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Chapter 6: Problem 17

The enthalpy change for the reaction $$ \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ is \(-891 \mathrm{kJ}\) for the reaction as written. a. What quantity of heat is released for each mole of water formed? b. What quantity of heat is released for each mole of oxygen reacted?

Short Answer

Expert verified
a. The quantity of heat released for each mole of water formed is \( -445.5\ \mathrm{kJ/mol} \). b. The quantity of heat released for each mole of oxygen reacted is \( -445.5\ \mathrm{kJ/mol} \).

Step by step solution

01

Analyze the balanced reaction

The balanced chemical equation for the given reaction is: \( CH_4(g) + 2 O_2(g) \longrightarrow CO_2(g) + 2 H_2O(l) \) The stoichiometry of the reaction indicates that for every mole of methane (CH4) reacted, two moles of water (H2O) are formed, and two moles of oxygen (O2) are consumed. Therefore, we can use the given enthalpy change to determine the heat released per mole of water and per mole of oxygen.
02

Calculate the heat released per mole of water formed

We know the enthalpy change of the reaction is -891 kJ. This is the energy change when one mole of methane reacts with two moles of oxygen to produce one mole of carbon dioxide and two moles of water. We can now calculate the amount of heat released for each mole of water formed. Given that for 2 moles of H2O the heat released is -891 kJ, we can calculate the heat for 1 mole of H2O in the following way: Heat released per mole of H2O = \( \frac{-891\ \mathrm{kJ}}{2\ \mathrm{moles\ of\ H_2O}} \)
03

Calculate the heat released per mole of oxygen reacted

We know the enthalpy change of the reaction is -891 kJ. This is the energy change when one mole of methane reacts with two moles of oxygen to produce one mole of carbon dioxide and two moles of water. We can now calculate the amount of heat released for each mole of oxygen reacted. Given that for 2 moles of O2 the heat released is -891 kJ, we can calculate the heat for 1 mole of O2 in the following way: Heat released per mole of O2 = \( \frac{-891\ \mathrm{kJ}}{2\ \mathrm{moles\ of\ O_2}} \)
04

Calculate the values

Now, let's compute the values we've set up in steps 2 and 3. Heat released per mole of H2O: \( \frac{-891\ \mathrm{kJ}}{2\ \mathrm{moles\ of\ H_2O}} = -445.5\ \mathrm{kJ\ per\ mole\ of\ H_2O} \) Heat released per mole of O2: \( \frac{-891\ \mathrm{kJ}}{2\ \mathrm{moles\ of\ O_2}} = -445.5\ \mathrm{kJ\ per\ mole\ of\ O_2} \) In conclusion, a. The quantity of heat released for each mole of water formed is -445.5 kJ/mol. b. The quantity of heat released for each mole of oxygen reacted is -445.5 kJ/mol.

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Most popular questions from this chapter

Explain the advantages and disadvantages of hydrogen as an alternative fuel.

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