Input interpretation
![H_2SO_4 sulfuric acid + Cr chromium ⟶ H_2 hydrogen + Cr_2(SO_4)_3 chromium sulfate](../image_source/f293f5c15c98bc45635c49a61d936d37.png)
H_2SO_4 sulfuric acid + Cr chromium ⟶ H_2 hydrogen + Cr_2(SO_4)_3 chromium sulfate
Balanced equation
![Balance the chemical equation algebraically: H_2SO_4 + Cr ⟶ H_2 + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Cr ⟶ c_3 H_2 + c_4 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cr: H: | 2 c_1 = 2 c_3 O: | 4 c_1 = 12 c_4 S: | c_1 = 3 c_4 Cr: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 Cr ⟶ 3 H_2 + Cr_2(SO_4)_3](../image_source/937d0958fa90601413fe3c426fd5c989.png)
Balance the chemical equation algebraically: H_2SO_4 + Cr ⟶ H_2 + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Cr ⟶ c_3 H_2 + c_4 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cr: H: | 2 c_1 = 2 c_3 O: | 4 c_1 = 12 c_4 S: | c_1 = 3 c_4 Cr: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 Cr ⟶ 3 H_2 + Cr_2(SO_4)_3
Structures
![+ ⟶ +](../image_source/28a5f03cb87f3a7c242a1f12c9e9b08d.png)
+ ⟶ +
Names
![sulfuric acid + chromium ⟶ hydrogen + chromium sulfate](../image_source/337570db2589285110379fc3e202b080.png)
sulfuric acid + chromium ⟶ hydrogen + chromium sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + Cr ⟶ H_2 + Cr_2(SO_4)_3 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 H_2SO_4 + 2 Cr ⟶ 3 H_2 + Cr_2(SO_4)_3 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 | 3 | -3 Cr | 2 | -2 H_2 | 3 | 3 Cr_2(SO_4)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) Cr | 2 | -2 | ([Cr])^(-2) H_2 | 3 | 3 | ([H2])^3 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] 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])^(-3) ([Cr])^(-2) ([H2])^3 [Cr2(SO4)3] = (([H2])^3 [Cr2(SO4)3])/(([H2SO4])^3 ([Cr])^2)](../image_source/19745550ac0614e6f48afc304a89a569.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + Cr ⟶ H_2 + Cr_2(SO_4)_3 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 H_2SO_4 + 2 Cr ⟶ 3 H_2 + Cr_2(SO_4)_3 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 | 3 | -3 Cr | 2 | -2 H_2 | 3 | 3 Cr_2(SO_4)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) Cr | 2 | -2 | ([Cr])^(-2) H_2 | 3 | 3 | ([H2])^3 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] 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])^(-3) ([Cr])^(-2) ([H2])^3 [Cr2(SO4)3] = (([H2])^3 [Cr2(SO4)3])/(([H2SO4])^3 ([Cr])^2)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + Cr ⟶ H_2 + Cr_2(SO_4)_3 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 H_2SO_4 + 2 Cr ⟶ 3 H_2 + Cr_2(SO_4)_3 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 | 3 | -3 Cr | 2 | -2 H_2 | 3 | 3 Cr_2(SO_4)_3 | 1 | 1 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 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) Cr | 2 | -2 | -1/2 (Δ[Cr])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(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[H2SO4])/(Δt) = -1/2 (Δ[Cr])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/cd47c78a49d4bc768c2aa18b06299ea4.png)
Construct the rate of reaction expression for: H_2SO_4 + Cr ⟶ H_2 + Cr_2(SO_4)_3 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 H_2SO_4 + 2 Cr ⟶ 3 H_2 + Cr_2(SO_4)_3 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 | 3 | -3 Cr | 2 | -2 H_2 | 3 | 3 Cr_2(SO_4)_3 | 1 | 1 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 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) Cr | 2 | -2 | -1/2 (Δ[Cr])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(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[H2SO4])/(Δt) = -1/2 (Δ[Cr])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfuric acid | chromium | hydrogen | chromium sulfate formula | H_2SO_4 | Cr | H_2 | Cr_2(SO_4)_3 Hill formula | H_2O_4S | Cr | H_2 | Cr_2O_12S_3 name | sulfuric acid | chromium | hydrogen | chromium sulfate IUPAC name | sulfuric acid | chromium | molecular hydrogen | chromium(+3) cation trisulfate](../image_source/e55d2d1d2a0a69801c7d0edd28ccb4ed.png)
| sulfuric acid | chromium | hydrogen | chromium sulfate formula | H_2SO_4 | Cr | H_2 | Cr_2(SO_4)_3 Hill formula | H_2O_4S | Cr | H_2 | Cr_2O_12S_3 name | sulfuric acid | chromium | hydrogen | chromium sulfate IUPAC name | sulfuric acid | chromium | molecular hydrogen | chromium(+3) cation trisulfate
Substance properties
![| sulfuric acid | chromium | hydrogen | chromium sulfate molar mass | 98.07 g/mol | 51.9961 g/mol | 2.016 g/mol | 392.2 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) melting point | 10.371 °C | 1857 °C | -259.2 °C | boiling point | 279.6 °C | 2672 °C | -252.8 °C | 330 °C density | 1.8305 g/cm^3 | 7.14 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 1.84 g/cm^3 solubility in water | very soluble | insoluble | | surface tension | 0.0735 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | odorless | odorless | odorless](../image_source/b1e565bb08c31d88a9343d956271677b.png)
| sulfuric acid | chromium | hydrogen | chromium sulfate molar mass | 98.07 g/mol | 51.9961 g/mol | 2.016 g/mol | 392.2 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) melting point | 10.371 °C | 1857 °C | -259.2 °C | boiling point | 279.6 °C | 2672 °C | -252.8 °C | 330 °C density | 1.8305 g/cm^3 | 7.14 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 1.84 g/cm^3 solubility in water | very soluble | insoluble | | surface tension | 0.0735 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | odorless | odorless | odorless
Units