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H2SO4 + Cl2O7 = SO3 + HClO4

Input interpretation

H_2SO_4 sulfuric acid + Cl_2O_7 dichlorine heptoxide ⟶ SO_3 sulfur trioxide + HClO_4 perchloric acid
H_2SO_4 sulfuric acid + Cl_2O_7 dichlorine heptoxide ⟶ SO_3 sulfur trioxide + HClO_4 perchloric acid

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + HClO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Cl_2O_7 ⟶ c_3 SO_3 + c_4 HClO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cl: H: | 2 c_1 = c_4 O: | 4 c_1 + 7 c_2 = 3 c_3 + 4 c_4 S: | c_1 = c_3 Cl: | 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + Cl_2O_7 ⟶ SO_3 + 2 HClO_4
Balance the chemical equation algebraically: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + HClO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Cl_2O_7 ⟶ c_3 SO_3 + c_4 HClO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cl: H: | 2 c_1 = c_4 O: | 4 c_1 + 7 c_2 = 3 c_3 + 4 c_4 S: | c_1 = c_3 Cl: | 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + Cl_2O_7 ⟶ SO_3 + 2 HClO_4

Structures

+ ⟶ +
+ ⟶ +

Names

sulfuric acid + dichlorine heptoxide ⟶ sulfur trioxide + perchloric acid
sulfuric acid + dichlorine heptoxide ⟶ sulfur trioxide + perchloric acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + HClO_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: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + 2 HClO_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_2SO_4 | 1 | -1 Cl_2O_7 | 1 | -1 SO_3 | 1 | 1 HClO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) Cl_2O_7 | 1 | -1 | ([Cl2O7])^(-1) SO_3 | 1 | 1 | [SO3] HClO_4 | 2 | 2 | ([HClO4])^2 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 = ([H2SO4])^(-1) ([Cl2O7])^(-1) [SO3] ([HClO4])^2 = ([SO3] ([HClO4])^2)/([H2SO4] [Cl2O7])
Construct the equilibrium constant, K, expression for: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + HClO_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: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + 2 HClO_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_2SO_4 | 1 | -1 Cl_2O_7 | 1 | -1 SO_3 | 1 | 1 HClO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) Cl_2O_7 | 1 | -1 | ([Cl2O7])^(-1) SO_3 | 1 | 1 | [SO3] HClO_4 | 2 | 2 | ([HClO4])^2 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 = ([H2SO4])^(-1) ([Cl2O7])^(-1) [SO3] ([HClO4])^2 = ([SO3] ([HClO4])^2)/([H2SO4] [Cl2O7])

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + HClO_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: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + 2 HClO_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_2SO_4 | 1 | -1 Cl_2O_7 | 1 | -1 SO_3 | 1 | 1 HClO_4 | 2 | 2 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_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) Cl_2O_7 | 1 | -1 | -(Δ[Cl2O7])/(Δt) SO_3 | 1 | 1 | (Δ[SO3])/(Δt) HClO_4 | 2 | 2 | 1/2 (Δ[HClO4])/(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 = -(Δ[H2SO4])/(Δt) = -(Δ[Cl2O7])/(Δt) = (Δ[SO3])/(Δt) = 1/2 (Δ[HClO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + HClO_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: H_2SO_4 + Cl_2O_7 ⟶ SO_3 + 2 HClO_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_2SO_4 | 1 | -1 Cl_2O_7 | 1 | -1 SO_3 | 1 | 1 HClO_4 | 2 | 2 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_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) Cl_2O_7 | 1 | -1 | -(Δ[Cl2O7])/(Δt) SO_3 | 1 | 1 | (Δ[SO3])/(Δt) HClO_4 | 2 | 2 | 1/2 (Δ[HClO4])/(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 = -(Δ[H2SO4])/(Δt) = -(Δ[Cl2O7])/(Δt) = (Δ[SO3])/(Δt) = 1/2 (Δ[HClO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | dichlorine heptoxide | sulfur trioxide | perchloric acid formula | H_2SO_4 | Cl_2O_7 | SO_3 | HClO_4 Hill formula | H_2O_4S | Cl_2O_7 | O_3S | ClHO_4 name | sulfuric acid | dichlorine heptoxide | sulfur trioxide | perchloric acid IUPAC name | sulfuric acid | perchloryl perchlorate | sulfur trioxide | perchloric acid
| sulfuric acid | dichlorine heptoxide | sulfur trioxide | perchloric acid formula | H_2SO_4 | Cl_2O_7 | SO_3 | HClO_4 Hill formula | H_2O_4S | Cl_2O_7 | O_3S | ClHO_4 name | sulfuric acid | dichlorine heptoxide | sulfur trioxide | perchloric acid IUPAC name | sulfuric acid | perchloryl perchlorate | sulfur trioxide | perchloric acid

Substance properties

| sulfuric acid | dichlorine heptoxide | sulfur trioxide | perchloric acid molar mass | 98.07 g/mol | 182.9 g/mol | 80.06 g/mol | 100.5 g/mol phase | liquid (at STP) | | liquid (at STP) | liquid (at STP) melting point | 10.371 °C | -91.5 °C | 16.8 °C | -112 °C boiling point | 279.6 °C | 82 °C | 44.7 °C | 90 °C density | 1.8305 g/cm^3 | 1.9 g/cm^3 | 1.97 g/cm^3 | 1.77 g/cm^3 solubility in water | very soluble | reacts | reacts | very soluble surface tension | 0.0735 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 0.00159 Pa s (at 30 °C) | 8×10^-4 Pa s (at 25 °C) odor | odorless | | | odorless
| sulfuric acid | dichlorine heptoxide | sulfur trioxide | perchloric acid molar mass | 98.07 g/mol | 182.9 g/mol | 80.06 g/mol | 100.5 g/mol phase | liquid (at STP) | | liquid (at STP) | liquid (at STP) melting point | 10.371 °C | -91.5 °C | 16.8 °C | -112 °C boiling point | 279.6 °C | 82 °C | 44.7 °C | 90 °C density | 1.8305 g/cm^3 | 1.9 g/cm^3 | 1.97 g/cm^3 | 1.77 g/cm^3 solubility in water | very soluble | reacts | reacts | very soluble surface tension | 0.0735 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 0.00159 Pa s (at 30 °C) | 8×10^-4 Pa s (at 25 °C) odor | odorless | | | odorless

Units

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