Math Problem Statement

Given that ΔH°f [CO(g)] = –110.5 kJ/mol and ΔH°f [COCl2(g)] = –219.1 kJ/mol,

what is the standard enthalpy of reaction, ΔHrxn, for the synthesis of 1 mol phosgene, COCl2, from carbon monoxide, CO, and chlorine gas, Cl2(g)?

Select one:

–109 kJ

+111 kJ

+330 kJ

–219 kJ

–111 kJ

Solution

The standard enthalpy of reaction, ΔHrxn\Delta H_{\text{rxn}}^\circ, can be determined using the enthalpy of formation values:

ΔHrxn=ΔHf(products)ΔHf(reactants)\Delta H_{\text{rxn}}^\circ = \sum \Delta H_f^\circ \text{(products)} - \sum \Delta H_f^\circ \text{(reactants)}

Given data:

  • ΔHf[CO(g)]=110.5\Delta H_f^\circ [CO(g)] = -110.5 kJ/mol
  • ΔHf[COCl2(g)]=219.1\Delta H_f^\circ [COCl_2(g)] = -219.1 kJ/mol
  • ΔHf[Cl2(g)]=0\Delta H_f^\circ [Cl_2(g)] = 0 kJ/mol (since it is in its elemental form)

Balanced reaction:

CO(g)+Cl2(g)COCl2(g)\text{CO}(g) + \text{Cl}_2(g) \rightarrow \text{COCl}_2(g)

Applying the equation:

[ \Delta H_{\text{rxn}}^\circ = \left[ \Delta H_f^\circ \text{(COCl}_2\text{)} \right] - \left[ \Delta H_f^\circ \text{(CO)} + \Delta H_f^\circ \text{(Cl}_2\text{)} \right] ]

=(219.1)(110.5+0)= (-219.1) - (-110.5 + 0)

=219.1+110.5= -219.1 + 110.5

=108.6109 kJ= -108.6 \approx -109 \text{ kJ}

Answer:

The correct answer is –109 kJ.


Would you like further explanation on enthalpy calculations?

Here are some related questions for practice:

  1. How do you calculate the enthalpy of reaction when multiple moles of reactants are involved?
  2. Why is the enthalpy of formation of elemental substances in their standard state zero?
  3. What is Hess’s Law, and how does it help in determining reaction enthalpies?
  4. How does bond enthalpy relate to enthalpy of reaction?
  5. How does the enthalpy of reaction relate to spontaneity in chemical reactions?

Tip:

The enthalpy of formation values always refer to the formation of one mole of a compound from its elements in their standard states.

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Math Problem Analysis

Mathematical Concepts

Thermodynamics
Enthalpy of Formation
Standard Enthalpy of Reaction

Formulas

ΔHrxn = ΣΔHf(products) - ΣΔHf(reactants)
ΔHrxn = ΔHf(COCl2) - [ΔHf(CO) + ΔHf(Cl2)]

Theorems

Hess's Law

Suitable Grade Level

Grades 11-12