Re: How do you find the enthalpy change of eutralization of HNO3 with NaOH?

Greetings, Bethany:

I will assume that you encountered this experiment in a
textbook, and not in a laboratory.  The reason I assume this
relates to your statement that no water is used, when you
immediately afterwards include the phrase "each 2mol dm-3".
This leads me to take the time to try to clarify the
description of the experiment.

So:  The "dm-3" portion of that translates (assuming that
the 3 is an exponent) as "per cubic decimeter".  Since a
decimeter is a tenth of a meter, it is the same as ten
centimeters.  Also, since it happens that a liter is a cube
that is ten centimeters on a side, it follows that "dm-3"
can just as easily be translated as "per liter".

So if we have 2 moles of HNO3 per liter, and we have 2 moles
of NaOH per liter, then we are probably talking about liters
of water.  Chemists seldom use liters of air in their
reactions!  And when they DO use air, or some substance
other than water, they ALWAYS say so.

Also, please note that pure NaOH (for example) is a solid
substance.  Two moles of sodium hydroxide has a mass of only
about 56 grams.  By itself, it does NOT occupy a liter of
space!  This is one major reason why water is involved in so
many chemists' reactions:  It acts as a "space-filler".  If
we want to react X grams of Substance A with Y grams of
Substance B, but one of these substances occupies ten times
the volume of the other, how can we mix them simply and
thoroughly?  The answer chosen is to use water.  The unequal
volumes of the two substances can be separately mixed with
amounts of water that ARE equal.

Other reasons to use water include the fact that most
substances don't chemically react with water, the fact that
a great many substances mix very thoroughly indeed with
water, AND the fact that when something dissolves in water,
the total volume of liquid hardly increases at all!  (There
is space between water molecules, which can accommodate
molecules of other substances.)  Such a mixture is usually
called a "solution", but occasionally you may need to refer
to the mixture as a "suspension".  (Note:  you DO have to be
concerned about changes in the volume of water, if you are
working with suspensions.)  So, if we take the average
Substance A and mix it with water,  Substance A becomes very
evenly distributed throughout the volume of space occupied
by the water -- and that's all.  Since they probably won't
chemically react, Substance A remains Substance A.  Now do
the same for Substance B ... and when the two volumes of
water are mixed together, we KNOW that Substances A and B
are being thoroughly mixed with each other!

Next, you specifically mentioned "(ml)=25", which is a
standard reference to 25 milliliters.  A milliliter is a
cube one centimeter on a side, and is defined as being one
thousandth of a liter.  Since a liter measures 10x10x10
centimeters, it should be obvious that there are a thousand
cubic centimeters in a liter.  Also/again, whenever chemists
describe a measurement such as 25 milliliters, if they don't
specify some substance other than water, then it is usually
quite safe for you to assume that they ARE describing some
mixture that is mostly water.

Two more reasons that water is used so often:  It is easy to
manipulate in precise volumes, and it has a large "specific
heat" (the amount of heat energy it takes to change the
temperature of a unit mass of substance by one degree --
usually Celsius or degrees C).  Those two factors let us
"scale" the rate of a chemical reaction.  If two subtances
happen to react with so much violence as to destroy
laboratory equipment, we can simply diulte the substances
with so much water that their reaction becomes safely
measurable, in a highly controlled way.

Enough clarification; on to your Question, concerning how to
find the energy released per mole -- which stll needs a bit
of clarification!  A mole of what?  Hydrogen nitrate (more
often called "nitric acid") or sodium hydroxide?  Many
chemical reactions are not so convenient as this one, in
which one mole of each of the two substances will react
COMPLETELY, when mixed.  Historically, when chemists simply
didn't know outcomes such as this in advance, they had a
simple answer:  Pick one!  Pick a mole of some substance,
and let it react completely with some other substance, and
measure the energy.  The heat released can then be described
in terms of that single mole of the selected substance.
(Afterwards, the resulting chemical compound(s) can be
studied to learn exactly what sort of reaction occurred, and
how many moles were involved, of the other substance.)

So, since this particular case has a one-to-one ratio of
involved moles of substances, the "per mole" in your
Question can refer to EITHER the hydrogen nitrate or the
sodium hydroxide.  Feel free to pick one!

The experiment describes using 25 milliliters of each of
nitric acid and sodium hydroxide solutions.  So the total
volume of water is 50 milliliters, which conveniently has a
mass of 50 grams.  And that is your mass of water; its
temperature change you gave as 6.5, which would be degrees
Celsius (the mystery C in your Question).

Next, since 25 milliliters is 1/40 of a liter, and since for
each chemical reactant two moles were mixed with one liter
of water, it follows that the reaction in the 50 ml of water
involved 1/20 of a mole of each of hydrogen nitrate and
sodium hydroxide.

Finally, after you do the energy computation which you
already know, you simply mulitply that by 20 to get your
desired Answer.