Input interpretation
![H_2SO_4 sulfuric acid + S mixed sulfur + KMnO_4 potassium permanganate ⟶ H_2O water + K_2SO_4 potassium sulfate + SO_2 sulfur dioxide + MnSO_4 manganese(II) sulfate](../image_source/d50d9a699d6963c668ac46171c3db512.png)
H_2SO_4 sulfuric acid + S mixed sulfur + KMnO_4 potassium permanganate ⟶ H_2O water + K_2SO_4 potassium sulfate + SO_2 sulfur dioxide + MnSO_4 manganese(II) sulfate
Balanced equation
![Balance the chemical equation algebraically: H_2SO_4 + S + KMnO_4 ⟶ H_2O + K_2SO_4 + SO_2 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 S + c_3 KMnO_4 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 SO_2 + c_7 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Mn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_3 = c_4 + 4 c_5 + 2 c_6 + 4 c_7 S: | c_1 + c_2 = c_5 + c_6 + c_7 K: | c_3 = 2 c_5 Mn: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/2 + 1 c_3 = 2 c_4 = c_1 c_5 = 1 c_6 = (3 c_1)/2 - 2 c_7 = 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 2 S + 2 KMnO_4 ⟶ 2 H_2O + K_2SO_4 + SO_2 + 2 MnSO_4](../image_source/cc72a792e9cd335ddf2ddc5ae0fdaeff.png)
Balance the chemical equation algebraically: H_2SO_4 + S + KMnO_4 ⟶ H_2O + K_2SO_4 + SO_2 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 S + c_3 KMnO_4 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 SO_2 + c_7 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Mn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_3 = c_4 + 4 c_5 + 2 c_6 + 4 c_7 S: | c_1 + c_2 = c_5 + c_6 + c_7 K: | c_3 = 2 c_5 Mn: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/2 + 1 c_3 = 2 c_4 = c_1 c_5 = 1 c_6 = (3 c_1)/2 - 2 c_7 = 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 2 S + 2 KMnO_4 ⟶ 2 H_2O + K_2SO_4 + SO_2 + 2 MnSO_4
Structures
![+ + ⟶ + + +](../image_source/1552fc696051cc90f449004346fd3c44.png)
+ + ⟶ + + +
Names
![sulfuric acid + mixed sulfur + potassium permanganate ⟶ water + potassium sulfate + sulfur dioxide + manganese(II) sulfate](../image_source/fc02b65299bbda1f3af3ce6e4a187782.png)
sulfuric acid + mixed sulfur + potassium permanganate ⟶ water + potassium sulfate + sulfur dioxide + manganese(II) sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + S + KMnO_4 ⟶ H_2O + K_2SO_4 + SO_2 + MnSO_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: 2 H_2SO_4 + 2 S + 2 KMnO_4 ⟶ 2 H_2O + K_2SO_4 + SO_2 + 2 MnSO_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 | 2 | -2 S | 2 | -2 KMnO_4 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 SO_2 | 1 | 1 MnSO_4 | 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 | 2 | -2 | ([H2SO4])^(-2) S | 2 | -2 | ([S])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] SO_2 | 1 | 1 | [SO2] MnSO_4 | 2 | 2 | ([MnSO4])^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])^(-2) ([S])^(-2) ([KMnO4])^(-2) ([H2O])^2 [K2SO4] [SO2] ([MnSO4])^2 = (([H2O])^2 [K2SO4] [SO2] ([MnSO4])^2)/(([H2SO4])^2 ([S])^2 ([KMnO4])^2)](../image_source/86357b0a8ba6fa75d9e58a1992f0a506.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + S + KMnO_4 ⟶ H_2O + K_2SO_4 + SO_2 + MnSO_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: 2 H_2SO_4 + 2 S + 2 KMnO_4 ⟶ 2 H_2O + K_2SO_4 + SO_2 + 2 MnSO_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 | 2 | -2 S | 2 | -2 KMnO_4 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 SO_2 | 1 | 1 MnSO_4 | 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 | 2 | -2 | ([H2SO4])^(-2) S | 2 | -2 | ([S])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] SO_2 | 1 | 1 | [SO2] MnSO_4 | 2 | 2 | ([MnSO4])^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])^(-2) ([S])^(-2) ([KMnO4])^(-2) ([H2O])^2 [K2SO4] [SO2] ([MnSO4])^2 = (([H2O])^2 [K2SO4] [SO2] ([MnSO4])^2)/(([H2SO4])^2 ([S])^2 ([KMnO4])^2)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + S + KMnO_4 ⟶ H_2O + K_2SO_4 + SO_2 + MnSO_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: 2 H_2SO_4 + 2 S + 2 KMnO_4 ⟶ 2 H_2O + K_2SO_4 + SO_2 + 2 MnSO_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 | 2 | -2 S | 2 | -2 KMnO_4 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 SO_2 | 1 | 1 MnSO_4 | 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 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) S | 2 | -2 | -1/2 (Δ[S])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(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 = -1/2 (Δ[H2SO4])/(Δt) = -1/2 (Δ[S])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[SO2])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/2ec8c6338f35393ca34cd520d361098c.png)
Construct the rate of reaction expression for: H_2SO_4 + S + KMnO_4 ⟶ H_2O + K_2SO_4 + SO_2 + MnSO_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: 2 H_2SO_4 + 2 S + 2 KMnO_4 ⟶ 2 H_2O + K_2SO_4 + SO_2 + 2 MnSO_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 | 2 | -2 S | 2 | -2 KMnO_4 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 SO_2 | 1 | 1 MnSO_4 | 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 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) S | 2 | -2 | -1/2 (Δ[S])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(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 = -1/2 (Δ[H2SO4])/(Δt) = -1/2 (Δ[S])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[SO2])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfuric acid | mixed sulfur | potassium permanganate | water | potassium sulfate | sulfur dioxide | manganese(II) sulfate formula | H_2SO_4 | S | KMnO_4 | H_2O | K_2SO_4 | SO_2 | MnSO_4 Hill formula | H_2O_4S | S | KMnO_4 | H_2O | K_2O_4S | O_2S | MnSO_4 name | sulfuric acid | mixed sulfur | potassium permanganate | water | potassium sulfate | sulfur dioxide | manganese(II) sulfate IUPAC name | sulfuric acid | sulfur | potassium permanganate | water | dipotassium sulfate | sulfur dioxide | manganese(+2) cation sulfate](../image_source/5c838d768950c919c1d2f22bf306e252.png)
| sulfuric acid | mixed sulfur | potassium permanganate | water | potassium sulfate | sulfur dioxide | manganese(II) sulfate formula | H_2SO_4 | S | KMnO_4 | H_2O | K_2SO_4 | SO_2 | MnSO_4 Hill formula | H_2O_4S | S | KMnO_4 | H_2O | K_2O_4S | O_2S | MnSO_4 name | sulfuric acid | mixed sulfur | potassium permanganate | water | potassium sulfate | sulfur dioxide | manganese(II) sulfate IUPAC name | sulfuric acid | sulfur | potassium permanganate | water | dipotassium sulfate | sulfur dioxide | manganese(+2) cation sulfate