Input interpretation
![KMnO_4 potassium permanganate ⟶ K2MnO4MnO2O2](../image_source/979bd761f1c47e418e10de5ba0d17b85.png)
KMnO_4 potassium permanganate ⟶ K2MnO4MnO2O2
Balanced equation
![Balance the chemical equation algebraically: KMnO_4 ⟶ K2MnO4MnO2O2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 ⟶ c_2 K2MnO4MnO2O2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn and O: K: | c_1 = 2 c_2 Mn: | c_1 = 2 c_2 O: | 4 c_1 = 8 c_2 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 = 2 c_2 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 ⟶ K2MnO4MnO2O2](../image_source/2386bb8f0b6713438f4c824d5941bc0d.png)
Balance the chemical equation algebraically: KMnO_4 ⟶ K2MnO4MnO2O2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 ⟶ c_2 K2MnO4MnO2O2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn and O: K: | c_1 = 2 c_2 Mn: | c_1 = 2 c_2 O: | 4 c_1 = 8 c_2 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 = 2 c_2 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 ⟶ K2MnO4MnO2O2
Structures
![⟶ K2MnO4MnO2O2](../image_source/a1f46ea752a986fd689176a8ad31ad28.png)
⟶ K2MnO4MnO2O2
Names
![potassium permanganate ⟶ K2MnO4MnO2O2](../image_source/ba94cb398833ca6ac4699abbe248be0a.png)
potassium permanganate ⟶ K2MnO4MnO2O2
Equilibrium constant
![Construct the equilibrium constant, K, expression for: KMnO_4 ⟶ K2MnO4MnO2O2 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 KMnO_4 ⟶ K2MnO4MnO2O2 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 KMnO_4 | 2 | -2 K2MnO4MnO2O2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 2 | -2 | ([KMnO4])^(-2) K2MnO4MnO2O2 | 1 | 1 | [K2MnO4MnO2O2] 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 = ([KMnO4])^(-2) [K2MnO4MnO2O2] = ([K2MnO4MnO2O2])/([KMnO4])^2](../image_source/17cb03e386eed81e988a1447b5a5691d.png)
Construct the equilibrium constant, K, expression for: KMnO_4 ⟶ K2MnO4MnO2O2 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 KMnO_4 ⟶ K2MnO4MnO2O2 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 KMnO_4 | 2 | -2 K2MnO4MnO2O2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 2 | -2 | ([KMnO4])^(-2) K2MnO4MnO2O2 | 1 | 1 | [K2MnO4MnO2O2] 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 = ([KMnO4])^(-2) [K2MnO4MnO2O2] = ([K2MnO4MnO2O2])/([KMnO4])^2
Rate of reaction
![Construct the rate of reaction expression for: KMnO_4 ⟶ K2MnO4MnO2O2 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 KMnO_4 ⟶ K2MnO4MnO2O2 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 KMnO_4 | 2 | -2 K2MnO4MnO2O2 | 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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) K2MnO4MnO2O2 | 1 | 1 | (Δ[K2MnO4MnO2O2])/(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[KMnO4])/(Δt) = (Δ[K2MnO4MnO2O2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/b219c9bc23fd0994c17ef0ee8d336fb9.png)
Construct the rate of reaction expression for: KMnO_4 ⟶ K2MnO4MnO2O2 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 KMnO_4 ⟶ K2MnO4MnO2O2 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 KMnO_4 | 2 | -2 K2MnO4MnO2O2 | 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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) K2MnO4MnO2O2 | 1 | 1 | (Δ[K2MnO4MnO2O2])/(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[KMnO4])/(Δt) = (Δ[K2MnO4MnO2O2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| potassium permanganate | K2MnO4MnO2O2 formula | KMnO_4 | K2MnO4MnO2O2 Hill formula | KMnO_4 | K2Mn2O8 name | potassium permanganate |](../image_source/2325a0d721137930c8c1778ed55143b3.png)
| potassium permanganate | K2MnO4MnO2O2 formula | KMnO_4 | K2MnO4MnO2O2 Hill formula | KMnO_4 | K2Mn2O8 name | potassium permanganate |
Substance properties
![| potassium permanganate | K2MnO4MnO2O2 molar mass | 158.03 g/mol | 316.06 g/mol phase | solid (at STP) | melting point | 240 °C | density | 1 g/cm^3 | odor | odorless |](../image_source/e959b094ae533877eeecd6e9d5a02c7e.png)
| potassium permanganate | K2MnO4MnO2O2 molar mass | 158.03 g/mol | 316.06 g/mol phase | solid (at STP) | melting point | 240 °C | density | 1 g/cm^3 | odor | odorless |
Units