Input interpretation
![H_2 hydrogen + Cr_2O_3 chromium(III) oxide ⟶ H_2O water + Cr chromium](../image_source/405b09eb867d96657b3219183678d8d0.png)
H_2 hydrogen + Cr_2O_3 chromium(III) oxide ⟶ H_2O water + Cr chromium
Balanced equation
![Balance the chemical equation algebraically: H_2 + Cr_2O_3 ⟶ H_2O + Cr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 Cr_2O_3 ⟶ c_3 H_2O + c_4 Cr Set the number of atoms in the reactants equal to the number of atoms in the products for H, Cr and O: H: | 2 c_1 = 2 c_3 Cr: | 2 c_2 = c_4 O: | 3 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 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2 + Cr_2O_3 ⟶ 3 H_2O + 2 Cr](../image_source/ecc24160914372c8e7dff0aef562bd3d.png)
Balance the chemical equation algebraically: H_2 + Cr_2O_3 ⟶ H_2O + Cr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 Cr_2O_3 ⟶ c_3 H_2O + c_4 Cr Set the number of atoms in the reactants equal to the number of atoms in the products for H, Cr and O: H: | 2 c_1 = 2 c_3 Cr: | 2 c_2 = c_4 O: | 3 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 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2 + Cr_2O_3 ⟶ 3 H_2O + 2 Cr
Structures
![+ ⟶ +](../image_source/6e852a1f7b9090dbdbb38eb9ca6a494e.png)
+ ⟶ +
Names
![hydrogen + chromium(III) oxide ⟶ water + chromium](../image_source/f6275bce9e8815dfc6beba4961987866.png)
hydrogen + chromium(III) oxide ⟶ water + chromium
Reaction thermodynamics
Enthalpy
![| hydrogen | chromium(III) oxide | water | chromium molecular enthalpy | 0 kJ/mol | -1140 kJ/mol | -285.8 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -1140 kJ/mol | -857.5 kJ/mol | 0 kJ/mol | H_initial = -1140 kJ/mol | | H_final = -857.5 kJ/mol | ΔH_rxn^0 | -857.5 kJ/mol - -1140 kJ/mol = 282.2 kJ/mol (endothermic) | | |](../image_source/a5d52c39cddb487522f954ab0f6821f5.png)
| hydrogen | chromium(III) oxide | water | chromium molecular enthalpy | 0 kJ/mol | -1140 kJ/mol | -285.8 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -1140 kJ/mol | -857.5 kJ/mol | 0 kJ/mol | H_initial = -1140 kJ/mol | | H_final = -857.5 kJ/mol | ΔH_rxn^0 | -857.5 kJ/mol - -1140 kJ/mol = 282.2 kJ/mol (endothermic) | | |
Entropy
![| hydrogen | chromium(III) oxide | water | chromium molecular entropy | 115 J/(mol K) | 81 J/(mol K) | 69.91 J/(mol K) | 24 J/(mol K) total entropy | 345 J/(mol K) | 81 J/(mol K) | 209.7 J/(mol K) | 48 J/(mol K) | S_initial = 426 J/(mol K) | | S_final = 257.7 J/(mol K) | ΔS_rxn^0 | 257.7 J/(mol K) - 426 J/(mol K) = -168.3 J/(mol K) (exoentropic) | | |](../image_source/def45cbb05d044ae9d9ffbeb576148e6.png)
| hydrogen | chromium(III) oxide | water | chromium molecular entropy | 115 J/(mol K) | 81 J/(mol K) | 69.91 J/(mol K) | 24 J/(mol K) total entropy | 345 J/(mol K) | 81 J/(mol K) | 209.7 J/(mol K) | 48 J/(mol K) | S_initial = 426 J/(mol K) | | S_final = 257.7 J/(mol K) | ΔS_rxn^0 | 257.7 J/(mol K) - 426 J/(mol K) = -168.3 J/(mol K) (exoentropic) | | |
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2 + Cr_2O_3 ⟶ H_2O + Cr 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 H_2 + Cr_2O_3 ⟶ 3 H_2O + 2 Cr 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_2 | 3 | -3 Cr_2O_3 | 1 | -1 H_2O | 3 | 3 Cr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 3 | -3 | ([H2])^(-3) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) H_2O | 3 | 3 | ([H2O])^3 Cr | 2 | 2 | ([Cr])^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 = ([H2])^(-3) ([Cr2O3])^(-1) ([H2O])^3 ([Cr])^2 = (([H2O])^3 ([Cr])^2)/(([H2])^3 [Cr2O3])](../image_source/80c2d8d8389a783ba4f5830b48539655.png)
Construct the equilibrium constant, K, expression for: H_2 + Cr_2O_3 ⟶ H_2O + Cr 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 H_2 + Cr_2O_3 ⟶ 3 H_2O + 2 Cr 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_2 | 3 | -3 Cr_2O_3 | 1 | -1 H_2O | 3 | 3 Cr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 3 | -3 | ([H2])^(-3) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) H_2O | 3 | 3 | ([H2O])^3 Cr | 2 | 2 | ([Cr])^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 = ([H2])^(-3) ([Cr2O3])^(-1) ([H2O])^3 ([Cr])^2 = (([H2O])^3 ([Cr])^2)/(([H2])^3 [Cr2O3])
Rate of reaction
![Construct the rate of reaction expression for: H_2 + Cr_2O_3 ⟶ H_2O + Cr 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 H_2 + Cr_2O_3 ⟶ 3 H_2O + 2 Cr 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_2 | 3 | -3 Cr_2O_3 | 1 | -1 H_2O | 3 | 3 Cr | 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 H_2 | 3 | -3 | -1/3 (Δ[H2])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Cr | 2 | 2 | 1/2 (Δ[Cr])/(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[H2])/(Δt) = -(Δ[Cr2O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[Cr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/afa9463dc0f69b0b925bb9000b97f6f2.png)
Construct the rate of reaction expression for: H_2 + Cr_2O_3 ⟶ H_2O + Cr 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 H_2 + Cr_2O_3 ⟶ 3 H_2O + 2 Cr 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_2 | 3 | -3 Cr_2O_3 | 1 | -1 H_2O | 3 | 3 Cr | 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 H_2 | 3 | -3 | -1/3 (Δ[H2])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Cr | 2 | 2 | 1/2 (Δ[Cr])/(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[H2])/(Δt) = -(Δ[Cr2O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[Cr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| hydrogen | chromium(III) oxide | water | chromium formula | H_2 | Cr_2O_3 | H_2O | Cr name | hydrogen | chromium(III) oxide | water | chromium IUPAC name | molecular hydrogen | | water | chromium](../image_source/001cfb06dbdd8cf2d83df18a0d339bd7.png)
| hydrogen | chromium(III) oxide | water | chromium formula | H_2 | Cr_2O_3 | H_2O | Cr name | hydrogen | chromium(III) oxide | water | chromium IUPAC name | molecular hydrogen | | water | chromium
Substance properties
![| hydrogen | chromium(III) oxide | water | chromium molar mass | 2.016 g/mol | 151.99 g/mol | 18.015 g/mol | 51.9961 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -259.2 °C | 2435 °C | 0 °C | 1857 °C boiling point | -252.8 °C | 4000 °C | 99.9839 °C | 2672 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 4.8 g/cm^3 | 1 g/cm^3 | 7.14 g/cm^3 solubility in water | | insoluble | | insoluble surface tension | | | 0.0728 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless | odorless](../image_source/9c6960687ebb5be2109149b4bc3abc26.png)
| hydrogen | chromium(III) oxide | water | chromium molar mass | 2.016 g/mol | 151.99 g/mol | 18.015 g/mol | 51.9961 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -259.2 °C | 2435 °C | 0 °C | 1857 °C boiling point | -252.8 °C | 4000 °C | 99.9839 °C | 2672 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 4.8 g/cm^3 | 1 g/cm^3 | 7.14 g/cm^3 solubility in water | | insoluble | | insoluble surface tension | | | 0.0728 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless | odorless
Units