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CrCe2 | 4 | 4 | 1/4 (Δ[CrCe2])/(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[O2])/(Δt) = -1/4 (Δ[Cr])/(Δt) = -1/4 (Δ[HCe2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/4 (Δ[CrCe2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| oxygen | chromium | HCe2 | water | CrCe2 formula | O_2 | Cr | HCe2 | H_2O | CrCe2 Hill formula | O_2 | Cr | HCe2 | H_2O | Ce2Cr name | oxygen | chromium | | water | IUPAC name | molecular oxygen | chromium | | water |
| oxygen | chromium | HCe2 | water | CrCe2 formula | O_2 | Cr | HCe2 | H_2O | CrCe2 Hill formula | O_2 | Cr | HCe2 | H_2O | Ce2Cr name | oxygen | chromium | | water | IUPAC name | molecular oxygen | chromium | | water |

Substance properties

| oxygen | chromium | HCe2 | water | CrCe2 molar mass | 31.998 g/mol | 51.9961 g/mol | 281.24 g/mol | 18.015 g/mol | 332.228 g/mol phase | gas (at STP) | solid (at STP) | | liquid (at STP) | melting point | -218 °C | 1857 °C | | 0 °C | boiling point | -183 °C | 2672 °C | | 99.9839 °C | density | 0.001429 g/cm^3 (at 0 °C) | 7.14 g/cm^3 | | 1 g/cm^3 | solubility in water | | insoluble | | | surface tension | 0.01347 N/m | | | 0.0728 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | odorless | | odorless |
| oxygen | chromium | HCe2 | water | CrCe2 molar mass | 31.998 g/mol | 51.9961 g/mol | 281.24 g/mol | 18.015 g/mol | 332.228 g/mol phase | gas (at STP) | solid (at STP) | | liquid (at STP) | melting point | -218 °C | 1857 °C | | 0 °C | boiling point | -183 °C | 2672 °C | | 99.9839 °C | density | 0.001429 g/cm^3 (at 0 °C) | 7.14 g/cm^3 | | 1 g/cm^3 | solubility in water | | insoluble | | | surface tension | 0.01347 N/m | | | 0.0728 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | odorless | | odorless |

Units

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