Input interpretation
![H_2SO_4 (sulfuric acid) + P (red phosphorus) ⟶ H_2O (water) + SO_2 (sulfur dioxide) + H_3PO_4 (phosphoric acid)](../image_source/6da09fc7a82ff0a765afb998f6e67810.png)
H_2SO_4 (sulfuric acid) + P (red phosphorus) ⟶ H_2O (water) + SO_2 (sulfur dioxide) + H_3PO_4 (phosphoric acid)
Balanced equation
![Balance the chemical equation algebraically: H_2SO_4 + P ⟶ H_2O + SO_2 + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 P ⟶ c_3 H_2O + c_4 SO_2 + c_5 H_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and P: H: | 2 c_1 = 2 c_3 + 3 c_5 O: | 4 c_1 = c_3 + 2 c_4 + 4 c_5 S: | c_1 = c_4 P: | c_2 = c_5 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 = 1 c_4 = 5/2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 2 c_3 = 2 c_4 = 5 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2SO_4 + 2 P ⟶ 2 H_2O + 5 SO_2 + 2 H_3PO_4](../image_source/a1e260dadb3078b964eeabc644390ef2.png)
Balance the chemical equation algebraically: H_2SO_4 + P ⟶ H_2O + SO_2 + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 P ⟶ c_3 H_2O + c_4 SO_2 + c_5 H_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and P: H: | 2 c_1 = 2 c_3 + 3 c_5 O: | 4 c_1 = c_3 + 2 c_4 + 4 c_5 S: | c_1 = c_4 P: | c_2 = c_5 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 = 1 c_4 = 5/2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 2 c_3 = 2 c_4 = 5 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2SO_4 + 2 P ⟶ 2 H_2O + 5 SO_2 + 2 H_3PO_4
Structures
![+ ⟶ + +](../image_source/6b9297d497abac84ad89e211ebde1ffa.png)
+ ⟶ + +
Names
![sulfuric acid + red phosphorus ⟶ water + sulfur dioxide + phosphoric acid](../image_source/eb38a6cbeceb8e3bdfe7b1657ccac17b.png)
sulfuric acid + red phosphorus ⟶ water + sulfur dioxide + phosphoric acid
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + P ⟶ H_2O + SO_2 + H_3PO_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: 5 H_2SO_4 + 2 P ⟶ 2 H_2O + 5 SO_2 + 2 H_3PO_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 | 5 | -5 P | 2 | -2 H_2O | 2 | 2 SO_2 | 5 | 5 H_3PO_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 | 5 | -5 | ([H2SO4])^(-5) P | 2 | -2 | ([P])^(-2) H_2O | 2 | 2 | ([H2O])^2 SO_2 | 5 | 5 | ([SO2])^5 H_3PO_4 | 2 | 2 | ([H3PO4])^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])^(-5) ([P])^(-2) ([H2O])^2 ([SO2])^5 ([H3PO4])^2 = (([H2O])^2 ([SO2])^5 ([H3PO4])^2)/(([H2SO4])^5 ([P])^2)](../image_source/89c34d14d41cd0ca0c7f83885b70faef.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + P ⟶ H_2O + SO_2 + H_3PO_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: 5 H_2SO_4 + 2 P ⟶ 2 H_2O + 5 SO_2 + 2 H_3PO_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 | 5 | -5 P | 2 | -2 H_2O | 2 | 2 SO_2 | 5 | 5 H_3PO_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 | 5 | -5 | ([H2SO4])^(-5) P | 2 | -2 | ([P])^(-2) H_2O | 2 | 2 | ([H2O])^2 SO_2 | 5 | 5 | ([SO2])^5 H_3PO_4 | 2 | 2 | ([H3PO4])^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])^(-5) ([P])^(-2) ([H2O])^2 ([SO2])^5 ([H3PO4])^2 = (([H2O])^2 ([SO2])^5 ([H3PO4])^2)/(([H2SO4])^5 ([P])^2)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + P ⟶ H_2O + SO_2 + H_3PO_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: 5 H_2SO_4 + 2 P ⟶ 2 H_2O + 5 SO_2 + 2 H_3PO_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 | 5 | -5 P | 2 | -2 H_2O | 2 | 2 SO_2 | 5 | 5 H_3PO_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 | 5 | -5 | -1/5 (Δ[H2SO4])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) SO_2 | 5 | 5 | 1/5 (Δ[SO2])/(Δt) H_3PO_4 | 2 | 2 | 1/2 (Δ[H3PO4])/(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[H2SO4])/(Δt) = -1/2 (Δ[P])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/5 (Δ[SO2])/(Δt) = 1/2 (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/5815e9011567ec5be364e8b0b2b02062.png)
Construct the rate of reaction expression for: H_2SO_4 + P ⟶ H_2O + SO_2 + H_3PO_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: 5 H_2SO_4 + 2 P ⟶ 2 H_2O + 5 SO_2 + 2 H_3PO_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 | 5 | -5 P | 2 | -2 H_2O | 2 | 2 SO_2 | 5 | 5 H_3PO_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 | 5 | -5 | -1/5 (Δ[H2SO4])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) SO_2 | 5 | 5 | 1/5 (Δ[SO2])/(Δt) H_3PO_4 | 2 | 2 | 1/2 (Δ[H3PO4])/(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[H2SO4])/(Δt) = -1/2 (Δ[P])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/5 (Δ[SO2])/(Δt) = 1/2 (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfuric acid | red phosphorus | water | sulfur dioxide | phosphoric acid formula | H_2SO_4 | P | H_2O | SO_2 | H_3PO_4 Hill formula | H_2O_4S | P | H_2O | O_2S | H_3O_4P name | sulfuric acid | red phosphorus | water | sulfur dioxide | phosphoric acid IUPAC name | sulfuric acid | phosphorus | water | sulfur dioxide | phosphoric acid](../image_source/4f1988b09365db2b866bbd8536015486.png)
| sulfuric acid | red phosphorus | water | sulfur dioxide | phosphoric acid formula | H_2SO_4 | P | H_2O | SO_2 | H_3PO_4 Hill formula | H_2O_4S | P | H_2O | O_2S | H_3O_4P name | sulfuric acid | red phosphorus | water | sulfur dioxide | phosphoric acid IUPAC name | sulfuric acid | phosphorus | water | sulfur dioxide | phosphoric acid
Substance properties
![| sulfuric acid | red phosphorus | water | sulfur dioxide | phosphoric acid molar mass | 98.07 g/mol | 30.973761998 g/mol | 18.015 g/mol | 64.06 g/mol | 97.994 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | liquid (at STP) melting point | 10.371 °C | 579.2 °C | 0 °C | -73 °C | 42.4 °C boiling point | 279.6 °C | | 99.9839 °C | -10 °C | 158 °C density | 1.8305 g/cm^3 | 2.16 g/cm^3 | 1 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 1.685 g/cm^3 solubility in water | very soluble | insoluble | | | very soluble surface tension | 0.0735 N/m | | 0.0728 N/m | 0.02859 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.282×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | | odorless](../image_source/5c340128959b72049d1ce96b5eaa16cd.png)
| sulfuric acid | red phosphorus | water | sulfur dioxide | phosphoric acid molar mass | 98.07 g/mol | 30.973761998 g/mol | 18.015 g/mol | 64.06 g/mol | 97.994 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | liquid (at STP) melting point | 10.371 °C | 579.2 °C | 0 °C | -73 °C | 42.4 °C boiling point | 279.6 °C | | 99.9839 °C | -10 °C | 158 °C density | 1.8305 g/cm^3 | 2.16 g/cm^3 | 1 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 1.685 g/cm^3 solubility in water | very soluble | insoluble | | | very soluble surface tension | 0.0735 N/m | | 0.0728 N/m | 0.02859 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.282×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | | odorless
Units