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Chapter 5: Q5.3-66E (page 272)

Calculate \[{\bf{\Delta H}}_{{\bf{298 }}}^{\bf{^\circ }}\] for the process \[{\bf{C}}{{\bf{o}}_{\bf{3}}}{{\bf{O}}_{\bf{4}}}\left( {\bf{s}} \right) \to {\bf{3Co}}\left( {\bf{s}} \right){\bf{ + 2}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right)\]

from the following information:

\[\begin{array}{c}{\bf{Co(s) + }}\frac{{\bf{1}}}{{\bf{2}}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{CoO(s) \Delta H}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ = - 237}}{\bf{.9kJ}}\\{\bf{3CoO(s) + }}\frac{{\bf{1}}}{{\bf{2}}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{C}}{{\bf{o}}_{\bf{3}}}{{\bf{O}}_{\bf{4}}}{\bf{(s) \Delta H}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ = - 177}}{\bf{.5kJ}}\end{array}\]

Short Answer

Expert verified

The change in enthalpy of the given chemical equation will be \[\Delta {\rm{H}}_{298}^^\circ = 891.2{\rm{kJ}}\].

Step by step solution

01

Use Hess’s law

To solve the given problem, we are going to use the Hess鈥檚 law and follow the steps below.

\[\begin{array}{l}{\rm{Co(s) + }}\frac{1}{2}{{\rm{O}}_{\rm{2}}}{\rm{(g)}} \to {\rm{CoO(s)}}..................{\rm{(1) }}\Delta {\rm{H}}_{298}^^\circ = - 237.9{\rm{kJ}}\\{\rm{3CoO(s) + }}\frac{1}{2}{{\rm{O}}_{\rm{2}}}{\rm{(g)}} \to {\rm{C}}{{\rm{o}}_{\rm{3}}}{{\rm{O}}_{\rm{4}}}{\rm{(s)}}..........{\rm{(2) }}\Delta {\rm{H}}_{298}^^\circ = - 177.5{\rm{kJ}}\\{\rm{Multiply equation}}\;{\rm{(1) by 3 and equation}}\;{\rm{(2) by 1, and add them}}{\rm{.}}\end{array}\]

02

Change in enthalpy

Now, to get the value of the change in enthalpy of the given equation, we have perform a simple mathematical operation on equation (3), which is shown below.

\[\begin{array}{l}{\rm{3Co(s) + 2}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}} \to {\rm{C}}{{\rm{o}}_{\rm{3}}}{{\rm{O}}_{\rm{4}}}{\rm{(s)}}..........{\rm{(3) }}\Delta {\rm{H}}_{298}^^\circ = ( - 237.9 \times 3 - 177.5){\rm{kJ}}\\{\rm{ = }} - 891.2{\rm{kJ}}\\{\rm{By reversing equation (3), we get: }}\\{\bf{C}}{{\bf{o}}_{\bf{3}}}{{\bf{O}}_{\bf{4}}}{\bf{(s)}} \to {\bf{3Co(s) + 2}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}...........{\bf{(4) \Delta H}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ = 891}}{\bf{.2kJ}}\end{array}\]

Hence, the change in enthalpy of the given chemical equation will be \[\Delta {\rm{H}}_{298}^^\circ = 891.2{\rm{kJ}}\].

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Most popular questions from this chapter

How much heat is produced by burning 4.00 moles of acetylene under standard conditions?

Would the amount of heat absorbed by the dissolution in Example 5.6 appear greater, lesser, or remain the same if the heat capacity of the calorimeter were taken into account? Explain your answer

Water gas, a mixture of \({{\bf{H}}_{\bf{2}}}\) and CO, is an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon:\({\bf{C}}\left( {\bf{s}} \right){\bf{ + }}{{\bf{H}}_{\bf{2}}}{\bf{O}}\left( {\bf{g}} \right) \to {\bf{CO}}\left( {\bf{g}} \right){\bf{ + }}{{\bf{H}}_{\bf{2}}}\left( {\bf{g}} \right)\).

(a) Assuming that coke has the same enthalpy of formation as graphite, calculate \({\bf{\Delta H}}_{{\bf{298}}}^{\bf{0}}\)for this reaction.

(b) Methanol, a liquid fuel that could possibly replace gasoline, can be prepared from water gas and additional hydrogen at high temperature and pressure in the presence of a suitable catalyst:\({\bf{2}}{{\bf{H}}_{\bf{2}}}\left( {\bf{g}} \right){\bf{ + CO}}\left( {\bf{g}} \right) \to {\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{OH}}\left( {\bf{g}} \right)\).

Under the conditions of the reaction, methanol forms as a gas. Calculate \({\bf{\Delta H}}_{{\bf{298}}}^{\bf{0}}\)for this reaction and for the condensation of gaseous methanol to liquid methanol.

(c) Calculate the heat of combustion of 1 mole of liquid methanol to H2O(g) and CO2(g).

When 1.0g of fructose, C6H12O6(s), a sugar commonly found in fruits, is burned in oxygen in a bomb calorimeter, the temperature of the calorimeter increases by 1.58藲C. If the heat capacity of the contents is 9.90kJ/藲C, what is q for this combustion?

One method of generating electricity is by burning coal to heat water, which produces steam that drives an electric generator. To determine the rate at which coal is to be fed into the burner in this type of plant, the heat of combustion per ton of coal must be determined using a bomb calorimeter. When 1.00g of coal is burned in a bomb calorimeter (figure 5.17), the temperature increases by 1.48藲C. If the heat capacity of the calorimeter is 21.6 kJ/藲C, determine the heat produced by the combustion of a ton of coal (2.000 脳 103).
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