Chem 109 - General Chemistry - Spring 2011

Lecture Notes 19: 4 March

Calorimetry, cont.

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_pT, where C_p is the molar heat capacity at constant pressure (= 75.3 J C^-1mol^-1 for water).

q= q_water + q_calorimeter

q_water= {(2.50 kg H₂O)(1000g/kg) / (18.02 g H₂O/mole)}{75.3 J C^-1mol^-1}{1.195 °C} = 1.25 x 10⁴J

q_calorimeter = CT = (1.00 x 10³J°C^-1)(1.195 °C) = 1.195 x 10³J

q_tot= 1.25 x 10⁴J + 1.195 x 10³J = 1.369 x 10⁴J

E/g = (1.369 x 10⁴J) / 1.40 g = 9.78 kJ/g

Notice 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.

Hess's Law

Hess's Law states that changes in enthalpy in any process depends only on the nature of the reactants and products, and is independent of the number of steps in the process or the pathway taken. Hess's Law is thus a result of the fact that enthalpy is a state function.

Hess's Law turns out to be extremely useful for determining the energy of various processes, and thus the conditions necessary for reactions to proceed. The pathway independence is particularly nice, because we can look at processes that have never been observed to occur in a laboratory, and reasonably discuss the thermochemistry of processes that might occur at the Earth's core or the heart of a comet etc.

In order to use Hess's Law we need to keep some properties of enthalpy in mind.

When a reaction is written in reverse, the sign of H is reversed.

The magnitude of H is directly proportional to the amount of reactants. Thus if the coefficients of a reaction are multiplied, then H is multiplied by the same amount.

Standard Enthalpies (Heats) of Formation

Formation Reactions and Standard Enthalpies of Formation: If we consider a reaction in which compounds are formed from elements in their standard states then the value of H is the standard enthalpy (heat) of formation.

Standard States:

The form of a pure substance stable at one atm and 25°C. (Actually other temperatures are tabulated, so have to check when looking at tabulated values.)
For a substance in solution the standard state is defined for a concentration of exactly one molar.
For an element the standard state is the form stable at one atm and 25°C. Note that many elements have allotropes: different forms of the pure element. For example carbon has 3 allotropes, the most common of which are graphite and diamond. Graphite is the stable form (a diamond is not forever at 1 atm and 25°C!).
- The enthalpy of formation of a pure element in its standard state is defined to be 0.

With this information we can now find H for any chemical reaction!

Example: Find the value of H for the reaction:

2 CO₂ + 7 H₂ C₂H₆ + 4 H₂O_(g)

From Table find H values:

Often just list compounds, since known to be from elements.
C + O₂ CO₂	H = -393.5 kJ mol^-1
2 C + 3 H₂ C₂H₆	H = -84.6 kJ mol^-1
H₂ + 1/2 O₂ H₂O_(g)	H = -241.8 kJ mol^-1

now we can put the reactions together, adding the enthalpies for products, and subtracting enthalpies for reactants (since the reaction directions are reversed), and multiplying enthalpy values by the coefficients of the balanced equation (since all of the formation reactions were based on coefficients of one).

-2 (H_CO₂) -7 (H_H₂) + (H_C₂H₆) + 4 (H_H₂O) = H_rxn

-2 (-393.5 kJ mol^-1) - 7 (0) + (-84.6 kJ mol^-1) + 4 (-241.8 kJ mol^-1) = -2.648 x 10²kJ mol^-1

Atomic Structure & Electromagnetic Radiation (Light)

Electromagnetic Radiation comprises the various types of forms of radiation which propagate through space not associated with mass. The visible spectrum encompasses a very narrow region of the overall electromagnetic spectrum as seen below and on figure 7.2 on p 276 of your text.

diagram of electromagnetic spectrum

Electromagnetic radiation behaves in most circumstances as waves [Figure 7.1 p 276] and can thus be characterized as waves.

Labeled sine wave diagram

Three parameters determine a wave:

Frequency (f or ), the rate at which wave crests pass a given point. Units = sec^-1 (s^-1) or Hz (animation on slide)
Wavelength (l), the distance between repeating points on a wave (crest - crest, etc.). Units = meters, nm, Å (= 10^-10m) etc.
Speed (v), rate of propagation of a given point on a wave. Units = m/sec = m*s^-1.