Input interpretation
KNO_3 potassium nitrate + K_2CO_3 pearl ash + CrO_2 magtrieve™ ⟶ CO_2 carbon dioxide + K_2CrO_4 potassium chromate + KNO_2 potassium nitrite
Balanced equation
Balance the chemical equation algebraically: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KNO_3 + c_2 K_2CO_3 + c_3 CrO_2 ⟶ c_4 CO_2 + c_5 K_2CrO_4 + c_6 KNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, N, O, C and Cr: K: | c_1 + 2 c_2 = 2 c_5 + c_6 N: | c_1 = c_6 O: | 3 c_1 + 3 c_2 + 2 c_3 = 2 c_4 + 4 c_5 + 2 c_6 C: | c_2 = c_4 Cr: | c_3 = c_5 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2
Structures
+ + CrO_2 ⟶ + +
Names
potassium nitrate + pearl ash + magtrieve™ ⟶ carbon dioxide + potassium chromate + potassium nitrite
Equilibrium constant
![Construct the equilibrium constant, K, expression for: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 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: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 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 KNO_3 | 1 | -1 K_2CO_3 | 1 | -1 CrO_2 | 1 | -1 CO_2 | 1 | 1 K_2CrO_4 | 1 | 1 KNO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KNO_3 | 1 | -1 | ([KNO3])^(-1) K_2CO_3 | 1 | -1 | ([K2CO3])^(-1) CrO_2 | 1 | -1 | ([CrO2])^(-1) CO_2 | 1 | 1 | [CO2] K_2CrO_4 | 1 | 1 | [K2CrO4] KNO_2 | 1 | 1 | [KNO2] 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 = ([KNO3])^(-1) ([K2CO3])^(-1) ([CrO2])^(-1) [CO2] [K2CrO4] [KNO2] = ([CO2] [K2CrO4] [KNO2])/([KNO3] [K2CO3] [CrO2])](../image_source/5f54b81454388a11c2e78b6063a2d8a6.png)
Construct the equilibrium constant, K, expression for: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 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: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 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 KNO_3 | 1 | -1 K_2CO_3 | 1 | -1 CrO_2 | 1 | -1 CO_2 | 1 | 1 K_2CrO_4 | 1 | 1 KNO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KNO_3 | 1 | -1 | ([KNO3])^(-1) K_2CO_3 | 1 | -1 | ([K2CO3])^(-1) CrO_2 | 1 | -1 | ([CrO2])^(-1) CO_2 | 1 | 1 | [CO2] K_2CrO_4 | 1 | 1 | [K2CrO4] KNO_2 | 1 | 1 | [KNO2] 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 = ([KNO3])^(-1) ([K2CO3])^(-1) ([CrO2])^(-1) [CO2] [K2CrO4] [KNO2] = ([CO2] [K2CrO4] [KNO2])/([KNO3] [K2CO3] [CrO2])
Rate of reaction
![Construct the rate of reaction expression for: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 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: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 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 KNO_3 | 1 | -1 K_2CO_3 | 1 | -1 CrO_2 | 1 | -1 CO_2 | 1 | 1 K_2CrO_4 | 1 | 1 KNO_2 | 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 KNO_3 | 1 | -1 | -(Δ[KNO3])/(Δt) K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) CrO_2 | 1 | -1 | -(Δ[CrO2])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) K_2CrO_4 | 1 | 1 | (Δ[K2CrO4])/(Δt) KNO_2 | 1 | 1 | (Δ[KNO2])/(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 = -(Δ[KNO3])/(Δt) = -(Δ[K2CO3])/(Δt) = -(Δ[CrO2])/(Δt) = (Δ[CO2])/(Δt) = (Δ[K2CrO4])/(Δt) = (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/d821a71433ab431602e49f8fd700ae91.png)
Construct the rate of reaction expression for: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 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: KNO_3 + K_2CO_3 + CrO_2 ⟶ CO_2 + K_2CrO_4 + KNO_2 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 KNO_3 | 1 | -1 K_2CO_3 | 1 | -1 CrO_2 | 1 | -1 CO_2 | 1 | 1 K_2CrO_4 | 1 | 1 KNO_2 | 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 KNO_3 | 1 | -1 | -(Δ[KNO3])/(Δt) K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) CrO_2 | 1 | -1 | -(Δ[CrO2])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) K_2CrO_4 | 1 | 1 | (Δ[K2CrO4])/(Δt) KNO_2 | 1 | 1 | (Δ[KNO2])/(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 = -(Δ[KNO3])/(Δt) = -(Δ[K2CO3])/(Δt) = -(Δ[CrO2])/(Δt) = (Δ[CO2])/(Δt) = (Δ[K2CrO4])/(Δt) = (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| potassium nitrate | pearl ash | magtrieve™ | carbon dioxide | potassium chromate | potassium nitrite formula | KNO_3 | K_2CO_3 | CrO_2 | CO_2 | K_2CrO_4 | KNO_2 Hill formula | KNO_3 | CK_2O_3 | CrO_2 | CO_2 | CrK_2O_4 | KNO_2 name | potassium nitrate | pearl ash | magtrieve™ | carbon dioxide | potassium chromate | potassium nitrite IUPAC name | potassium nitrate | dipotassium carbonate | | carbon dioxide | dipotassium dioxido-dioxochromium | potassium nitrite