Input interpretation
![H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + BaO_2 barium peroxide ⟶ H_2O water + O_2 oxygen + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + BaSO_4 barium sulfate](../image_source/d45eef31cb48a0c6bc10f6c2922e6c9a.png)
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + BaO_2 barium peroxide ⟶ H_2O water + O_2 oxygen + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + BaSO_4 barium sulfate
Balanced equation
![Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + BaO_2 ⟶ H_2O + O_2 + K_2SO_4 + MnSO_4 + BaSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 BaO_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 K_2SO_4 + c_7 MnSO_4 + c_8 BaSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Ba: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 2 c_3 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 + 4 c_8 S: | c_1 = c_6 + c_7 + c_8 K: | c_2 = 2 c_6 Mn: | c_2 = c_7 Ba: | c_3 = c_8 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_2 = (2 c_1)/3 - 2/3 c_3 = 1 c_4 = c_1 c_5 = (5 c_1)/6 - 1/3 c_6 = c_1/3 - 1/3 c_7 = (2 c_1)/3 - 2/3 c_8 = 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 3 c_6 = 1 c_7 = 2 c_8 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 2 KMnO_4 + BaO_2 ⟶ 4 H_2O + 3 O_2 + K_2SO_4 + 2 MnSO_4 + BaSO_4](../image_source/9a71a783107ccf0ef4d77754d7287829.png)
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + BaO_2 ⟶ H_2O + O_2 + K_2SO_4 + MnSO_4 + BaSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 BaO_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 K_2SO_4 + c_7 MnSO_4 + c_8 BaSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Ba: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 2 c_3 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 + 4 c_8 S: | c_1 = c_6 + c_7 + c_8 K: | c_2 = 2 c_6 Mn: | c_2 = c_7 Ba: | c_3 = c_8 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_2 = (2 c_1)/3 - 2/3 c_3 = 1 c_4 = c_1 c_5 = (5 c_1)/6 - 1/3 c_6 = c_1/3 - 1/3 c_7 = (2 c_1)/3 - 2/3 c_8 = 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 3 c_6 = 1 c_7 = 2 c_8 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 2 KMnO_4 + BaO_2 ⟶ 4 H_2O + 3 O_2 + K_2SO_4 + 2 MnSO_4 + BaSO_4
Structures
![+ + ⟶ + + + +](../image_source/4100f3b0230448935b188a02ced825c1.png)
+ + ⟶ + + + +
Names
![sulfuric acid + potassium permanganate + barium peroxide ⟶ water + oxygen + potassium sulfate + manganese(II) sulfate + barium sulfate](../image_source/61a89b779bca171c9e1a921a208487d3.png)
sulfuric acid + potassium permanganate + barium peroxide ⟶ water + oxygen + potassium sulfate + manganese(II) sulfate + barium sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + BaO_2 ⟶ H_2O + O_2 + K_2SO_4 + MnSO_4 + BaSO_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: 4 H_2SO_4 + 2 KMnO_4 + BaO_2 ⟶ 4 H_2O + 3 O_2 + K_2SO_4 + 2 MnSO_4 + BaSO_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 | 4 | -4 KMnO_4 | 2 | -2 BaO_2 | 1 | -1 H_2O | 4 | 4 O_2 | 3 | 3 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 BaSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) BaO_2 | 1 | -1 | ([BaO2])^(-1) H_2O | 4 | 4 | ([H2O])^4 O_2 | 3 | 3 | ([O2])^3 K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 BaSO_4 | 1 | 1 | [BaSO4] 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])^(-4) ([KMnO4])^(-2) ([BaO2])^(-1) ([H2O])^4 ([O2])^3 [K2SO4] ([MnSO4])^2 [BaSO4] = (([H2O])^4 ([O2])^3 [K2SO4] ([MnSO4])^2 [BaSO4])/(([H2SO4])^4 ([KMnO4])^2 [BaO2])](../image_source/ada447fbacee89293206ce51430aade4.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + BaO_2 ⟶ H_2O + O_2 + K_2SO_4 + MnSO_4 + BaSO_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: 4 H_2SO_4 + 2 KMnO_4 + BaO_2 ⟶ 4 H_2O + 3 O_2 + K_2SO_4 + 2 MnSO_4 + BaSO_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 | 4 | -4 KMnO_4 | 2 | -2 BaO_2 | 1 | -1 H_2O | 4 | 4 O_2 | 3 | 3 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 BaSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) BaO_2 | 1 | -1 | ([BaO2])^(-1) H_2O | 4 | 4 | ([H2O])^4 O_2 | 3 | 3 | ([O2])^3 K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 BaSO_4 | 1 | 1 | [BaSO4] 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])^(-4) ([KMnO4])^(-2) ([BaO2])^(-1) ([H2O])^4 ([O2])^3 [K2SO4] ([MnSO4])^2 [BaSO4] = (([H2O])^4 ([O2])^3 [K2SO4] ([MnSO4])^2 [BaSO4])/(([H2SO4])^4 ([KMnO4])^2 [BaO2])
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + BaO_2 ⟶ H_2O + O_2 + K_2SO_4 + MnSO_4 + BaSO_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: 4 H_2SO_4 + 2 KMnO_4 + BaO_2 ⟶ 4 H_2O + 3 O_2 + K_2SO_4 + 2 MnSO_4 + BaSO_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 | 4 | -4 KMnO_4 | 2 | -2 BaO_2 | 1 | -1 H_2O | 4 | 4 O_2 | 3 | 3 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 BaSO_4 | 1 | 1 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) BaO_2 | 1 | -1 | -(Δ[BaO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) O_2 | 3 | 3 | 1/3 (Δ[O2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) BaSO_4 | 1 | 1 | (Δ[BaSO4])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[BaO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[O2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = (Δ[BaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/e3ea7c73fcdff69992c5bf1b9bc073a4.png)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + BaO_2 ⟶ H_2O + O_2 + K_2SO_4 + MnSO_4 + BaSO_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: 4 H_2SO_4 + 2 KMnO_4 + BaO_2 ⟶ 4 H_2O + 3 O_2 + K_2SO_4 + 2 MnSO_4 + BaSO_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 | 4 | -4 KMnO_4 | 2 | -2 BaO_2 | 1 | -1 H_2O | 4 | 4 O_2 | 3 | 3 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 BaSO_4 | 1 | 1 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) BaO_2 | 1 | -1 | -(Δ[BaO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) O_2 | 3 | 3 | 1/3 (Δ[O2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) BaSO_4 | 1 | 1 | (Δ[BaSO4])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[BaO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[O2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = (Δ[BaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfuric acid | potassium permanganate | barium peroxide | water | oxygen | potassium sulfate | manganese(II) sulfate | barium sulfate formula | H_2SO_4 | KMnO_4 | BaO_2 | H_2O | O_2 | K_2SO_4 | MnSO_4 | BaSO_4 Hill formula | H_2O_4S | KMnO_4 | BaO_2 | H_2O | O_2 | K_2O_4S | MnSO_4 | BaO_4S name | sulfuric acid | potassium permanganate | barium peroxide | water | oxygen | potassium sulfate | manganese(II) sulfate | barium sulfate IUPAC name | sulfuric acid | potassium permanganate | barium(+2) cation peroxide | water | molecular oxygen | dipotassium sulfate | manganese(+2) cation sulfate | barium(+2) cation sulfate](../image_source/a83ae27877bf6655c35b7c23fa6afdfe.png)
| sulfuric acid | potassium permanganate | barium peroxide | water | oxygen | potassium sulfate | manganese(II) sulfate | barium sulfate formula | H_2SO_4 | KMnO_4 | BaO_2 | H_2O | O_2 | K_2SO_4 | MnSO_4 | BaSO_4 Hill formula | H_2O_4S | KMnO_4 | BaO_2 | H_2O | O_2 | K_2O_4S | MnSO_4 | BaO_4S name | sulfuric acid | potassium permanganate | barium peroxide | water | oxygen | potassium sulfate | manganese(II) sulfate | barium sulfate IUPAC name | sulfuric acid | potassium permanganate | barium(+2) cation peroxide | water | molecular oxygen | dipotassium sulfate | manganese(+2) cation sulfate | barium(+2) cation sulfate
Substance properties
![| sulfuric acid | potassium permanganate | barium peroxide | water | oxygen | potassium sulfate | manganese(II) sulfate | barium sulfate molar mass | 98.07 g/mol | 158.03 g/mol | 169.325 g/mol | 18.015 g/mol | 31.998 g/mol | 174.25 g/mol | 150.99 g/mol | 233.38 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | 450 °C | 0 °C | -218 °C | | 710 °C | 1345 °C boiling point | 279.6 °C | | | 99.9839 °C | -183 °C | | | density | 1.8305 g/cm^3 | 1 g/cm^3 | 4.96 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | | 3.25 g/cm^3 | 4.5 g/cm^3 solubility in water | very soluble | | slightly soluble | | | soluble | soluble | insoluble 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 | odorless | | |](../image_source/c93869befcebdc5b4d03ca6896aaa2de.png)
| sulfuric acid | potassium permanganate | barium peroxide | water | oxygen | potassium sulfate | manganese(II) sulfate | barium sulfate molar mass | 98.07 g/mol | 158.03 g/mol | 169.325 g/mol | 18.015 g/mol | 31.998 g/mol | 174.25 g/mol | 150.99 g/mol | 233.38 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | 450 °C | 0 °C | -218 °C | | 710 °C | 1345 °C boiling point | 279.6 °C | | | 99.9839 °C | -183 °C | | | density | 1.8305 g/cm^3 | 1 g/cm^3 | 4.96 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | | 3.25 g/cm^3 | 4.5 g/cm^3 solubility in water | very soluble | | slightly soluble | | | soluble | soluble | insoluble 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 | odorless | | |
Units