Input interpretation
H_2SO_4 sulfuric acid + S mixed sulfur + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + K_2SO_4 potassium sulfate + SO_2 sulfur dioxide + Cr_2(SO_4)_3 chromium sulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + S + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + SO_2 + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 S + c_3 K_2Cr_2O_7 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 SO_2 + c_7 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, Cr and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_3 = c_4 + 4 c_5 + 2 c_6 + 12 c_7 S: | c_1 + c_2 = c_5 + c_6 + 3 c_7 Cr: | 2 c_3 = 2 c_7 K: | 2 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/2 - 1/2 c_3 = 1 c_4 = c_1 c_5 = 1 c_6 = (3 c_1)/2 - 9/2 c_7 = 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 5 and solve for the remaining coefficients: c_1 = 5 c_2 = 2 c_3 = 1 c_4 = 5 c_5 = 1 c_6 = 3 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2SO_4 + 2 S + K_2Cr_2O_7 ⟶ 5 H_2O + K_2SO_4 + 3 SO_2 + Cr_2(SO_4)_3
Structures
+ + ⟶ + + +
Names
sulfuric acid + mixed sulfur + potassium dichromate ⟶ water + potassium sulfate + sulfur dioxide + chromium sulfate
Equilibrium constant
![K_c = ([H2O]^5 [K2SO4] [SO2]^3 [Cr2(SO4)3])/([H2SO4]^5 [S]^2 [K2Cr2O7])](../image_source/41ac77798d4437c95bd2424885d0b81e.png)
K_c = ([H2O]^5 [K2SO4] [SO2]^3 [Cr2(SO4)3])/([H2SO4]^5 [S]^2 [K2Cr2O7])
Rate of reaction
![rate = -1/5 (Δ[H2SO4])/(Δt) = -1/2 (Δ[S])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/5 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/3 (Δ[SO2])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/c59a3a450622b7999479db3eef35d428.png)
rate = -1/5 (Δ[H2SO4])/(Δt) = -1/2 (Δ[S])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/5 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/3 (Δ[SO2])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | mixed sulfur | potassium dichromate | water | potassium sulfate | sulfur dioxide | chromium sulfate formula | H_2SO_4 | S | K_2Cr_2O_7 | H_2O | K_2SO_4 | SO_2 | Cr_2(SO_4)_3 Hill formula | H_2O_4S | S | Cr_2K_2O_7 | H_2O | K_2O_4S | O_2S | Cr_2O_12S_3 name | sulfuric acid | mixed sulfur | potassium dichromate | water | potassium sulfate | sulfur dioxide | chromium sulfate IUPAC name | sulfuric acid | sulfur | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | dipotassium sulfate | sulfur dioxide | chromium(+3) cation trisulfate