Download Experiment Six - Seattle Central College

Experiment Six:
Thermodynamics Part One: Calorimetry
Purpose:
Determine the calorimeter constant
Determine the specific heat of a known metal.
Determine the Heat of Fusion of water
Introduction
Thermodynamics is the study of the energy changes that accompany chemical and
physical transformations. To get a basic understanding of this process, we need to recall
the first law of thermodynamics, known as the law of conservation of energy. This law
suggests that energy can be transferred from one system to another in many forms. Also, it can
not be created or destroyed. Clearly stated, “The energy of the universe is constant.”
How do chemists use the First Law? Atoms and molecules – the ‘stuff’ of chemistry –
release heat, light, sound and motion during the course of chemical reactions. These
‘external’ forms of energy can be measured. We then assert, using the First Law, that the
‘internal energy’ of the atoms and molecules (the ‘system’ in thermodynamic language)
must have changed by an equal and opposite amount to the observed ‘external energy’ we
measured. This concept of ‘internal energy’ or ‘chemical energy’ is central to our
understanding of how atoms and molecules behave.
Calorimetry
The apparatus used for measuring the heat (q) associated with a chemical reaction or
physical transformation is called a calorimeter (the name taken from the calorie, a unit of
heat, where 1 cal = 4.184 J). The calorimeter measures energy changes in the system
(chemical reaction) by acting as the surroundings around which energy freely flows. In
this experiment, the calorimeter will consist of a stacked pair of Styrofoam cups, water
and a thermometer. The purpose of the Styrofoam cups is to keep heat from being lost to
the room (thermal isolation), while the water serves to absorb the heat produced by the
chemical or physical change under investigation. Inevitably, some of the heat from our
reaction of interest is absorbed by the Styrofoam cups and the thermometer and this will
be determined in Part 1. Water is an excellent choice to absorb heat in the calorimeter due
to its extremely high heat capacity.
For the physical process, using the First Law, we can write:
∆Hsystem = -qcalorimeter = +qsystem
where ∆Hsystem is the enthalpy change of the system, qsystem is heat evolved or absorbed in
the system, and qcalorimeter is the heat absorbed by the calorimeter (the water + cup +
thermometer), which is what we measure. Recall that enthalpy is the energy change in
the reaction for atoms and molecules reacting, while heat is the energy released or
absorbed during the process doing work on the surroundings.
But how, exactly, do we measure the heat absorbed by the calorimeter? When you think
about measuring heat, you probably think of using a thermometer. But thermometers
measure temperature, which is related to the intensity of the random motion associated
with heat, not the amount of heat itself. (The analogy is the speedometer of your car,
which tells you how fast you are going, but not how much kinetic energy you have.)
The connection between changes in temperature and the corresponding changes in
‘internal’ (thermal) energy are made via a constant, relating heat and temperature. This
value is called the heat capacity (C), or the ability of an object to retain heat. Every
substance has its own particular set of internal motions and an energy associated with that
process. Every substance has a different set of atoms, joined in different ways, thus every
substance has a different heat capacity. Different amounts of the same substance also
have different heat capacities, so discussing the heat capacity of a pure substance relative
to a standard sample size (one mole or one gram) ensures values can be compared across
the board (Physicists and engineers usually think in terms of mass, while chemists think
in terms of moles!). Note: The heat capacity per gram is different for every different
substance, but the heat capacity per mole of similar materials (all noble gases and most
metals) can be very similar, further evidence supporting the notion that heat is simply
energy associated with the internal motion of the atoms in the substance. You will check
this idea in Part III of the experiment.
The units of heat capacity are ‘energy per degree’, or J/ºC, or J/K (one degree change
Celsius is equal to one degree change Kelvin). In practical application, molar heat
capacity (cp) is the energy required to raise 1 mole of material by one degree, while the
specific heat (c) is the amount of heat required to raise 1 gram of material by one degree.
There will be quite a few formulas and definitions to keep straight, so understand these
definitions now!
Overview of the experiment:
This experiment has three parts:
I.
Determine the heat capacity of the calorimeter.
II.
Measure the heat capacity of different metals (Zn, Al, and Pb)
III.
Measure the heat of fusion of ice.
Part One determines the heat capacity of the calorimeter ( C cal ) which is equal to the heat
capacity of 100 mL of water and the heat capacity of the Styrofoam cups:
Ccal = Ccold water + Chot water
Ccal is determined by measuring the temperature change that occurs when a known
amount of hot water is added to the calorimeter. The heat lost by the hot water is equal
to the heat gained by the cold water plus the heat absorb by the calorimeter. For example,
Tc equals the temperature of the cold water (100 mL of cool water in a Styrofoam cup), Ti
equals the temperature of 100 mL of hot water added to it, and Tf equals the temperature
after mixing. By this rational, then the heat lost by hot water is equal to the heat gained
Joules
by the cold water (the specific heat of water is 4.184
, and the density of water is
g•º C
1.00 g/mL) but the calorimeter absorbs some heat:
qhot water +qcold water + qcal = 0
qcal = -( qhot water +qcold water)
Note: Tf-Ti is a negative number, indicating heat is lost by the water!
The heat capacity of the calorimeter is therefore the heat gained by the calorimeter
divided by the temperature change of the calorimeter:
Ccal =
qcal
(Tf − Tc )
Once Ccal is determined, we can use the calorimeter to measure unknown amounts of heat
(q) produced from a variety of physical and chemical changes that are commonly
encountered in the lab.
Part Two measures the heat capacity of a metallic element, calculated in three ways: the
heat capacity (C), the specific heat capacity per gram (specific heat, c), and the molar
heat capacity per mole (cp). The method for finding C is very simple: you heat a known
mass of metal in a flask of boiling water, remove it (letting it ‘dry’ in the steam just
above the water), then quickly place it in the calorimeter with 100 mL of water in the
Styrofoam cups. The The ∆Tmetal is equal to temperature of the boiling water, Tmetal initial
minus the temperature of the water in the calorimeter after the addition of the metal, Tf.
The change in cold water in the calorimeter, ∆Tcold water is the difference in temperature of
the cold water in the calorimenter, Tf and the temperature of the water after the addition
of the hot metal, Ti. The water in the cup heats up while the metal cools down and,
according to the First Law, the heat lost by the metal is equal the heat gained by the
water. Both changes involve calculating q from q=C∆T.
-qmetal = +(qcold water + qcal)
heat lost = heat gained
-Cmetal•∆Tmetal = Cwater • ∆Tcold water + Ccal• ∆Tcal
qmetal =mmetal•cmetal•∆Tmetal
Cmetal = mmetal•cmetal
∆Tmetal = Tf – Tmetal initial
qcold water =mwate•cwater•∆Tcold water
qcal = Ccal•∆Tcal
Ccal from Part 1!
∆Tcal = Tf – Tc ∆Tcold water= Tf – Tc
The three metals available (Al, Brass, Pb) more-or-less span the periodic table, with a
7.7:1 ratio in the mass of the atoms. If we postulate that ‘heat’ is just the kinetic and
potential energy associated with the invisible microscopic motion of these atoms, how
might the differences in mass affect the heat capacity? You can compare the values of c
and cp for the three metals to answer this question. You should choose one metal, and repeat each measurement three times, allowing the metal to heat in the water bath for at
least 30 seconds between trials. (Be sure that the water is actually boiling during this
time!) It is not necessary to discard the water in the calorimeter after each measurement.
To achieve the best results you will need to be sure the water in the calorimeter is
thoroughly mixed and that the initial T reading is recorded just before you transfer the hot
metal to the calorimeter. Once you are ‘set up’, each measurement should take no more
than a few minutes. Remember that this simple measurement is actually probing an
important atomic property! You will obtain data from the other two metals from other
groups in the lab. You are responsible for calculations of c and cp for all three metals.
Part Three uses a similar technique for determining the heat of fusion of ice. In this case
the water in the calorimeter cools off as the ice melts, and the ‘First Law’ equations are a
bit more complicated. Water undergoes a phase change and a heat change. There are
two separate processes involved in this experiment.
1. The heat of fusion is the energy required to convert H2O(s) into H2O(l) (it is the
energy of the phase transition). This is the first part of the total heat change.
2. Once the ice has melted, the cold water (at 0ºC) mixes with the warm water in the
calorimeter, the second heat change.
In order to find the heat of fusion (∆Hfusion) we need to separate these two effects.
Heat lost by the calorimeter = CcalΔTcal (use Ccal from Part 1)
Heat gained (ice melting) = (moles of ice x ΔHfusion) – we are solving for ∆Hfusion!
Heat gained (ice water) = micecwater∆Tice water
ΔTice water is the temperature change of the ice cube after it melted as it heated. (Tf-Tice)
-qlost = +qgained
qice + qwater + qcal =0
qtotal = qice+qwater
-qcal = Ccal • ∆Tcal = +qtotal
qtotal = (molesice)(∆Hfusion) + (massice)(4.184
∆Tcal = Tf – Tc
Joules
)(∆Twater)
g•º C
∆Twater = Tf - Tice
The two ‘unknowns’ in these equations are: ∆Hfusion and mice. The mass of ice can be
obtained by weighing the calorimeter after the ice has melted. Alternatively, you could
try weighing the ice before you use it, but the suggested method is more productive.
General comments: One of the most important factors is making sure that the
temperature of the water, both before and at the end of a measurement, is uniform
throughout the container. Practice ‘swirling’ the calorimeter, with the thermometer
positioned slightly away from the bottom and walls of the cup (so that it is completely
surrounded by the solution). Since small temperature ‘drifts’ are inevitable, be sure to
record the temperature just before you add anything to the calorimeter.
Procedure
Part 1: Finding the Heat Capacity of the Calorimeter
1. Put exactly 100 mL of room temperature deionized water into the small
Styrofoam cup. Stack this into the larger 2 Styrofoam cups, obtain a thermometer
and fitted lid. Allow this system (the calorimeter) to stand until the temperature
remains constant. Record this temperature (Tc) using the digital thermometers.
2. Put exactly 100 mL of deionized water into a beaker. Heat the water to 65ºC
using a hotplate. Measure and record the temperature (Ti), of this hot water using
the thermometer, and immediately transfer all of the hot water into the calorimeter
containing the room temperature water. Swirl the solution to insure proper
mixing. Immediately take a temperature reading (to 0.2 degree) and continue to
take readings at 15 second intervals until it settles down at Tf.
3. Calculate Ccal.
a. The heat lost (qlost) by the hot water is gained by the calorimeter (qcal):
qcal = -( qhot water +qcold water)
qcal = -(100g · 4.184
Joules
Joules
(Tf-Ti) + 100g · 4.184
(Tf-Tc)
g•º C
g•º C
b. The heat capacity of the calorimeter is therefore the heat gained by the
calorimeter divided by the temperature change of the calorimeter:
Ccal =
qcal
(Tf − Tc )
4. Repeat the above procedure twice and determine an average Ccal.
You must calculate Ccal before proceeding to the next section.
Note that you can save about 10 minutes in Part II if you heat the water while you are
working on Part I. (see Part 2 step 1).
Part Two: Measuring the Heat Capacity of a Metal
1. Fill the 400 mL beaker to the 250 mL mark with water and heat it to boiling on the
hot plate (set on HIGH) or Bunsen burner.
2. Get your known metal from the stockroom and transfer the ID code to your data
sheet. Weigh the metal on the analytical balance and record the mass. Tie a string to
the metal and suspend the metal in the beaker containing the boiling water for at least
5 minutes. Do not lay the metal on the bottom of the beaker.
3. Refill the Styrofoam cup with 100 mL of ‘room temperature’ water. Swirl the water
until you have a steady value for the initial temperature. Record the temperature of
the water [Tc (cold water, 0C)].
4. Using the string, lift the metal out of the water and suspend it in the vapor until most
of the water has dripped off. Quickly place the metal in the calorimeter and swirl
until the temperature reaches its maximum value. Record this as the final temperature
of the metal and water [Tf (water+metal)].
5. Measure and record the temperature of the boiling water for the initial
temperature of the metal [Ti (metal)] (the boiling point varies slightly with
atmospheric pressure).
6. Return the metal to the boiling water for at least 5 minutes and repeat steps 3-4 for
a total of three trials. You can either “re-use” the hot water making sure that it
gets replenished so that the metal is still completely submerged.
7. Empty the water in the calorimeter and refill with another 100 mL of water. Be
sure to record the new Tc (water) after the water has been changed.
Part 3: Heat of Fusion of Water
1. Fill the calorimeter with 100 mL of ‘room temperature’ water and record the mass
of the filled cup and the initial temperature, Tc (water). Use the top loading
balance.
2. Obtain one or two ice cubes, (5-10 grams of ice) dry it off with a piece of paper
towel and add it to the calorimeter. Swirl until all the ice melts, i.e., until the
temperature reaches a constant value, Tf (water+ice).
3. Weigh the calorimeter, mass (water + ice) using the toploading balance to
determine the mass of the ice cube(s).
4. Repeat this procedure twice more. Prepare a table similar to that below in your
notebook.
5. Measure the temperature of an ice bath (crushed ice in water) and record this
value as the initial temperature of the ice cube, Tice (ice cube).
Calculations:
1. Calculate c for the three metals and compare these values with the literature
values for these metals. Record the literature values in the table next to the
experimental values.
2. Calculate ∆Hfusion for one mole of water. Compare this value to the one in the
textbook. Note: Watch units of J/mol or kJ/mol!
Data Sheet
Part 1: Finding the Heat Capacity of the Calorimeter
Temperature Reading after the mixing hot water and cold water.
Time in seconds
0
15
30
45
60
Temperature Trial 1
Trial 1
Mass of Hot water, grams
Density of water @65oC 0.098058 grams/mL
Tc –Temperature of cool water
in the calorimeter
Ti – Temperature of hot water
0
C
Tf – Temperature of combined
hot and cool water in the
calorimeter
0
C
ΔThot water, 0C
ΔTcalorimeter, 0C
q cal , (J)
Ccal, )(J/mol 0C)
Temperature Trial 2
Trial 2
Temperature Trial 3
Trial 3
Show calculations below.
Data Sheet
Part Two: Measuring the Heat Capacity of a Metal
Affix metal ID code here._________________________________
Mass of metal
Moles of metal
Ti (metal) 0C
Tc (water, 0C)
Tf (water+metal)
∆T (metal) 0C
∆T (water) 0C
Ccal (J/0C) (Part I)
q calorimeter(J)
q cold water (J)
q metal (J)
c (metal)(J/g•0C)
C (metal) (J/0C)
cp(metal)(J/mol 0C)
Show calculations below.
Data Sheet
Part 3: Heat of Fusion of Water
Mass filled cup (g)
Mass (water+ice) (g)
Mass of ice (g)
Moles of ice
Tc (Cal) (0C)
Tice (ice cube) (0C)
Tf (water+ice) (0C)
ΔT(water from ice)
ΔT (Cal) (0C)
Ccal (J/0C)
c (water) (J/g•ºC)
q (total) J
q (water) J
ΔHfusion (J/mol)
4.184
4.184
4.184
Show calculations below.