Input interpretation
H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate + C6H4(CH3)2CH3 ⟶ H_2O water + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + C_6H_5COOH benzoic acid
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 + C6H4(CH3)2CH3 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + C_6H_5COOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2Cr_2O_7 + c_3 C6H4(CH3)2CH3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 C_6H_5COOH Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr, K and C: H: | 2 c_1 + 13 c_3 = 2 c_4 + 6 c_7 O: | 4 c_1 + 7 c_2 = c_4 + 4 c_5 + 12 c_6 + 2 c_7 S: | c_1 = c_5 + 3 c_6 Cr: | 2 c_2 = 2 c_6 K: | 2 c_2 = 2 c_5 C: | 9 c_3 = 7 c_7 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 = 146/21 c_2 = 73/42 c_3 = 1 c_4 = 403/42 c_5 = 73/42 c_6 = 73/42 c_7 = 9/7 Multiply by the least common denominator, 42, to eliminate fractional coefficients: c_1 = 292 c_2 = 73 c_3 = 42 c_4 = 403 c_5 = 73 c_6 = 73 c_7 = 54 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 292 H_2SO_4 + 73 K_2Cr_2O_7 + 42 C6H4(CH3)2CH3 ⟶ 403 H_2O + 73 K_2SO_4 + 73 Cr_2(SO_4)_3 + 54 C_6H_5COOH
Structures
+ + C6H4(CH3)2CH3 ⟶ + + +
Names
sulfuric acid + potassium dichromate + C6H4(CH3)2CH3 ⟶ water + potassium sulfate + chromium sulfate + benzoic acid
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + C6H4(CH3)2CH3 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + C_6H_5COOH 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: 292 H_2SO_4 + 73 K_2Cr_2O_7 + 42 C6H4(CH3)2CH3 ⟶ 403 H_2O + 73 K_2SO_4 + 73 Cr_2(SO_4)_3 + 54 C_6H_5COOH 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 | 292 | -292 K_2Cr_2O_7 | 73 | -73 C6H4(CH3)2CH3 | 42 | -42 H_2O | 403 | 403 K_2SO_4 | 73 | 73 Cr_2(SO_4)_3 | 73 | 73 C_6H_5COOH | 54 | 54 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 292 | -292 | ([H2SO4])^(-292) K_2Cr_2O_7 | 73 | -73 | ([K2Cr2O7])^(-73) C6H4(CH3)2CH3 | 42 | -42 | ([C6H4(CH3)2CH3])^(-42) H_2O | 403 | 403 | ([H2O])^403 K_2SO_4 | 73 | 73 | ([K2SO4])^73 Cr_2(SO_4)_3 | 73 | 73 | ([Cr2(SO4)3])^73 C_6H_5COOH | 54 | 54 | ([C6H5COOH])^54 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])^(-292) ([K2Cr2O7])^(-73) ([C6H4(CH3)2CH3])^(-42) ([H2O])^403 ([K2SO4])^73 ([Cr2(SO4)3])^73 ([C6H5COOH])^54 = (([H2O])^403 ([K2SO4])^73 ([Cr2(SO4)3])^73 ([C6H5COOH])^54)/(([H2SO4])^292 ([K2Cr2O7])^73 ([C6H4(CH3)2CH3])^42)](../image_source/e6bd25e62b169d73ec3735e90e16e0b1.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + C6H4(CH3)2CH3 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + C_6H_5COOH 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: 292 H_2SO_4 + 73 K_2Cr_2O_7 + 42 C6H4(CH3)2CH3 ⟶ 403 H_2O + 73 K_2SO_4 + 73 Cr_2(SO_4)_3 + 54 C_6H_5COOH 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 | 292 | -292 K_2Cr_2O_7 | 73 | -73 C6H4(CH3)2CH3 | 42 | -42 H_2O | 403 | 403 K_2SO_4 | 73 | 73 Cr_2(SO_4)_3 | 73 | 73 C_6H_5COOH | 54 | 54 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 292 | -292 | ([H2SO4])^(-292) K_2Cr_2O_7 | 73 | -73 | ([K2Cr2O7])^(-73) C6H4(CH3)2CH3 | 42 | -42 | ([C6H4(CH3)2CH3])^(-42) H_2O | 403 | 403 | ([H2O])^403 K_2SO_4 | 73 | 73 | ([K2SO4])^73 Cr_2(SO_4)_3 | 73 | 73 | ([Cr2(SO4)3])^73 C_6H_5COOH | 54 | 54 | ([C6H5COOH])^54 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])^(-292) ([K2Cr2O7])^(-73) ([C6H4(CH3)2CH3])^(-42) ([H2O])^403 ([K2SO4])^73 ([Cr2(SO4)3])^73 ([C6H5COOH])^54 = (([H2O])^403 ([K2SO4])^73 ([Cr2(SO4)3])^73 ([C6H5COOH])^54)/(([H2SO4])^292 ([K2Cr2O7])^73 ([C6H4(CH3)2CH3])^42)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + C6H4(CH3)2CH3 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + C_6H_5COOH 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: 292 H_2SO_4 + 73 K_2Cr_2O_7 + 42 C6H4(CH3)2CH3 ⟶ 403 H_2O + 73 K_2SO_4 + 73 Cr_2(SO_4)_3 + 54 C_6H_5COOH 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 | 292 | -292 K_2Cr_2O_7 | 73 | -73 C6H4(CH3)2CH3 | 42 | -42 H_2O | 403 | 403 K_2SO_4 | 73 | 73 Cr_2(SO_4)_3 | 73 | 73 C_6H_5COOH | 54 | 54 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 | 292 | -292 | -1/292 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 73 | -73 | -1/73 (Δ[K2Cr2O7])/(Δt) C6H4(CH3)2CH3 | 42 | -42 | -1/42 (Δ[C6H4(CH3)2CH3])/(Δt) H_2O | 403 | 403 | 1/403 (Δ[H2O])/(Δt) K_2SO_4 | 73 | 73 | 1/73 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 73 | 73 | 1/73 (Δ[Cr2(SO4)3])/(Δt) C_6H_5COOH | 54 | 54 | 1/54 (Δ[C6H5COOH])/(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 = -1/292 (Δ[H2SO4])/(Δt) = -1/73 (Δ[K2Cr2O7])/(Δt) = -1/42 (Δ[C6H4(CH3)2CH3])/(Δt) = 1/403 (Δ[H2O])/(Δt) = 1/73 (Δ[K2SO4])/(Δt) = 1/73 (Δ[Cr2(SO4)3])/(Δt) = 1/54 (Δ[C6H5COOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/f93572e5e67738e473eef9a62c69bae0.png)
Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + C6H4(CH3)2CH3 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + C_6H_5COOH 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: 292 H_2SO_4 + 73 K_2Cr_2O_7 + 42 C6H4(CH3)2CH3 ⟶ 403 H_2O + 73 K_2SO_4 + 73 Cr_2(SO_4)_3 + 54 C_6H_5COOH 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 | 292 | -292 K_2Cr_2O_7 | 73 | -73 C6H4(CH3)2CH3 | 42 | -42 H_2O | 403 | 403 K_2SO_4 | 73 | 73 Cr_2(SO_4)_3 | 73 | 73 C_6H_5COOH | 54 | 54 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 | 292 | -292 | -1/292 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 73 | -73 | -1/73 (Δ[K2Cr2O7])/(Δt) C6H4(CH3)2CH3 | 42 | -42 | -1/42 (Δ[C6H4(CH3)2CH3])/(Δt) H_2O | 403 | 403 | 1/403 (Δ[H2O])/(Δt) K_2SO_4 | 73 | 73 | 1/73 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 73 | 73 | 1/73 (Δ[Cr2(SO4)3])/(Δt) C_6H_5COOH | 54 | 54 | 1/54 (Δ[C6H5COOH])/(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 = -1/292 (Δ[H2SO4])/(Δt) = -1/73 (Δ[K2Cr2O7])/(Δt) = -1/42 (Δ[C6H4(CH3)2CH3])/(Δt) = 1/403 (Δ[H2O])/(Δt) = 1/73 (Δ[K2SO4])/(Δt) = 1/73 (Δ[Cr2(SO4)3])/(Δt) = 1/54 (Δ[C6H5COOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | potassium dichromate | C6H4(CH3)2CH3 | water | potassium sulfate | chromium sulfate | benzoic acid formula | H_2SO_4 | K_2Cr_2O_7 | C6H4(CH3)2CH3 | H_2O | K_2SO_4 | Cr_2(SO_4)_3 | C_6H_5COOH Hill formula | H_2O_4S | Cr_2K_2O_7 | C9H13 | H_2O | K_2O_4S | Cr_2O_12S_3 | C_7H_6O_2 name | sulfuric acid | potassium dichromate | | water | potassium sulfate | chromium sulfate | benzoic acid IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | | water | dipotassium sulfate | chromium(+3) cation trisulfate | benzoic acid
Substance properties
| sulfuric acid | potassium dichromate | C6H4(CH3)2CH3 | water | potassium sulfate | chromium sulfate | benzoic acid molar mass | 98.07 g/mol | 294.18 g/mol | 121.2 g/mol | 18.015 g/mol | 174.25 g/mol | 392.2 g/mol | 122.12 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | liquid (at STP) | solid (at STP) melting point | 10.371 °C | 398 °C | | 0 °C | | | 123 °C boiling point | 279.6 °C | | | 99.9839 °C | | 330 °C | 249 °C density | 1.8305 g/cm^3 | 2.67 g/cm^3 | | 1 g/cm^3 | | 1.84 g/cm^3 | 1.316 g/cm^3 solubility in water | very soluble | | | | soluble | | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | 0.03 N/m dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | 0.00148 Pa s (at 125 °C) odor | odorless | odorless | | odorless | | odorless |
Units
