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H2O + NH3 + Cr2(SO4)3 = (NH4)2SO4 + Cr(OH)3

Input interpretation

H_2O water + NH_3 ammonia + Cr_2(SO_4)_3 chromium sulfate ⟶ (NH_4)_2SO_4 ammonium sulfate + Cr(OH)3
H_2O water + NH_3 ammonia + Cr_2(SO_4)_3 chromium sulfate ⟶ (NH_4)_2SO_4 ammonium sulfate + Cr(OH)3

Balanced equation

Balance the chemical equation algebraically: H_2O + NH_3 + Cr_2(SO_4)_3 ⟶ (NH_4)_2SO_4 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 Cr_2(SO_4)_3 ⟶ c_4 (NH_4)_2SO_4 + 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, N, Cr and S: H: | 2 c_1 + 3 c_2 = 8 c_4 + 3 c_5 O: | c_1 + 12 c_3 = 4 c_4 + 3 c_5 N: | c_2 = 2 c_4 Cr: | 2 c_3 = c_5 S: | 3 c_3 = c_4 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 6 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 6 NH_3 + Cr_2(SO_4)_3 ⟶ 3 (NH_4)_2SO_4 + 2 Cr(OH)3
Balance the chemical equation algebraically: H_2O + NH_3 + Cr_2(SO_4)_3 ⟶ (NH_4)_2SO_4 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 Cr_2(SO_4)_3 ⟶ c_4 (NH_4)_2SO_4 + 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, N, Cr and S: H: | 2 c_1 + 3 c_2 = 8 c_4 + 3 c_5 O: | c_1 + 12 c_3 = 4 c_4 + 3 c_5 N: | c_2 = 2 c_4 Cr: | 2 c_3 = c_5 S: | 3 c_3 = c_4 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 6 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 6 NH_3 + Cr_2(SO_4)_3 ⟶ 3 (NH_4)_2SO_4 + 2 Cr(OH)3

Structures

+ + ⟶ + Cr(OH)3
+ + ⟶ + Cr(OH)3

Names

water + ammonia + chromium sulfate ⟶ ammonium sulfate + Cr(OH)3
water + ammonia + chromium sulfate ⟶ ammonium sulfate + Cr(OH)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + NH_3 + Cr_2(SO_4)_3 ⟶ (NH_4)_2SO_4 + 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: 6 H_2O + 6 NH_3 + Cr_2(SO_4)_3 ⟶ 3 (NH_4)_2SO_4 + 2 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 | 6 | -6 NH_3 | 6 | -6 Cr_2(SO_4)_3 | 1 | -1 (NH_4)_2SO_4 | 3 | 3 Cr(OH)3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) NH_3 | 6 | -6 | ([NH3])^(-6) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) (NH_4)_2SO_4 | 3 | 3 | ([(NH4)2SO4])^3 Cr(OH)3 | 2 | 2 | ([Cr(OH)3])^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 = ([H2O])^(-6) ([NH3])^(-6) ([Cr2(SO4)3])^(-1) ([(NH4)2SO4])^3 ([Cr(OH)3])^2 = (([(NH4)2SO4])^3 ([Cr(OH)3])^2)/(([H2O])^6 ([NH3])^6 [Cr2(SO4)3])
Construct the equilibrium constant, K, expression for: H_2O + NH_3 + Cr_2(SO_4)_3 ⟶ (NH_4)_2SO_4 + 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: 6 H_2O + 6 NH_3 + Cr_2(SO_4)_3 ⟶ 3 (NH_4)_2SO_4 + 2 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 | 6 | -6 NH_3 | 6 | -6 Cr_2(SO_4)_3 | 1 | -1 (NH_4)_2SO_4 | 3 | 3 Cr(OH)3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) NH_3 | 6 | -6 | ([NH3])^(-6) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) (NH_4)_2SO_4 | 3 | 3 | ([(NH4)2SO4])^3 Cr(OH)3 | 2 | 2 | ([Cr(OH)3])^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 = ([H2O])^(-6) ([NH3])^(-6) ([Cr2(SO4)3])^(-1) ([(NH4)2SO4])^3 ([Cr(OH)3])^2 = (([(NH4)2SO4])^3 ([Cr(OH)3])^2)/(([H2O])^6 ([NH3])^6 [Cr2(SO4)3])

Rate of reaction

Construct the rate of reaction expression for: H_2O + NH_3 + Cr_2(SO_4)_3 ⟶ (NH_4)_2SO_4 + 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: 6 H_2O + 6 NH_3 + Cr_2(SO_4)_3 ⟶ 3 (NH_4)_2SO_4 + 2 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 | 6 | -6 NH_3 | 6 | -6 Cr_2(SO_4)_3 | 1 | -1 (NH_4)_2SO_4 | 3 | 3 Cr(OH)3 | 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_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) NH_3 | 6 | -6 | -1/6 (Δ[NH3])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) (NH_4)_2SO_4 | 3 | 3 | 1/3 (Δ[(NH4)2SO4])/(Δt) Cr(OH)3 | 2 | 2 | 1/2 (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 = -1/6 (Δ[H2O])/(Δt) = -1/6 (Δ[NH3])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[(NH4)2SO4])/(Δt) = 1/2 (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 + NH_3 + Cr_2(SO_4)_3 ⟶ (NH_4)_2SO_4 + 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: 6 H_2O + 6 NH_3 + Cr_2(SO_4)_3 ⟶ 3 (NH_4)_2SO_4 + 2 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 | 6 | -6 NH_3 | 6 | -6 Cr_2(SO_4)_3 | 1 | -1 (NH_4)_2SO_4 | 3 | 3 Cr(OH)3 | 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_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) NH_3 | 6 | -6 | -1/6 (Δ[NH3])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) (NH_4)_2SO_4 | 3 | 3 | 1/3 (Δ[(NH4)2SO4])/(Δt) Cr(OH)3 | 2 | 2 | 1/2 (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 = -1/6 (Δ[H2O])/(Δt) = -1/6 (Δ[NH3])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[(NH4)2SO4])/(Δt) = 1/2 (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | ammonia | chromium sulfate | ammonium sulfate | Cr(OH)3 formula | H_2O | NH_3 | Cr_2(SO_4)_3 | (NH_4)_2SO_4 | Cr(OH)3 Hill formula | H_2O | H_3N | Cr_2O_12S_3 | H_8N_2O_4S | H3CrO3 name | water | ammonia | chromium sulfate | ammonium sulfate | IUPAC name | water | ammonia | chromium(+3) cation trisulfate | |
| water | ammonia | chromium sulfate | ammonium sulfate | Cr(OH)3 formula | H_2O | NH_3 | Cr_2(SO_4)_3 | (NH_4)_2SO_4 | Cr(OH)3 Hill formula | H_2O | H_3N | Cr_2O_12S_3 | H_8N_2O_4S | H3CrO3 name | water | ammonia | chromium sulfate | ammonium sulfate | IUPAC name | water | ammonia | chromium(+3) cation trisulfate | |

Substance properties

| water | ammonia | chromium sulfate | ammonium sulfate | Cr(OH)3 molar mass | 18.015 g/mol | 17.031 g/mol | 392.2 g/mol | 132.1 g/mol | 103.02 g/mol phase | liquid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | melting point | 0 °C | -77.73 °C | | 280 °C | boiling point | 99.9839 °C | -33.33 °C | 330 °C | | density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 1.84 g/cm^3 | 1.77 g/cm^3 | surface tension | 0.0728 N/m | 0.0234 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | | odor | odorless | | odorless | odorless |
| water | ammonia | chromium sulfate | ammonium sulfate | Cr(OH)3 molar mass | 18.015 g/mol | 17.031 g/mol | 392.2 g/mol | 132.1 g/mol | 103.02 g/mol phase | liquid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | melting point | 0 °C | -77.73 °C | | 280 °C | boiling point | 99.9839 °C | -33.33 °C | 330 °C | | density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 1.84 g/cm^3 | 1.77 g/cm^3 | surface tension | 0.0728 N/m | 0.0234 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | | odor | odorless | | odorless | odorless |

Units

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