Input interpretation
![H_2SO_4 sulfuric acid + C activated charcoal + CrO_3 chromium trioxide ⟶ H_2O water + CO_2 carbon dioxide + Cr_2(SO_4)_3 chromium sulfate](../image_source/540ef1dea3b596a40d606efba4a50730.png)
H_2SO_4 sulfuric acid + C activated charcoal + CrO_3 chromium trioxide ⟶ H_2O water + CO_2 carbon dioxide + Cr_2(SO_4)_3 chromium sulfate
Balanced equation
![Balance the chemical equation algebraically: H_2SO_4 + C + CrO_3 ⟶ H_2O + CO_2 + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 C + c_3 CrO_3 ⟶ c_4 H_2O + c_5 CO_2 + c_6 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, C and Cr: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_3 = c_4 + 2 c_5 + 12 c_6 S: | c_1 = 3 c_6 C: | c_2 = c_5 Cr: | c_3 = 2 c_6 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3/2 c_3 = 2 c_4 = 3 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 3 c_3 = 4 c_4 = 6 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2SO_4 + 3 C + 4 CrO_3 ⟶ 6 H_2O + 3 CO_2 + 2 Cr_2(SO_4)_3](../image_source/ca9c504667ac2fb8ea7732bf224073c9.png)
Balance the chemical equation algebraically: H_2SO_4 + C + CrO_3 ⟶ H_2O + CO_2 + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 C + c_3 CrO_3 ⟶ c_4 H_2O + c_5 CO_2 + c_6 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, C and Cr: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_3 = c_4 + 2 c_5 + 12 c_6 S: | c_1 = 3 c_6 C: | c_2 = c_5 Cr: | c_3 = 2 c_6 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3/2 c_3 = 2 c_4 = 3 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 3 c_3 = 4 c_4 = 6 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2SO_4 + 3 C + 4 CrO_3 ⟶ 6 H_2O + 3 CO_2 + 2 Cr_2(SO_4)_3
Structures
![+ + ⟶ + +](../image_source/fab206baa73f4000acc5a334cfca3c50.png)
+ + ⟶ + +
Names
![sulfuric acid + activated charcoal + chromium trioxide ⟶ water + carbon dioxide + chromium sulfate](../image_source/133c4ceb212c85dd5a376d1bc2e9b740.png)
sulfuric acid + activated charcoal + chromium trioxide ⟶ water + carbon dioxide + chromium sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + C + CrO_3 ⟶ H_2O + CO_2 + Cr_2(SO_4)_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_2SO_4 + 3 C + 4 CrO_3 ⟶ 6 H_2O + 3 CO_2 + 2 Cr_2(SO_4)_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 | 6 | -6 C | 3 | -3 CrO_3 | 4 | -4 H_2O | 6 | 6 CO_2 | 3 | 3 Cr_2(SO_4)_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_2SO_4 | 6 | -6 | ([H2SO4])^(-6) C | 3 | -3 | ([C])^(-3) CrO_3 | 4 | -4 | ([CrO3])^(-4) H_2O | 6 | 6 | ([H2O])^6 CO_2 | 3 | 3 | ([CO2])^3 Cr_2(SO_4)_3 | 2 | 2 | ([Cr2(SO4)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 = ([H2SO4])^(-6) ([C])^(-3) ([CrO3])^(-4) ([H2O])^6 ([CO2])^3 ([Cr2(SO4)3])^2 = (([H2O])^6 ([CO2])^3 ([Cr2(SO4)3])^2)/(([H2SO4])^6 ([C])^3 ([CrO3])^4)](../image_source/558004134a904eff4954d99b467baa6b.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + C + CrO_3 ⟶ H_2O + CO_2 + Cr_2(SO_4)_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_2SO_4 + 3 C + 4 CrO_3 ⟶ 6 H_2O + 3 CO_2 + 2 Cr_2(SO_4)_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 | 6 | -6 C | 3 | -3 CrO_3 | 4 | -4 H_2O | 6 | 6 CO_2 | 3 | 3 Cr_2(SO_4)_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_2SO_4 | 6 | -6 | ([H2SO4])^(-6) C | 3 | -3 | ([C])^(-3) CrO_3 | 4 | -4 | ([CrO3])^(-4) H_2O | 6 | 6 | ([H2O])^6 CO_2 | 3 | 3 | ([CO2])^3 Cr_2(SO_4)_3 | 2 | 2 | ([Cr2(SO4)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 = ([H2SO4])^(-6) ([C])^(-3) ([CrO3])^(-4) ([H2O])^6 ([CO2])^3 ([Cr2(SO4)3])^2 = (([H2O])^6 ([CO2])^3 ([Cr2(SO4)3])^2)/(([H2SO4])^6 ([C])^3 ([CrO3])^4)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + C + CrO_3 ⟶ H_2O + CO_2 + Cr_2(SO_4)_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_2SO_4 + 3 C + 4 CrO_3 ⟶ 6 H_2O + 3 CO_2 + 2 Cr_2(SO_4)_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 | 6 | -6 C | 3 | -3 CrO_3 | 4 | -4 H_2O | 6 | 6 CO_2 | 3 | 3 Cr_2(SO_4)_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_2SO_4 | 6 | -6 | -1/6 (Δ[H2SO4])/(Δt) C | 3 | -3 | -1/3 (Δ[C])/(Δt) CrO_3 | 4 | -4 | -1/4 (Δ[CrO3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) Cr_2(SO_4)_3 | 2 | 2 | 1/2 (Δ[Cr2(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 = -1/6 (Δ[H2SO4])/(Δt) = -1/3 (Δ[C])/(Δt) = -1/4 (Δ[CrO3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/2 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/9239d72c89b731ef88c3d205c14082b4.png)
Construct the rate of reaction expression for: H_2SO_4 + C + CrO_3 ⟶ H_2O + CO_2 + Cr_2(SO_4)_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_2SO_4 + 3 C + 4 CrO_3 ⟶ 6 H_2O + 3 CO_2 + 2 Cr_2(SO_4)_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 | 6 | -6 C | 3 | -3 CrO_3 | 4 | -4 H_2O | 6 | 6 CO_2 | 3 | 3 Cr_2(SO_4)_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_2SO_4 | 6 | -6 | -1/6 (Δ[H2SO4])/(Δt) C | 3 | -3 | -1/3 (Δ[C])/(Δt) CrO_3 | 4 | -4 | -1/4 (Δ[CrO3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) Cr_2(SO_4)_3 | 2 | 2 | 1/2 (Δ[Cr2(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 = -1/6 (Δ[H2SO4])/(Δt) = -1/3 (Δ[C])/(Δt) = -1/4 (Δ[CrO3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/2 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfuric acid | activated charcoal | chromium trioxide | water | carbon dioxide | chromium sulfate formula | H_2SO_4 | C | CrO_3 | H_2O | CO_2 | Cr_2(SO_4)_3 Hill formula | H_2O_4S | C | CrO_3 | H_2O | CO_2 | Cr_2O_12S_3 name | sulfuric acid | activated charcoal | chromium trioxide | water | carbon dioxide | chromium sulfate IUPAC name | sulfuric acid | carbon | trioxochromium | water | carbon dioxide | chromium(+3) cation trisulfate](../image_source/cb72ac085b7f2822c2be41ff265cc3ba.png)
| sulfuric acid | activated charcoal | chromium trioxide | water | carbon dioxide | chromium sulfate formula | H_2SO_4 | C | CrO_3 | H_2O | CO_2 | Cr_2(SO_4)_3 Hill formula | H_2O_4S | C | CrO_3 | H_2O | CO_2 | Cr_2O_12S_3 name | sulfuric acid | activated charcoal | chromium trioxide | water | carbon dioxide | chromium sulfate IUPAC name | sulfuric acid | carbon | trioxochromium | water | carbon dioxide | chromium(+3) cation trisulfate