Answer to Question #268422 in Chemical Engineering for Tj2

Question

A reaction between methanol and oxygen can be used to produce formaldehyde: 2𝐶𝐻3𝑂𝐻 + 𝑂2 (𝑔) → 2𝐻𝐶𝐻𝑂(𝑔) + 2𝐻2𝑂(𝑙): ∆𝐻̂𝑟 𝑜 = −326.2 𝑘𝐽/𝑚𝑜𝑙 The standard heat of combustion of hydrogen is: 𝐻2 (𝑔) + 1 2 𝑂2 (𝑔) → 𝐻2𝑂(𝑙): ∆𝐻̂𝑟 𝑜 = −285.8 𝑘𝐽/𝑚𝑜𝑙 (a) Use these heats of reaction and Hess’s law to determine the standard heat of the direct decomposition of methanol to form formaldehyde: 𝐶𝐻3𝑂𝐻(𝑙) → 𝐻𝐶𝐻𝑂(𝑔) + 𝐻2(𝑔)

Answer 1

There are total pf 3 reactions:

(1) 2CH₃OH + O₂ --> 2HCHO + 2H₂O $(\Delta{H}^0_r=-326.2\ kJ/mol)$

(2) H₂ + 1/2O₂ --> H₂O $(\Delta{H}^0_r=-285.8\ kJ/mol)$

(3) CH₃OH --> HCHO + H₂

To obtain reaction (3) as an algebraic sum of reactions (1) and (2) according to Hess's law, the reaction (1) should be divided by 2, while reaction (2) should be reversed. The same conversions apply to corresponding heats of each reaction: the heat of reaction (1) is divided by 2, and heat of reaction (2) changes its sign. As a result we get:

(1) CH₃OH + 1/2O₂ --> HCHO + H₂O $(\Delta{H}^0_r=-163.1\ kJ/mol)$

(2) H₂O --> H₂ + 1/2O₂ $(\Delta{H}^0_r=285.8\ kJ/mol)$

The desired reaction (3) is now an algebraic sum of reactions (1) and (2):

CH₃OH +  ̶1̶/̶2̶O̶_2̶ +  ̶H̶_2̶O̶ --> HCHO +  ̶H̶_2̶O̶ + H₂ +  ̶1̶/̶2̶O̶_2̶

Therefore,

$\Delta{H^0_r(3)}=\Delta{H^0_r(1)}+\Delta{H^0_r(2)}=-163.1+285.8=122.7\ kJ/mol$

Answer: 122.7 kJ/mol