0.9 Energetics of chemical reactions  (Page 3/7)

Second, and perhaps more importantly for our purposes, we can use the known specific heat of water to measurethe heat released in any chemical reaction. To analyze a previous example, we observed that the combustion of 1.0g of methane gasreleased sufficient heat to increase the temperature of 1000g of water by 13.3°C. The heat capacity of 1000g of water must be $1000g4.184\frac{J}{g°C}=4184\frac{J}{°C}$ . Therefore, by , elevating the temperature of 1000g of water by 13.3°C must require $55,650J=55.65\mathrm{kJ}$ of heat. Therefore, burning 1.0g of methane gas produces exactly 55.65kJ of heat.

The method of measuring reaction energies by capturing the heat evolved in a water bath and measuring thetemperature rise produced in that water bath is called calorimetry . This method is dependent on the equivalence of heat and work as transfers of energy, and on thelaw of conservation of energy. Following this procedure, we can straightforwardly measure the heat released or absorbed in anyeasily performed chemical reaction. For reactions which are difficult to initiate or which occur only under restrictedconditions or which are exceedingly slow, we will require alternative methods.

Observation 2: hess' law of reaction energies

Hydrogen gas, which is of potential interest nationally as a clean fuel, can be generated by the reaction ofcarbon (coal) and water:

Calorimetry reveals that this reaction requires the input of 90.1kJ of heat for every mole of $C\left(s\right)$ consumed. By convention, when heat is absorbed during a reaction, we consider the quantity of heat to be a positive number: inchemical terms, $q> 0$ for an endothermic reaction. When heat is evolved, the reaction is exothermic and $q< 0$ by convention.

It is interesting to ask where this input energy goes when the reaction occurs. One way to answer thisquestion is to consider the fact that the reaction converts one fuel, $C\left(s\right)$ , into another, $H_2\left(g\right)$ . To compare the energy available in each fuel, we can measure theheat evolved in the combustion of each fuel with one mole of oxygen gas. We observe that

produces 393.5kJ for one mole of carbon burned; hence $q=-393.5\mathrm{kJ}$ . The reaction

produces 483.6kJ for two moles of hydrogen gas burned, so $q=-483.6\mathrm{kJ}$ . It is evident that more energy is available from combustion of thehydrogen fuel than from combustion of the carbon fuel, so it is not surprising that conversion of the carbon fuel to hydrogen fuelrequires the input of energy.

Of considerable importance is the observation that the heat input in , 90.1kJ, is exactly equal to the difference between the heat evolved, -393.5kJ, in the combustion of carbon and the heat evolved, -483.6kJ, in the combustion of hydrogen . This is not a coincidence: if we take the combustion of carbon and add to it the reverse of the combustion of hydrogen , we get $$C\left(s\right)+O_2\left(g\right)\to C{O}_2\left(g\right)$$ $$2H_{2}O\left(g\right)\to 2H_2\left(g\right)+O_2\left(g\right)$$

Canceling the $O_2\left(g\right)$ from both sides, since it is net neither a reactant nor product, is equivalent to . Thus, taking the combustion of carbon and "subtracting" the combustion of hydrogen (or more accurately, adding the reverse of the combustion of hydrogen ) yields . And, the heat of the combustion of carbon minus the heat of the combustion of hydrogen equals the heat of .