- [Instructor] A constant pressure calorimeter
can be used to find the change in entropy
for a chemical reaction.
Let's look at the chemical reaction
between an aqueous solution of silver nitrate
and aqueous solution of sodium chloride
to form a precipitate of silver chloride
and an aqueous solution of sodium nitrate.
Let's say we have 25.0 milliliters
of a 0.100 molar solution of silver nitrate
and 25.0 milliliters of a 0.100 molar solution
of sodium chloride.
Both solutions are initially at a temperature
of 25.000 degrees Celsius.
Next, we add our two solutions to our calorimeter
which has made of two coffee cups.
And since the top coffee cup is loose fitting,
this reaction is under the constant pressure
of the atmosphere.
So this is constant pressure calorimetry.
After the two aqueous solutions mix, the reaction occurs
and we watch the thermometer in the calorimeter.
In this case, the temperature of the solution increases
and the final temperature,
the highest one reached in our experiment
is 25.781 degrees Celsius.
So the change in the temperature of the solution
would be the final temperature
minus the initial temperature,
which is 25.781 minus 25.0
which is equal to positive 0.781 degrees Celsius.
The total volume of solution would be 25 plus 25,
which is equal to 50.0 milliliters of solution.
If we assume the density of the solution
is one gram per milliliter,
50.0 milliliters is equal to 50.0 grams.
Next we need to solve for the heat gained by the water
and we can use the Q is equal to MC delta T equation.
So we're solving for the heat,
which is symbolized by Q,
M is the mass of our solution
which we saw was 50.0 grams,
So we can plug that in.
We can assume that the specific heat of the solution
is the same as the specific heat of water,
which is 4.18 joules per gram degrees Celsius
and the change in the temperature of the solution
was 0.781 degrees Celsius.
So we can plug that in as well.
Grams cancels out, degrees Celsius cancels out
and we find that Q is equal to
positive 1.63 times 10 to the second joules.
The positive sign means that energy was gained by the water.
But let's think about the distinction
between system and surroundings.
The system consists of the reactants
and products for our particular reaction
and the surroundings are everything else
which includes the water.
So in this case,
since the temperature of the surroundings increased, right?
We saw an increase in the temperature,
that means that heat flowed
from the system to the surroundings
and so the surroundings increased in energy
and that's what we see with this positive sign here.
If we assume a perfect transfer of heat
from the system to the surroundings,
if the surroundings gained energy,
that means the system lost energy.
So if we're thinking about the heat
transferred for the reaction,
it's the same in magnitude,
1.63 times 10 to the second joules.
However, we need to put a negative sign in here
which indicates that energy was given off by the reaction.
The heat that's transferred under constant pressure
is equal to the change in the entropy
of the reaction, delta H.
However, let's find the change in entropy, delta H
in terms of kilojoules per mole
of silver chloride for our units.
Since silver chloride is one of our products,
we first need to find moles of our reactants
and we're gonna do that using the molarity equation
which says that molarity
is equal to moles divided by liters.
For our silver nitrate solution,
the concentration was 0.100 molar
and trying to solve for moles so that's X.
The volume of our silver nitrate solution
was 25.0 milliliters
which is 0.0250 liters.
So we solve for X and we get 0.00250.
So that's how many moles of silver nitrate
that we started with
and it's the exact same calculation
for sodium chloride as well.
So this is also how many moles of sodium chloride we have.
Next, we go back to our balanced chemical equation
and we can see we have coefficients of one
in front of silver nitrate,
in front of sodium chloride
and in front of silver chloride.
Therefore, we're also going to produce 0.00250 moles
of silver chloride.
Next we're gonna calculate the change
in the entropy, delta H, for our reaction.
The heat that was transferred
was negative 1.63 times 10 to the second joules
and we're gonna divide that
by the moles of silver chloride
which was 0.00250 moles of silver chlorides.
This is equal to negative 65,200 joules
per mole of silver chloride
and we could convert that into kilojoules.
And so this is equal to negative 65.2 kilojoules
per mole of silver chloride.
We could stop right here and give this as our final answer,
but let's keep going
and convert two kilojoules per mole of reaction.
First, let's rewrite this.
We have negative 65.2 kilojoules
per mole of silver chlorides
and what it means by kilojoules per mole of reaction
is how the reaction is written
in the balanced equation down here.
So if we look at the balanced equation,
there's one mole of silver chloride
for how the reaction is written.
So we can write a conversion factor
of one mole of silver chloride
per one mole of reaction
and writing it this way for the conversion factor,
the moles of silver chloride would cancel out
and give us negative 65.2 kilojoules per mole of reaction.
So this could also be our final answer.
Finally, the negative sign
means that we have an exothermic reaction.
The reaction gave off energy
and this value when you do
a constant pressure calorimetry experiment
is often a little bit lower than the actual value
because in reality there's not always a perfect transfer
of heat from the reaction to the water.
Often some of the energy is lost to the environment.