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H2O + O2 + Au + KCN = KOH + KAu(CN)4

Input interpretation

H_2O water + O_2 oxygen + Au gold + KCN potassium cyanide ⟶ KOH potassium hydroxide + KAu(CN)4
H_2O water + O_2 oxygen + Au gold + KCN potassium cyanide ⟶ KOH potassium hydroxide + KAu(CN)4

Balanced equation

Balance the chemical equation algebraically: H_2O + O_2 + Au + KCN ⟶ KOH + KAu(CN)4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Au + c_4 KCN ⟶ c_5 KOH + c_6 KAu(CN)4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Au, C, K and N: H: | 2 c_1 = c_5 O: | c_1 + 2 c_2 = c_5 Au: | c_3 = c_6 C: | c_4 = 4 c_6 K: | c_4 = c_5 + c_6 N: | c_4 = 4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 4/3 c_4 = 16/3 c_5 = 4 c_6 = 4/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 6 c_2 = 3 c_3 = 4 c_4 = 16 c_5 = 12 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 3 O_2 + 4 Au + 16 KCN ⟶ 12 KOH + 4 KAu(CN)4
Balance the chemical equation algebraically: H_2O + O_2 + Au + KCN ⟶ KOH + KAu(CN)4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Au + c_4 KCN ⟶ c_5 KOH + c_6 KAu(CN)4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Au, C, K and N: H: | 2 c_1 = c_5 O: | c_1 + 2 c_2 = c_5 Au: | c_3 = c_6 C: | c_4 = 4 c_6 K: | c_4 = c_5 + c_6 N: | c_4 = 4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 4/3 c_4 = 16/3 c_5 = 4 c_6 = 4/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 6 c_2 = 3 c_3 = 4 c_4 = 16 c_5 = 12 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 3 O_2 + 4 Au + 16 KCN ⟶ 12 KOH + 4 KAu(CN)4

Structures

+ + + ⟶ + KAu(CN)4
+ + + ⟶ + KAu(CN)4

Names

water + oxygen + gold + potassium cyanide ⟶ potassium hydroxide + KAu(CN)4
water + oxygen + gold + potassium cyanide ⟶ potassium hydroxide + KAu(CN)4

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + O_2 + Au + KCN ⟶ KOH + KAu(CN)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: 6 H_2O + 3 O_2 + 4 Au + 16 KCN ⟶ 12 KOH + 4 KAu(CN)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_2O | 6 | -6 O_2 | 3 | -3 Au | 4 | -4 KCN | 16 | -16 KOH | 12 | 12 KAu(CN)4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) O_2 | 3 | -3 | ([O2])^(-3) Au | 4 | -4 | ([Au])^(-4) KCN | 16 | -16 | ([KCN])^(-16) KOH | 12 | 12 | ([KOH])^12 KAu(CN)4 | 4 | 4 | ([KAu(CN)4])^4 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 = ([H2O])^(-6) ([O2])^(-3) ([Au])^(-4) ([KCN])^(-16) ([KOH])^12 ([KAu(CN)4])^4 = (([KOH])^12 ([KAu(CN)4])^4)/(([H2O])^6 ([O2])^3 ([Au])^4 ([KCN])^16)
Construct the equilibrium constant, K, expression for: H_2O + O_2 + Au + KCN ⟶ KOH + KAu(CN)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: 6 H_2O + 3 O_2 + 4 Au + 16 KCN ⟶ 12 KOH + 4 KAu(CN)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_2O | 6 | -6 O_2 | 3 | -3 Au | 4 | -4 KCN | 16 | -16 KOH | 12 | 12 KAu(CN)4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) O_2 | 3 | -3 | ([O2])^(-3) Au | 4 | -4 | ([Au])^(-4) KCN | 16 | -16 | ([KCN])^(-16) KOH | 12 | 12 | ([KOH])^12 KAu(CN)4 | 4 | 4 | ([KAu(CN)4])^4 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 = ([H2O])^(-6) ([O2])^(-3) ([Au])^(-4) ([KCN])^(-16) ([KOH])^12 ([KAu(CN)4])^4 = (([KOH])^12 ([KAu(CN)4])^4)/(([H2O])^6 ([O2])^3 ([Au])^4 ([KCN])^16)

Rate of reaction

Construct the rate of reaction expression for: H_2O + O_2 + Au + KCN ⟶ KOH + KAu(CN)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: 6 H_2O + 3 O_2 + 4 Au + 16 KCN ⟶ 12 KOH + 4 KAu(CN)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_2O | 6 | -6 O_2 | 3 | -3 Au | 4 | -4 KCN | 16 | -16 KOH | 12 | 12 KAu(CN)4 | 4 | 4 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_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) Au | 4 | -4 | -1/4 (Δ[Au])/(Δt) KCN | 16 | -16 | -1/16 (Δ[KCN])/(Δt) KOH | 12 | 12 | 1/12 (Δ[KOH])/(Δt) KAu(CN)4 | 4 | 4 | 1/4 (Δ[KAu(CN)4])/(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[H2O])/(Δt) = -1/3 (Δ[O2])/(Δt) = -1/4 (Δ[Au])/(Δt) = -1/16 (Δ[KCN])/(Δt) = 1/12 (Δ[KOH])/(Δt) = 1/4 (Δ[KAu(CN)4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + O_2 + Au + KCN ⟶ KOH + KAu(CN)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: 6 H_2O + 3 O_2 + 4 Au + 16 KCN ⟶ 12 KOH + 4 KAu(CN)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_2O | 6 | -6 O_2 | 3 | -3 Au | 4 | -4 KCN | 16 | -16 KOH | 12 | 12 KAu(CN)4 | 4 | 4 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_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) Au | 4 | -4 | -1/4 (Δ[Au])/(Δt) KCN | 16 | -16 | -1/16 (Δ[KCN])/(Δt) KOH | 12 | 12 | 1/12 (Δ[KOH])/(Δt) KAu(CN)4 | 4 | 4 | 1/4 (Δ[KAu(CN)4])/(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[H2O])/(Δt) = -1/3 (Δ[O2])/(Δt) = -1/4 (Δ[Au])/(Δt) = -1/16 (Δ[KCN])/(Δt) = 1/12 (Δ[KOH])/(Δt) = 1/4 (Δ[KAu(CN)4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | oxygen | gold | potassium cyanide | potassium hydroxide | KAu(CN)4 formula | H_2O | O_2 | Au | KCN | KOH | KAu(CN)4 Hill formula | H_2O | O_2 | Au | CKN | HKO | C4AuKN4 name | water | oxygen | gold | potassium cyanide | potassium hydroxide | IUPAC name | water | molecular oxygen | gold | potassium cyanide | potassium hydroxide |
| water | oxygen | gold | potassium cyanide | potassium hydroxide | KAu(CN)4 formula | H_2O | O_2 | Au | KCN | KOH | KAu(CN)4 Hill formula | H_2O | O_2 | Au | CKN | HKO | C4AuKN4 name | water | oxygen | gold | potassium cyanide | potassium hydroxide | IUPAC name | water | molecular oxygen | gold | potassium cyanide | potassium hydroxide |

Substance properties

| water | oxygen | gold | potassium cyanide | potassium hydroxide | KAu(CN)4 molar mass | 18.015 g/mol | 31.998 g/mol | 196.966569 g/mol | 65.116 g/mol | 56.105 g/mol | 340.14 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | | solid (at STP) | melting point | 0 °C | -218 °C | 1063 °C | | 406 °C | boiling point | 99.9839 °C | -183 °C | 2856 °C | | 1327 °C | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 19.3 g/cm^3 | | 2.044 g/cm^3 | solubility in water | | | insoluble | | soluble | surface tension | 0.0728 N/m | 0.01347 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | | 0.001 Pa s (at 550 °C) | odor | odorless | odorless | | | |
| water | oxygen | gold | potassium cyanide | potassium hydroxide | KAu(CN)4 molar mass | 18.015 g/mol | 31.998 g/mol | 196.966569 g/mol | 65.116 g/mol | 56.105 g/mol | 340.14 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | | solid (at STP) | melting point | 0 °C | -218 °C | 1063 °C | | 406 °C | boiling point | 99.9839 °C | -183 °C | 2856 °C | | 1327 °C | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 19.3 g/cm^3 | | 2.044 g/cm^3 | solubility in water | | | insoluble | | soluble | surface tension | 0.0728 N/m | 0.01347 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | | 0.001 Pa s (at 550 °C) | odor | odorless | odorless | | | |

Units

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