Student Name
Course Name—Period #
The Molar Volume of a Gas
Abstract:
The molar volume of an ideal gas is accepted to be 22.4 L at 1 atm pressure and
0°C. Though gases seldom behave ideally, the molar volume of many gases is quite
close to this value. Since many chemical reactions involve gases, and by assuming
ideal behavior, we can use this value for molar volume in performing stoichiometric
calculations if the pressure, temperature and volume of the gases involved in the
reaction are known.
Introduction:
In 1811, Amadeo Avogadro proposed that at the same temperature and
pressure, equal volumes of different gases contain the same number of particles. By
using the ideal gas law, PV=nRT, at standard temperature and pressure, one mole of a
gas is found to occupy 22.4 L. By Avogadro’s hypothesis, this means one mole of any
ideal gas will occupy 22.4 L at STP.
In this experiment hydrogen gas is generated by the reaction between solid
magnesium and hydrochloric acid:
Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)
By measuring the temperature, pressure—which must be corrected to account for the
pressure due to water vapor—and volume of the hydrogen gas produced, and by
assuming ideal behavior, the ideal gas law can be used to find the moles of hydrogen
gas in the flask. The molar volume of the hydrogen gas under the experiment’s
conditions can then be found by using the proportion between volume and moles stated
by Avogadro. Then finally, the molar volume of the hydrogen gas at STP can be found
using the combined gas law.
Experimental:
For the first part of this experiment, we used a metric ruler, a 125 mL Erlenmeyer
flask, and a 600 mL beaker to prepare the water bath and reaction flask. First, we
obtained a piece of magnesium ribbon and measure its length to the nearest mm and
recorded. Then we placed the magnesium ribbon into the 125 mL Erlenmeyer flask.
Next we found the mass of a 1 m piece of magnesium ribbon and recorded it. Then we
filled the 600 mL beaker about ¾ full with tap water for the water bath—there should be
enough water to completely cover the gas level in the flask. The water bath’s
temperature should be stabilized at room temperature before performing the reaction.
The second part of the experiment’s preparation involved getting the CBL 2
interface and equipment ready. For this part of the experiment we used a Gas Pressure
and a Temperature sensors, a 20 mL syringe and a small beaker. After connecting the
sensors to the CBL 2 interface, we then firmly and snuggly placed the stopper
connected to the Gas Pressure sensor into the 125 mL Erlenmeyer flask. We then
obtained about 10 mL of 3.0 M hydrochloric acid in a small beaker. Then we drew up
5.0 mL of the hydrochloric acid into the 20 mL syringe and threaded it onto the two-way
valve on the stopper. We then submerged the Erlenmeyer flask into the water bath as
well as placed the Temperature sensor into the water bath while making sure the
probe’s tip is not touching the beaker.
Once we had everything set up and the flask still submerged, we started the
“DataMate” program to begin collecting pressure and temperature data every two
seconds. After about 20 seconds, we opened the two-way valve, squirted the 5.0 mL of
hydrochloric acid into the flask, and then closed the valve again. We gently swirled the
flask as the reaction took place, being careful to keep it submerged in the water bath.
After the pressure readings were no longer changing we stopped the data collection
process. We then removed the flask from the water bath and removed the stopper.
Then we used the graphing calculator on the CBL 2 unit to view the graph of the
pressure vs. time to find the maximum pressure change and recorded this value. Then
we viewed the temperature vs. time graph to determine the temperature of the water
bath and recorded this value as well.
After rinsing and cleaning the flask, we then repeated this experiment two more
times.
Analysis:
We first calculated the water vapor pressure in the flask at the experimental
temperatures involved by extrapolation since our reference table did not have our exact
experimental temperatures.
For Trial 1:
Known:
* experimental temperature (Texp) = 23.9286°C
* water vapor pressure (Pwater1) at 23°C (TP1) = 2.809 kPa
* water vapor pressure (Pwater2) at 24°C (TP2) = 2.984 kPa
Pwater exp  Pwater1
Pwater 2  Pwater1

Texp  TP1
TP2  TP1
Pwater exp  2.809 kPa
2.984 kPa  2.809 kPa
Pwater exp  2.809 kPa
0.175 kPa

23.9286 C  23 C
24 C  23 C
0.9286 C

1 C
Pwater exp = 2.972 kPa
We then calculated the ΔP for each of the three trials using the maximum and initial
pressures of the gases in the flask and the water vapor pressure. ΔP will be the partial
pressure of hydrogen gas in the flask.
I will note here that from this point on I am omitting Trial 1. After performing the
calculation stated below, ΔP is going to end up being a negative quantity for Trial 1.
Obviously, this set of data will not work.
For Trial 2:
Known:
* maximum pressure = 108.090 kPa
* initial pressure = 99.271 kPa
* water vapor pressure = 2.955 kPa
ΔP = Pmax − Pinitial − Pwater
ΔP = 108.090 kPa − 99.271 kPa − 2.955 kPa = 5.865 kPa
To find the moles of hydrogen gas in the flask we used PV=nRT where P is the partial
pressure (the ΔP from the data table) of H2, V is the volume of the flask, and T is the
temperature of the water bath (assumed to also be the temperature of the gases in the
flask).
For Trial 2:
Known:
* Pressure = 5.865 kPa
* Volume = 0.1345 L
* Temperature = 296.9833 K
PV = nRT
n
PV
RT
n
(5.865 kPa)(0.1345 L)
 3.20 x 10 4 mol H2
kPa
(8.31 Lmol
)(
296
.
9833
K
)
K
Using Avogardo’s law we found the molar volume of the H2(g) under our experimental
conditions.
For Trial 2:
Known:
* Volume of flask = 0.1345 L
* Moles of hydrogen gas = 3.20 x 10-4 moles
Vexp molar volume

nexp
1 mol
molar volume 
0.1345 L
 420. L H2
3.20 x 10 4 mol
Using the combined gas law we converted the above molar volumes to STP conditions.
For Trial 2:
Known:
* Partial Pressure of hydrogen gas (P1) = 5.865 kPa
* Volume of flask = 0.1345 L
* Temperature of gas = 296.9833 K
* Standard Pressure = 101.325 kPa
* Standard Temperature = 273.15 K
P1V1 P2 V2

T1
T2
V2 
P1V1T2
P2T1
V2 
(5.865 kPa)(420. L)(273.15 K )
 22.4 L H2
(101.325 kPa)(296.9833 K )
Therefore, from these two trials our average molar volume for this lab is 22.4 L for the
H2(g) since both trials were the same.
Next, we calculated the percent error for this experiment using the average molar
volume for the hydrogen gas.
Known:
* accepted value for the molar volume of an ideal gas at STP = 22.4 L
* experimental molar volume of hydrogen gas at STP = 22.4 L
 accepted value  experimental value 
 100
% error  

accepted
value


 22.4 L  22.4 L 
 100  0% error
% error  

22
.
4
L


Results / Conclusions:
As indicated by the 0% error for this experiment, our molar volume of 22.4 L for
hydrogen gas agrees with the accepted value for the molar volume of an ideal gas at
STP. Even when checking with a reference book (Chemistry, 6th Ed., Zumdahl) which
lists the molar volume of hydrogen gas at STP is 22.433 L, our results are still pretty
good given the precision of the lab.
It should be noted that when finding the moles of hydrogen gas in the flask there
are two methods in which this can be done. One method would use the stoichiometric
relationship between the magnesium and hydrogen gas in the reaction:
Mg(s) + 2H+(aq) → Mg2+(aq) + H2(g)
Since the magnesium will be the limiting reactant in this experiment—all the magnesium
does in fact react—this method would be acceptable provided the magnesium is pure
and not its oxide. Thus, the magnesium would have to “cleaned” and even then I
cannot be sure if all of the magnesium oxide, or any other contaminant, would be
removed. The method I choose to use involves the ideal gas law. I know that there will
be hydrogen gas in the flask after the reaction regardless of the state of magnesium.
Assuming ideal behavior by the hydrogen gas, the data can be obtained as we did it to
use the ideal gas law to find the moles of hydrogen gas.
Even though our results agree with the accepted value for ideal gases at STP,
there still could be a significant error in the data. The temperature obtained was the
temperature for the water bath. It is assumed that the temperature of the gases in the
flask is also the same temperature as the water bath. If this were the case, especially
since the water bath and hydrochloric acid were both at room temperature, why did the
temperatures differ from trial to trial? It should be noted that the reaction that took place
is exothermic and is responsible for the slight increase from room temperature.
However, in the time allotted for the trials (5 minutes maximum) there is no way, in my
opinion, that the temperature inside the flask and the water bath could come to an
equilibrium and be the same. Therefore, the possibility exist that the actual temperature
of the hydrogen gas used in this experiment is in error—I believe the temperature was
probably higher for the hydrogen than what is actually reported. This is especially true
since the pressure spikes early on in the reaction and drops back down. The heat
generated by the reaction would cause an increase in temperature inside the flask early
on. As the reaction approaches completion the amount of heat released would lower
causing the temperature to lower as the energy is distributed throughout the gas, the
glass of the flask, and the rest of the apparatus. This would then cause the pressure to
drop back down. It is the pressure spike we used to determine ΔP but we do not know
the actual temperature of the gas at that point in time.
As for our omitting the data for our first trial, the cause for our error is most likely
that we did not use sufficient magnesium, only 10.0 mm, to produce enough hydrogen
gas to cause a pressure change large enough to be detected.
There are two changes to the procedure that could improve the experiment
design. First, as mentioned earlier, using pure magnesium for the experiment (if it were
possible) would insure that we have the true number of moles of hydrogen gas inside
the flask. Secondly, inserting the Temperature sensor inside the flask by using the third
possible hole in the stopper would give a better temperature reading of the gas itself
and have the temperature be an assumption. It would also be interesting to see if other
gases that could be generated by a reaction inside the flask, like CO 2 and NH3, would
give the same results we achieved in this experiment.