C + P2O5 = CO2 + P

C activated charcoal + P2O5 ⟶ CO_2 carbon dioxide + P red phosphorus

Balance the chemical equation algebraically: C + P2O5 ⟶ CO_2 + P Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 P2O5 ⟶ c_3 CO_2 + c_4 P Set the number of atoms in the reactants equal to the number of atoms in the products for C, P and O: C: | c_1 = c_3 P: | 2 c_2 = c_4 O: | 5 c_2 = 2 c_3 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 = 5/2 c_2 = 1 c_3 = 5/2 c_4 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 2 c_3 = 5 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 C + 2 P2O5 ⟶ 5 CO_2 + 4 P

+ P2O5 ⟶ +

activated charcoal + P2O5 ⟶ carbon dioxide + red phosphorus

Construct the equilibrium constant, K, expression for: C + P2O5 ⟶ CO_2 + P 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: 5 C + 2 P2O5 ⟶ 5 CO_2 + 4 P 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 C | 5 | -5 P2O5 | 2 | -2 CO_2 | 5 | 5 P | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 5 | -5 | ([C])^(-5) P2O5 | 2 | -2 | ([P2O5])^(-2) CO_2 | 5 | 5 | ([CO2])^5 P | 4 | 4 | ([P])^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 = ([C])^(-5) ([P2O5])^(-2) ([CO2])^5 ([P])^4 = (([CO2])^5 ([P])^4)/(([C])^5 ([P2O5])^2)

Construct the rate of reaction expression for: C + P2O5 ⟶ CO_2 + P 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: 5 C + 2 P2O5 ⟶ 5 CO_2 + 4 P 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 C | 5 | -5 P2O5 | 2 | -2 CO_2 | 5 | 5 P | 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 C | 5 | -5 | -1/5 (Δ[C])/(Δt) P2O5 | 2 | -2 | -1/2 (Δ[P2O5])/(Δt) CO_2 | 5 | 5 | 1/5 (Δ[CO2])/(Δt) P | 4 | 4 | 1/4 (Δ[P])/(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 = -1/5 (Δ[C])/(Δt) = -1/2 (Δ[P2O5])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/4 (Δ[P])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | P2O5 | carbon dioxide | red phosphorus formula | C | P2O5 | CO_2 | P Hill formula | C | O5P2 | CO_2 | P name | activated charcoal | | carbon dioxide | red phosphorus IUPAC name | carbon | | carbon dioxide | phosphorus

| activated charcoal | P2O5 | carbon dioxide | red phosphorus molar mass | 12.011 g/mol | 141.94 g/mol | 44.009 g/mol | 30.973761998 g/mol phase | solid (at STP) | | gas (at STP) | solid (at STP) melting point | 3550 °C | | -56.56 °C (at triple point) | 579.2 °C boiling point | 4027 °C | | -78.5 °C (at sublimation point) | density | 2.26 g/cm^3 | | 0.00184212 g/cm^3 (at 20 °C) | 2.16 g/cm^3 solubility in water | insoluble | | | insoluble dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 20.2 °C) odor | | | odorless |