Rb + RbNO3 = N2 + Rb2O

Rb rubidium + RbNO_3 rubidium nitrate ⟶ N_2 nitrogen + Rb2O

Balance the chemical equation algebraically: Rb + RbNO_3 ⟶ N_2 + Rb2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Rb + c_2 RbNO_3 ⟶ c_3 N_2 + c_4 Rb2O Set the number of atoms in the reactants equal to the number of atoms in the products for Rb, N and O: Rb: | c_1 + c_2 = 2 c_4 N: | c_2 = 2 c_3 O: | 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 2 c_3 = 1 c_4 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 Rb + 2 RbNO_3 ⟶ N_2 + 6 Rb2O

+ ⟶ + Rb2O

rubidium + rubidium nitrate ⟶ nitrogen + Rb2O

Construct the equilibrium constant, K, expression for: Rb + RbNO_3 ⟶ N_2 + Rb2O 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 Rb + 2 RbNO_3 ⟶ N_2 + 6 Rb2O 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 Rb | 10 | -10 RbNO_3 | 2 | -2 N_2 | 1 | 1 Rb2O | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Rb | 10 | -10 | ([Rb])^(-10) RbNO_3 | 2 | -2 | ([RbNO3])^(-2) N_2 | 1 | 1 | [N2] Rb2O | 6 | 6 | ([Rb2O])^6 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 = ([Rb])^(-10) ([RbNO3])^(-2) [N2] ([Rb2O])^6 = ([N2] ([Rb2O])^6)/(([Rb])^10 ([RbNO3])^2)

Construct the rate of reaction expression for: Rb + RbNO_3 ⟶ N_2 + Rb2O 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 Rb + 2 RbNO_3 ⟶ N_2 + 6 Rb2O 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 Rb | 10 | -10 RbNO_3 | 2 | -2 N_2 | 1 | 1 Rb2O | 6 | 6 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 Rb | 10 | -10 | -1/10 (Δ[Rb])/(Δt) RbNO_3 | 2 | -2 | -1/2 (Δ[RbNO3])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) Rb2O | 6 | 6 | 1/6 (Δ[Rb2O])/(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[Rb])/(Δt) = -1/2 (Δ[RbNO3])/(Δt) = (Δ[N2])/(Δt) = 1/6 (Δ[Rb2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| rubidium | rubidium nitrate | nitrogen | Rb2O formula | Rb | RbNO_3 | N_2 | Rb2O Hill formula | Rb | NO_3Rb | N_2 | ORb2 name | rubidium | rubidium nitrate | nitrogen | IUPAC name | rubidium | rubidium(+1) cation nitrate | molecular nitrogen |

| rubidium | rubidium nitrate | nitrogen | Rb2O molar mass | 85.4678 g/mol | 147.47 g/mol | 28.014 g/mol | 186.935 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 38.5 °C | 310 °C | -210 °C | boiling point | 686 °C | 578 °C | -195.79 °C | density | 1.53 g/cm^3 | 3.11 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | solubility in water | reacts | | insoluble | surface tension | | | 0.0066 N/m | dynamic viscosity | | | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless |