Thermochemistry, cont.

Keep in mind that heat **always** flows naturally from hotter to cooler systems. Energy must be used up to move heat in the opposite direction, as in a refrigerator.

w (in chemistry) = the work done by or on the system:

- w = positive when work is done on the system (e.g. as gas is compressed)
- w = negative when the system does work on its surroundings (e.g. a gas moves a piston by expansion - notice that an ideal gas expanding in space
does no work!).

Note that if no heat is transferred to or from a system (it is isolated in a "thermos"), then all energy must appear as work. On the other hand, if no work is done, then all energy must appear as heat (this is utilized in *calorimetry* which is discussed below).

Example:A quantity of air in a cylinder expands against a piston doing 4.5 kJ of work while 10.0 kJ of heat is added. How much has the energy of the air changed?

E = q + w

- Heat is added, therefore q is (+)
- Work is done by the system (the air expands), therefore w is (-)

Most chemistry is done under conditions of constant pressure or constant volume (e.g. all of your body chemistry occurs at about atmospheric pressure - no pressure changes occur within single cells doing chemistry). Thus it is convenient to define a term for the heat involved in processes occurring with no change in pressure:

Enthalpy is often approximately = E for chemical processes, since little or no work is usually done in solution chemistry.

Calorimetry is the science of measuring heat. It is particularly useful because under two readily achievable laboratory conditions heat = E.

- For solution and solid state reactions at constant pressure there is no significant change in volume, so we can assume no work:
*therefore*heat = E. - If a reaction takes place in a rigid container, there can be no volume change, and no work can have occurred:
*therefore*

Heat is a measure of energy transferred between objects of different temperatures. We are already familiar with the units of temperature, what are the **units of heat**?

- joule (SI unit): It takes 4.184 J to raise 1 g of water at 20 °C 1 °C.
- calorie (metric, non-SI unit): It takes 1 cal to raise 1 g of water at 20 °C 1°C. Thus 1 cal = 4.184 J (defined).
- Calorie (large Calorie = nutritional Calorie): 1 Calorie = kilocalorie. [2000 Calorie burger is 8.4
*million*juoles!]

**Specific Heat** is the amount of heat it takes to raise 1 g of a specific substance 1 °C. Specific heats for other substances are relative to water, so no units (comparing results in canceling out units).

The heat transferred in a process (q) is summarized in the equation:

where m is the mass of substance and C_{sp} is the specific heat of the substance.

Example:750 calories of heat is transferred to 100.0 g of water at 20.00 °C. What will the new temperature of the water be assuming no heat is lost to the container or the surroundings?Known: heat capacity of water = 1 cal / (g°C) [assume exact for problem]; q = mC

_{sp}T

Adding the difference to the original temperature gives: 20.00 °C + 7.50 °C = 27.50 °C

Example:1.40 g of vegetable oil is placed in a bomb calorimeter with excess oxygen and ignited with a spark. If the calorimeter temperature changes from 20.000 °C to 21.195 °C, find the energy released per gram of oil . The calorimeter contains 2.50 kg of water. The calorimeter without water has a heat capacity of 1.00 kJ°C^{-1}.

q = nC _{p}T, where C_{p}is themolar heat capacityat constant pressure (= 75.3 J C^{-1}mol^{-1}for water).

q= q _{water}+ q_{calorimeter}

q _{water}= {(2.50 kg H_{2}O)(1000g/kg) / (18.02 g H_{2}O/mole)}{75.3 J C^{-1}mol^{-1}}{1.195 °C} = 1.25 x 10^{4}J

q _{calorimeter}= CT = (1.00 x 10^{3}J°C^{-1})(1.195 °C) = 1.195 x 10^{3}J

q _{tot}= 1.25 x 10^{4}J + 1.195 x 10^{3}J = 1.369 x 10^{4}J

E/g = (1.369 x 10 ^{4}J) / 1.40 g =9.78 kJ/gNotice that this is now the energy released, and it will also be the energy you could potentially get from consuming this much oil, since we are working with state functions, and the pathway (fire or metabolism) doesn't matter.

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*© R A Paselk*

*Last modified 6 March 2013*