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H2SO4 + H3CrO8 = H2O + O2 + Cr(SO4)3

Input interpretation

H_2SO_4 sulfuric acid + H3CrO8 ⟶ H_2O water + O_2 oxygen + Cr(SO4)3
H_2SO_4 sulfuric acid + H3CrO8 ⟶ H_2O water + O_2 oxygen + Cr(SO4)3

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + H3CrO8 ⟶ H_2O + O_2 + Cr(SO4)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 H3CrO8 ⟶ c_3 H_2O + c_4 O_2 + c_5 Cr(SO4)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cr: H: | 2 c_1 + 3 c_2 = 2 c_3 O: | 4 c_1 + 8 c_2 = c_3 + 2 c_4 + 12 c_5 S: | c_1 = 3 c_5 Cr: | c_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 = 3 c_2 = 1 c_3 = 9/2 c_4 = 7/4 c_5 = 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 4 c_3 = 18 c_4 = 7 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2SO_4 + 4 H3CrO8 ⟶ 18 H_2O + 7 O_2 + 4 Cr(SO4)3
Balance the chemical equation algebraically: H_2SO_4 + H3CrO8 ⟶ H_2O + O_2 + Cr(SO4)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 H3CrO8 ⟶ c_3 H_2O + c_4 O_2 + c_5 Cr(SO4)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cr: H: | 2 c_1 + 3 c_2 = 2 c_3 O: | 4 c_1 + 8 c_2 = c_3 + 2 c_4 + 12 c_5 S: | c_1 = 3 c_5 Cr: | c_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 = 3 c_2 = 1 c_3 = 9/2 c_4 = 7/4 c_5 = 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 4 c_3 = 18 c_4 = 7 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2SO_4 + 4 H3CrO8 ⟶ 18 H_2O + 7 O_2 + 4 Cr(SO4)3

Structures

+ H3CrO8 ⟶ + + Cr(SO4)3
+ H3CrO8 ⟶ + + Cr(SO4)3

Names

sulfuric acid + H3CrO8 ⟶ water + oxygen + Cr(SO4)3
sulfuric acid + H3CrO8 ⟶ water + oxygen + Cr(SO4)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + H3CrO8 ⟶ H_2O + O_2 + Cr(SO4)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: 12 H_2SO_4 + 4 H3CrO8 ⟶ 18 H_2O + 7 O_2 + 4 Cr(SO4)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_2SO_4 | 12 | -12 H3CrO8 | 4 | -4 H_2O | 18 | 18 O_2 | 7 | 7 Cr(SO4)3 | 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 | 12 | -12 | ([H2SO4])^(-12) H3CrO8 | 4 | -4 | ([H3CrO8])^(-4) H_2O | 18 | 18 | ([H2O])^18 O_2 | 7 | 7 | ([O2])^7 Cr(SO4)3 | 4 | 4 | ([Cr(SO4)3])^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])^(-12) ([H3CrO8])^(-4) ([H2O])^18 ([O2])^7 ([Cr(SO4)3])^4 = (([H2O])^18 ([O2])^7 ([Cr(SO4)3])^4)/(([H2SO4])^12 ([H3CrO8])^4)
Construct the equilibrium constant, K, expression for: H_2SO_4 + H3CrO8 ⟶ H_2O + O_2 + Cr(SO4)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: 12 H_2SO_4 + 4 H3CrO8 ⟶ 18 H_2O + 7 O_2 + 4 Cr(SO4)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_2SO_4 | 12 | -12 H3CrO8 | 4 | -4 H_2O | 18 | 18 O_2 | 7 | 7 Cr(SO4)3 | 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 | 12 | -12 | ([H2SO4])^(-12) H3CrO8 | 4 | -4 | ([H3CrO8])^(-4) H_2O | 18 | 18 | ([H2O])^18 O_2 | 7 | 7 | ([O2])^7 Cr(SO4)3 | 4 | 4 | ([Cr(SO4)3])^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])^(-12) ([H3CrO8])^(-4) ([H2O])^18 ([O2])^7 ([Cr(SO4)3])^4 = (([H2O])^18 ([O2])^7 ([Cr(SO4)3])^4)/(([H2SO4])^12 ([H3CrO8])^4)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + H3CrO8 ⟶ H_2O + O_2 + Cr(SO4)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: 12 H_2SO_4 + 4 H3CrO8 ⟶ 18 H_2O + 7 O_2 + 4 Cr(SO4)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_2SO_4 | 12 | -12 H3CrO8 | 4 | -4 H_2O | 18 | 18 O_2 | 7 | 7 Cr(SO4)3 | 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 | 12 | -12 | -1/12 (Δ[H2SO4])/(Δt) H3CrO8 | 4 | -4 | -1/4 (Δ[H3CrO8])/(Δt) H_2O | 18 | 18 | 1/18 (Δ[H2O])/(Δt) O_2 | 7 | 7 | 1/7 (Δ[O2])/(Δt) Cr(SO4)3 | 4 | 4 | 1/4 (Δ[Cr(SO4)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 = -1/12 (Δ[H2SO4])/(Δt) = -1/4 (Δ[H3CrO8])/(Δt) = 1/18 (Δ[H2O])/(Δt) = 1/7 (Δ[O2])/(Δt) = 1/4 (Δ[Cr(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + H3CrO8 ⟶ H_2O + O_2 + Cr(SO4)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: 12 H_2SO_4 + 4 H3CrO8 ⟶ 18 H_2O + 7 O_2 + 4 Cr(SO4)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_2SO_4 | 12 | -12 H3CrO8 | 4 | -4 H_2O | 18 | 18 O_2 | 7 | 7 Cr(SO4)3 | 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 | 12 | -12 | -1/12 (Δ[H2SO4])/(Δt) H3CrO8 | 4 | -4 | -1/4 (Δ[H3CrO8])/(Δt) H_2O | 18 | 18 | 1/18 (Δ[H2O])/(Δt) O_2 | 7 | 7 | 1/7 (Δ[O2])/(Δt) Cr(SO4)3 | 4 | 4 | 1/4 (Δ[Cr(SO4)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 = -1/12 (Δ[H2SO4])/(Δt) = -1/4 (Δ[H3CrO8])/(Δt) = 1/18 (Δ[H2O])/(Δt) = 1/7 (Δ[O2])/(Δt) = 1/4 (Δ[Cr(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | H3CrO8 | water | oxygen | Cr(SO4)3 formula | H_2SO_4 | H3CrO8 | H_2O | O_2 | Cr(SO4)3 Hill formula | H_2O_4S | H3CrO8 | H_2O | O_2 | CrO12S3 name | sulfuric acid | | water | oxygen | IUPAC name | sulfuric acid | | water | molecular oxygen |
| sulfuric acid | H3CrO8 | water | oxygen | Cr(SO4)3 formula | H_2SO_4 | H3CrO8 | H_2O | O_2 | Cr(SO4)3 Hill formula | H_2O_4S | H3CrO8 | H_2O | O_2 | CrO12S3 name | sulfuric acid | | water | oxygen | IUPAC name | sulfuric acid | | water | molecular oxygen |

Substance properties

| sulfuric acid | H3CrO8 | water | oxygen | Cr(SO4)3 molar mass | 98.07 g/mol | 183.01 g/mol | 18.015 g/mol | 31.998 g/mol | 340.2 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | melting point | 10.371 °C | | 0 °C | -218 °C | boiling point | 279.6 °C | | 99.9839 °C | -183 °C | density | 1.8305 g/cm^3 | | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | solubility in water | very soluble | | | | surface tension | 0.0735 N/m | | 0.0728 N/m | 0.01347 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |
| sulfuric acid | H3CrO8 | water | oxygen | Cr(SO4)3 molar mass | 98.07 g/mol | 183.01 g/mol | 18.015 g/mol | 31.998 g/mol | 340.2 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | melting point | 10.371 °C | | 0 °C | -218 °C | boiling point | 279.6 °C | | 99.9839 °C | -183 °C | density | 1.8305 g/cm^3 | | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | solubility in water | very soluble | | | | surface tension | 0.0735 N/m | | 0.0728 N/m | 0.01347 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |

Units

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