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H2SO4 + O2 + K2Cr2O3 = H2O + Cr2(SO4)3 + KHSO4

Input interpretation

H_2SO_4 sulfuric acid + O_2 oxygen + K2Cr2O3 ⟶ H_2O water + Cr_2(SO_4)_3 chromium sulfate + KHSO_4 potassium bisulfate
H_2SO_4 sulfuric acid + O_2 oxygen + K2Cr2O3 ⟶ H_2O water + Cr_2(SO_4)_3 chromium sulfate + KHSO_4 potassium bisulfate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + O_2 + K2Cr2O3 ⟶ H_2O + Cr_2(SO_4)_3 + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 O_2 + c_3 K2Cr2O3 ⟶ c_4 H_2O + c_5 Cr_2(SO_4)_3 + c_6 KHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Cr: H: | 2 c_1 = 2 c_4 + c_6 O: | 4 c_1 + 2 c_2 + 3 c_3 = c_4 + 12 c_5 + 4 c_6 S: | c_1 = 3 c_5 + c_6 K: | 2 c_3 = c_6 Cr: | 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 = 10 c_2 = 1 c_3 = 2 c_4 = 8 c_5 = 2 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 H_2SO_4 + O_2 + 2 K2Cr2O3 ⟶ 8 H_2O + 2 Cr_2(SO_4)_3 + 4 KHSO_4
Balance the chemical equation algebraically: H_2SO_4 + O_2 + K2Cr2O3 ⟶ H_2O + Cr_2(SO_4)_3 + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 O_2 + c_3 K2Cr2O3 ⟶ c_4 H_2O + c_5 Cr_2(SO_4)_3 + c_6 KHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Cr: H: | 2 c_1 = 2 c_4 + c_6 O: | 4 c_1 + 2 c_2 + 3 c_3 = c_4 + 12 c_5 + 4 c_6 S: | c_1 = 3 c_5 + c_6 K: | 2 c_3 = c_6 Cr: | 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 = 10 c_2 = 1 c_3 = 2 c_4 = 8 c_5 = 2 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 H_2SO_4 + O_2 + 2 K2Cr2O3 ⟶ 8 H_2O + 2 Cr_2(SO_4)_3 + 4 KHSO_4

Structures

+ + K2Cr2O3 ⟶ + +
+ + K2Cr2O3 ⟶ + +

Names

sulfuric acid + oxygen + K2Cr2O3 ⟶ water + chromium sulfate + potassium bisulfate
sulfuric acid + oxygen + K2Cr2O3 ⟶ water + chromium sulfate + potassium bisulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + O_2 + K2Cr2O3 ⟶ H_2O + Cr_2(SO_4)_3 + KHSO_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 H_2SO_4 + O_2 + 2 K2Cr2O3 ⟶ 8 H_2O + 2 Cr_2(SO_4)_3 + 4 KHSO_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 H_2SO_4 | 10 | -10 O_2 | 1 | -1 K2Cr2O3 | 2 | -2 H_2O | 8 | 8 Cr_2(SO_4)_3 | 2 | 2 KHSO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 10 | -10 | ([H2SO4])^(-10) O_2 | 1 | -1 | ([O2])^(-1) K2Cr2O3 | 2 | -2 | ([K2Cr2O3])^(-2) H_2O | 8 | 8 | ([H2O])^8 Cr_2(SO_4)_3 | 2 | 2 | ([Cr2(SO4)3])^2 KHSO_4 | 4 | 4 | ([KHSO4])^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 = ([H2SO4])^(-10) ([O2])^(-1) ([K2Cr2O3])^(-2) ([H2O])^8 ([Cr2(SO4)3])^2 ([KHSO4])^4 = (([H2O])^8 ([Cr2(SO4)3])^2 ([KHSO4])^4)/(([H2SO4])^10 [O2] ([K2Cr2O3])^2)
Construct the equilibrium constant, K, expression for: H_2SO_4 + O_2 + K2Cr2O3 ⟶ H_2O + Cr_2(SO_4)_3 + KHSO_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 H_2SO_4 + O_2 + 2 K2Cr2O3 ⟶ 8 H_2O + 2 Cr_2(SO_4)_3 + 4 KHSO_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 H_2SO_4 | 10 | -10 O_2 | 1 | -1 K2Cr2O3 | 2 | -2 H_2O | 8 | 8 Cr_2(SO_4)_3 | 2 | 2 KHSO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 10 | -10 | ([H2SO4])^(-10) O_2 | 1 | -1 | ([O2])^(-1) K2Cr2O3 | 2 | -2 | ([K2Cr2O3])^(-2) H_2O | 8 | 8 | ([H2O])^8 Cr_2(SO_4)_3 | 2 | 2 | ([Cr2(SO4)3])^2 KHSO_4 | 4 | 4 | ([KHSO4])^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 = ([H2SO4])^(-10) ([O2])^(-1) ([K2Cr2O3])^(-2) ([H2O])^8 ([Cr2(SO4)3])^2 ([KHSO4])^4 = (([H2O])^8 ([Cr2(SO4)3])^2 ([KHSO4])^4)/(([H2SO4])^10 [O2] ([K2Cr2O3])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + O_2 + K2Cr2O3 ⟶ H_2O + Cr_2(SO_4)_3 + KHSO_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 H_2SO_4 + O_2 + 2 K2Cr2O3 ⟶ 8 H_2O + 2 Cr_2(SO_4)_3 + 4 KHSO_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 H_2SO_4 | 10 | -10 O_2 | 1 | -1 K2Cr2O3 | 2 | -2 H_2O | 8 | 8 Cr_2(SO_4)_3 | 2 | 2 KHSO_4 | 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 H_2SO_4 | 10 | -10 | -1/10 (Δ[H2SO4])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) K2Cr2O3 | 2 | -2 | -1/2 (Δ[K2Cr2O3])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) Cr_2(SO_4)_3 | 2 | 2 | 1/2 (Δ[Cr2(SO4)3])/(Δt) KHSO_4 | 4 | 4 | 1/4 (Δ[KHSO4])/(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[H2SO4])/(Δt) = -(Δ[O2])/(Δt) = -1/2 (Δ[K2Cr2O3])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[Cr2(SO4)3])/(Δt) = 1/4 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + O_2 + K2Cr2O3 ⟶ H_2O + Cr_2(SO_4)_3 + KHSO_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 H_2SO_4 + O_2 + 2 K2Cr2O3 ⟶ 8 H_2O + 2 Cr_2(SO_4)_3 + 4 KHSO_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 H_2SO_4 | 10 | -10 O_2 | 1 | -1 K2Cr2O3 | 2 | -2 H_2O | 8 | 8 Cr_2(SO_4)_3 | 2 | 2 KHSO_4 | 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 H_2SO_4 | 10 | -10 | -1/10 (Δ[H2SO4])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) K2Cr2O3 | 2 | -2 | -1/2 (Δ[K2Cr2O3])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) Cr_2(SO_4)_3 | 2 | 2 | 1/2 (Δ[Cr2(SO4)3])/(Δt) KHSO_4 | 4 | 4 | 1/4 (Δ[KHSO4])/(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[H2SO4])/(Δt) = -(Δ[O2])/(Δt) = -1/2 (Δ[K2Cr2O3])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[Cr2(SO4)3])/(Δt) = 1/4 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | oxygen | K2Cr2O3 | water | chromium sulfate | potassium bisulfate formula | H_2SO_4 | O_2 | K2Cr2O3 | H_2O | Cr_2(SO_4)_3 | KHSO_4 Hill formula | H_2O_4S | O_2 | Cr2K2O3 | H_2O | Cr_2O_12S_3 | HKO_4S name | sulfuric acid | oxygen | | water | chromium sulfate | potassium bisulfate IUPAC name | sulfuric acid | molecular oxygen | | water | chromium(+3) cation trisulfate | potassium hydrogen sulfate
| sulfuric acid | oxygen | K2Cr2O3 | water | chromium sulfate | potassium bisulfate formula | H_2SO_4 | O_2 | K2Cr2O3 | H_2O | Cr_2(SO_4)_3 | KHSO_4 Hill formula | H_2O_4S | O_2 | Cr2K2O3 | H_2O | Cr_2O_12S_3 | HKO_4S name | sulfuric acid | oxygen | | water | chromium sulfate | potassium bisulfate IUPAC name | sulfuric acid | molecular oxygen | | water | chromium(+3) cation trisulfate | potassium hydrogen sulfate

Substance properties

| sulfuric acid | oxygen | K2Cr2O3 | water | chromium sulfate | potassium bisulfate molar mass | 98.07 g/mol | 31.998 g/mol | 230.186 g/mol | 18.015 g/mol | 392.2 g/mol | 136.16 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | 10.371 °C | -218 °C | | 0 °C | | 214 °C boiling point | 279.6 °C | -183 °C | | 99.9839 °C | 330 °C | density | 1.8305 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | | 1 g/cm^3 | 1.84 g/cm^3 | 2.32 g/cm^3 solubility in water | very soluble | | | | | surface tension | 0.0735 N/m | 0.01347 N/m | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | odorless | | odorless | odorless |
| sulfuric acid | oxygen | K2Cr2O3 | water | chromium sulfate | potassium bisulfate molar mass | 98.07 g/mol | 31.998 g/mol | 230.186 g/mol | 18.015 g/mol | 392.2 g/mol | 136.16 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | 10.371 °C | -218 °C | | 0 °C | | 214 °C boiling point | 279.6 °C | -183 °C | | 99.9839 °C | 330 °C | density | 1.8305 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | | 1 g/cm^3 | 1.84 g/cm^3 | 2.32 g/cm^3 solubility in water | very soluble | | | | | surface tension | 0.0735 N/m | 0.01347 N/m | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | odorless | | odorless | odorless |

Units

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