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HNO3 + Cd = H2O + Cd(NO3)2 + (NH4)(NO3)

Input interpretation

HNO_3 nitric acid + Cd cadmium ⟶ H_2O water + Cd(NO3)2 + NH_4NO_3 ammonium nitrate
HNO_3 nitric acid + Cd cadmium ⟶ H_2O water + Cd(NO3)2 + NH_4NO_3 ammonium nitrate

Balanced equation

Balance the chemical equation algebraically: HNO_3 + Cd ⟶ H_2O + Cd(NO3)2 + NH_4NO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Cd ⟶ c_3 H_2O + c_4 Cd(NO3)2 + c_5 NH_4NO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Cd: H: | c_1 = 2 c_3 + 4 c_5 N: | c_1 = 2 c_4 + 2 c_5 O: | 3 c_1 = c_3 + 6 c_4 + 3 c_5 Cd: | c_2 = c_4 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_1 = 10 c_2 = 4 c_3 = 3 c_4 = 4 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + 4 Cd ⟶ 3 H_2O + 4 Cd(NO3)2 + NH_4NO_3
Balance the chemical equation algebraically: HNO_3 + Cd ⟶ H_2O + Cd(NO3)2 + NH_4NO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Cd ⟶ c_3 H_2O + c_4 Cd(NO3)2 + c_5 NH_4NO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Cd: H: | c_1 = 2 c_3 + 4 c_5 N: | c_1 = 2 c_4 + 2 c_5 O: | 3 c_1 = c_3 + 6 c_4 + 3 c_5 Cd: | c_2 = c_4 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_1 = 10 c_2 = 4 c_3 = 3 c_4 = 4 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + 4 Cd ⟶ 3 H_2O + 4 Cd(NO3)2 + NH_4NO_3

Structures

+ ⟶ + Cd(NO3)2 +
+ ⟶ + Cd(NO3)2 +

Names

nitric acid + cadmium ⟶ water + Cd(NO3)2 + ammonium nitrate
nitric acid + cadmium ⟶ water + Cd(NO3)2 + ammonium nitrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + Cd ⟶ H_2O + Cd(NO3)2 + NH_4NO_3 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: 10 HNO_3 + 4 Cd ⟶ 3 H_2O + 4 Cd(NO3)2 + NH_4NO_3 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 HNO_3 | 10 | -10 Cd | 4 | -4 H_2O | 3 | 3 Cd(NO3)2 | 4 | 4 NH_4NO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 10 | -10 | ([HNO3])^(-10) Cd | 4 | -4 | ([Cd])^(-4) H_2O | 3 | 3 | ([H2O])^3 Cd(NO3)2 | 4 | 4 | ([Cd(NO3)2])^4 NH_4NO_3 | 1 | 1 | [NH4NO3] 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 = ([HNO3])^(-10) ([Cd])^(-4) ([H2O])^3 ([Cd(NO3)2])^4 [NH4NO3] = (([H2O])^3 ([Cd(NO3)2])^4 [NH4NO3])/(([HNO3])^10 ([Cd])^4)
Construct the equilibrium constant, K, expression for: HNO_3 + Cd ⟶ H_2O + Cd(NO3)2 + NH_4NO_3 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: 10 HNO_3 + 4 Cd ⟶ 3 H_2O + 4 Cd(NO3)2 + NH_4NO_3 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 HNO_3 | 10 | -10 Cd | 4 | -4 H_2O | 3 | 3 Cd(NO3)2 | 4 | 4 NH_4NO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 10 | -10 | ([HNO3])^(-10) Cd | 4 | -4 | ([Cd])^(-4) H_2O | 3 | 3 | ([H2O])^3 Cd(NO3)2 | 4 | 4 | ([Cd(NO3)2])^4 NH_4NO_3 | 1 | 1 | [NH4NO3] 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 = ([HNO3])^(-10) ([Cd])^(-4) ([H2O])^3 ([Cd(NO3)2])^4 [NH4NO3] = (([H2O])^3 ([Cd(NO3)2])^4 [NH4NO3])/(([HNO3])^10 ([Cd])^4)

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + Cd ⟶ H_2O + Cd(NO3)2 + NH_4NO_3 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: 10 HNO_3 + 4 Cd ⟶ 3 H_2O + 4 Cd(NO3)2 + NH_4NO_3 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 HNO_3 | 10 | -10 Cd | 4 | -4 H_2O | 3 | 3 Cd(NO3)2 | 4 | 4 NH_4NO_3 | 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 HNO_3 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) Cd | 4 | -4 | -1/4 (Δ[Cd])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Cd(NO3)2 | 4 | 4 | 1/4 (Δ[Cd(NO3)2])/(Δt) NH_4NO_3 | 1 | 1 | (Δ[NH4NO3])/(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 = -1/10 (Δ[HNO3])/(Δt) = -1/4 (Δ[Cd])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/4 (Δ[Cd(NO3)2])/(Δt) = (Δ[NH4NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + Cd ⟶ H_2O + Cd(NO3)2 + NH_4NO_3 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: 10 HNO_3 + 4 Cd ⟶ 3 H_2O + 4 Cd(NO3)2 + NH_4NO_3 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 HNO_3 | 10 | -10 Cd | 4 | -4 H_2O | 3 | 3 Cd(NO3)2 | 4 | 4 NH_4NO_3 | 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 HNO_3 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) Cd | 4 | -4 | -1/4 (Δ[Cd])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Cd(NO3)2 | 4 | 4 | 1/4 (Δ[Cd(NO3)2])/(Δt) NH_4NO_3 | 1 | 1 | (Δ[NH4NO3])/(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 = -1/10 (Δ[HNO3])/(Δt) = -1/4 (Δ[Cd])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/4 (Δ[Cd(NO3)2])/(Δt) = (Δ[NH4NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | cadmium | water | Cd(NO3)2 | ammonium nitrate formula | HNO_3 | Cd | H_2O | Cd(NO3)2 | NH_4NO_3 Hill formula | HNO_3 | Cd | H_2O | CdN2O6 | H_4N_2O_3 name | nitric acid | cadmium | water | | ammonium nitrate
| nitric acid | cadmium | water | Cd(NO3)2 | ammonium nitrate formula | HNO_3 | Cd | H_2O | Cd(NO3)2 | NH_4NO_3 Hill formula | HNO_3 | Cd | H_2O | CdN2O6 | H_4N_2O_3 name | nitric acid | cadmium | water | | ammonium nitrate

Substance properties

| nitric acid | cadmium | water | Cd(NO3)2 | ammonium nitrate molar mass | 63.012 g/mol | 112.414 g/mol | 18.015 g/mol | 236.42 g/mol | 80.04 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | | solid (at STP) melting point | -41.6 °C | 320.9 °C | 0 °C | | 169 °C boiling point | 83 °C | 765 °C | 99.9839 °C | | 210 °C density | 1.5129 g/cm^3 | 8.65 g/cm^3 | 1 g/cm^3 | | 1.73 g/cm^3 solubility in water | miscible | insoluble | | | surface tension | | | 0.0728 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | odorless | | odorless
| nitric acid | cadmium | water | Cd(NO3)2 | ammonium nitrate molar mass | 63.012 g/mol | 112.414 g/mol | 18.015 g/mol | 236.42 g/mol | 80.04 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | | solid (at STP) melting point | -41.6 °C | 320.9 °C | 0 °C | | 169 °C boiling point | 83 °C | 765 °C | 99.9839 °C | | 210 °C density | 1.5129 g/cm^3 | 8.65 g/cm^3 | 1 g/cm^3 | | 1.73 g/cm^3 solubility in water | miscible | insoluble | | | surface tension | | | 0.0728 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | odorless | | odorless

Units

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