Input interpretation
![C activated charcoal + As_2O_3 arsenic trioxide ⟶ CO_2 carbon dioxide + As gray arsenic](../image_source/2063f6be95b091ba8cd61efa86754dcd.png)
C activated charcoal + As_2O_3 arsenic trioxide ⟶ CO_2 carbon dioxide + As gray arsenic
Balanced equation
![Balance the chemical equation algebraically: C + As_2O_3 ⟶ CO_2 + As Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 As_2O_3 ⟶ c_3 CO_2 + c_4 As Set the number of atoms in the reactants equal to the number of atoms in the products for C, As and O: C: | c_1 = c_3 As: | 2 c_2 = c_4 O: | 3 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 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 C + 2 As_2O_3 ⟶ 3 CO_2 + 4 As](../image_source/0fc42fbcacff687d734429ddf64a7060.png)
Balance the chemical equation algebraically: C + As_2O_3 ⟶ CO_2 + As Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 As_2O_3 ⟶ c_3 CO_2 + c_4 As Set the number of atoms in the reactants equal to the number of atoms in the products for C, As and O: C: | c_1 = c_3 As: | 2 c_2 = c_4 O: | 3 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 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 C + 2 As_2O_3 ⟶ 3 CO_2 + 4 As
Structures
![+ ⟶ +](../image_source/6d9ab99bdf55ab19dcfdc21531f749d5.png)
+ ⟶ +
Names
![activated charcoal + arsenic trioxide ⟶ carbon dioxide + gray arsenic](../image_source/12dfc117034264047a13420ca48d60b1.png)
activated charcoal + arsenic trioxide ⟶ carbon dioxide + gray arsenic
Equilibrium constant
![Construct the equilibrium constant, K, expression for: C + As_2O_3 ⟶ CO_2 + As 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: 3 C + 2 As_2O_3 ⟶ 3 CO_2 + 4 As 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 | 3 | -3 As_2O_3 | 2 | -2 CO_2 | 3 | 3 As | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 3 | -3 | ([C])^(-3) As_2O_3 | 2 | -2 | ([As2O3])^(-2) CO_2 | 3 | 3 | ([CO2])^3 As | 4 | 4 | ([As])^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])^(-3) ([As2O3])^(-2) ([CO2])^3 ([As])^4 = (([CO2])^3 ([As])^4)/(([C])^3 ([As2O3])^2)](../image_source/f8ff3bbb4b2e45ed9519d2046a784ad0.png)
Construct the equilibrium constant, K, expression for: C + As_2O_3 ⟶ CO_2 + As 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: 3 C + 2 As_2O_3 ⟶ 3 CO_2 + 4 As 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 | 3 | -3 As_2O_3 | 2 | -2 CO_2 | 3 | 3 As | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 3 | -3 | ([C])^(-3) As_2O_3 | 2 | -2 | ([As2O3])^(-2) CO_2 | 3 | 3 | ([CO2])^3 As | 4 | 4 | ([As])^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])^(-3) ([As2O3])^(-2) ([CO2])^3 ([As])^4 = (([CO2])^3 ([As])^4)/(([C])^3 ([As2O3])^2)
Rate of reaction
![Construct the rate of reaction expression for: C + As_2O_3 ⟶ CO_2 + As 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: 3 C + 2 As_2O_3 ⟶ 3 CO_2 + 4 As 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 | 3 | -3 As_2O_3 | 2 | -2 CO_2 | 3 | 3 As | 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 | 3 | -3 | -1/3 (Δ[C])/(Δt) As_2O_3 | 2 | -2 | -1/2 (Δ[As2O3])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) As | 4 | 4 | 1/4 (Δ[As])/(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 = -1/3 (Δ[C])/(Δt) = -1/2 (Δ[As2O3])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/4 (Δ[As])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/d3b7bfe66ac5b934519d61d92299c295.png)
Construct the rate of reaction expression for: C + As_2O_3 ⟶ CO_2 + As 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: 3 C + 2 As_2O_3 ⟶ 3 CO_2 + 4 As 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 | 3 | -3 As_2O_3 | 2 | -2 CO_2 | 3 | 3 As | 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 | 3 | -3 | -1/3 (Δ[C])/(Δt) As_2O_3 | 2 | -2 | -1/2 (Δ[As2O3])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) As | 4 | 4 | 1/4 (Δ[As])/(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 = -1/3 (Δ[C])/(Δt) = -1/2 (Δ[As2O3])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/4 (Δ[As])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| activated charcoal | arsenic trioxide | carbon dioxide | gray arsenic formula | C | As_2O_3 | CO_2 | As name | activated charcoal | arsenic trioxide | carbon dioxide | gray arsenic IUPAC name | carbon | 2, 4, 5-trioxa-1, 3-diarsabicyclo[1.1.1]pentane | carbon dioxide | arsenic](../image_source/b8ced0b41486829c22ace11bfe42e152.png)
| activated charcoal | arsenic trioxide | carbon dioxide | gray arsenic formula | C | As_2O_3 | CO_2 | As name | activated charcoal | arsenic trioxide | carbon dioxide | gray arsenic IUPAC name | carbon | 2, 4, 5-trioxa-1, 3-diarsabicyclo[1.1.1]pentane | carbon dioxide | arsenic
Substance properties
![| activated charcoal | arsenic trioxide | carbon dioxide | gray arsenic molar mass | 12.011 g/mol | 197.84 g/mol | 44.009 g/mol | 74.921595 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 3550 °C | 312 °C | -56.56 °C (at triple point) | 817 °C boiling point | 4027 °C | 465 °C | -78.5 °C (at sublimation point) | 616 °C density | 2.26 g/cm^3 | 4.15 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 5.727 g/cm^3 solubility in water | insoluble | | | insoluble dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless](../image_source/f77e22f2a4b2fe3e5b5e76e50967e207.png)
| activated charcoal | arsenic trioxide | carbon dioxide | gray arsenic molar mass | 12.011 g/mol | 197.84 g/mol | 44.009 g/mol | 74.921595 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 3550 °C | 312 °C | -56.56 °C (at triple point) | 817 °C boiling point | 4027 °C | 465 °C | -78.5 °C (at sublimation point) | 616 °C density | 2.26 g/cm^3 | 4.15 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 5.727 g/cm^3 solubility in water | insoluble | | | insoluble dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless
Units