Determination of the Ideal Gas Law Constant
Chaney Tang
Chemistry 121 – N11
June 22, 2026
Abstract
The task of lab 7 was to determine the value of the ideal gas constant, R, by measuring
the pressure, volume, and temperature and amount of hydrogen gas produced from reaction of
magnesium with hydrochloric acid. A piece of magnesium ribbon of 0.0381 grams was used to
react with hydrochloric acid in a eudiometer tube, producing hydrogen gas that was collected by
water displacement in the eudiometer tube. The volume, temperature, and pressure of the
hydrogen gas were all recorded, and these values were used to calculate the ideal gas law
constant. After correcting for the vapor pressure of water and the pressure exerted by the water
column in the eudiometer, the experimental value of R was determined to be
0.0673(L*atm)/(mol*K). The class average was 0.0751L atm/mol K with a relative average error
of 8.50 % from the accepted value of 0.0821L atm/mol K.
Background
All gases obey an equation of state known as the ideal gas law. It is expressed as:
PV =nRT
where P is pressure, V is volume, n is the number of moles of gas, T is temperature in Kelvin,
and R is the ideal gas law constant. The value of R has been experimentally determined to be
0.0821(L*atm)/(mol*K). It should be noted that the ideal gas law is an oversimplification that
applies only to ideal gases which molecules have no volume and no tendency to stick together.
Real gas molecules do have a volume and do have the tendency to stick together. Although real
gases are different from ideal gases, they behave similarly ideally at room temperature and
atmospheric pressure which allows the experimental determination of R using a real gas such as
hydrogen.
In this experiment, hydrogen gas is produced by the reaction of magnesium with
hydrochloric acid. From the stoichiometry of this reaction, one mole of magnesium produces one
mole of hydrogen gas. The chemical reaction is expressed below:
Mg(s) + 2HCl(aq)H2(g) + MgCl2(aq)
By measuring mass of the magnesium consumed, the moles of hydrogen gas produced
can be calculated. The hydrogen gas is collected over water in a eudiometer tube, and its volume,
temperature, and pressure are measured. The pressure of the dry hydrogen gas can be obtained by
correcting the atmospheric pressure for the vapor pressure of water and the pressure exerted by
the water column inside the tube. After all variables are calculated, R can be calculated.
Chemicals and Equipment Used
Magnesium ribbon
Analytical balance
Concentrated hydrochloric acid
Eudiometer tube
Deionized water
800 mL beaker
Copper wire
Thermometer
Ruler
Timer
Wash bottle
Procedure and Observations
A piece magnesium ribbon was cut and weighed on an analytical balance, weighing
0.0381 grams. The magnesium ribbon was wrapped loosely around a 5-cm piece of copper wire
that was bent into shape of a fish head. An 800 mL beaker was filled with deionized water up to
500 mL. 4.0 mL of concentrated hydrochloric acid was poured into a eudiometer tube. The acid
on the walls of the tube was gently rinsed down with deionized water using a wash bottle. The
copper wire with the magnesium ribbon was inserted 4 cm from the open end. Then the
eudiometer tube was completely filled up with deionized water until it overflowed, ensuring no
air bubbles remained. A finger was placed over the open end, and the tube was then inverted,
placed into a tub of deionized water with the open end submerged in water. The tube was
clamped in place, so it would stay stationary with the open end approximately 0.5 cm from the
bottom of the tub.
The reaction started at 11: 53 am and ended at 12:50 pm. Small bubbles of gas formed on
magnesium ribbon and fizzed up the closed end of the eudiometer tube. The reaction proceeded
steadily during the time duration of the experiment. As the reaction progressed, the size of the
magnesium ribbon decreased until it disappeared. Additionally, the color of the magnesium
ribbon changed throughout the reaction, starting as very shiny, turning black, then white again.
After the reaction stopped and the magnesium had dissolved, the temperature of the
solution was measured three times, one minute apart, and the readings were averaged. With the
volume and height of the water column inside the eudiometer above the water, the pressure was
all recorded.
Results
Data Table
Data Analysis
All calculations can be found on the last page or page 80 of the Lab Report
Discussions
As mentioned previously, the purpose of this experiment was to determine the numerical
value of the ideal gas constant, R. The experimental value obtained was 0.0673 L*atm/(mol*K)
compared to the accepted value of 0.0821 L*atm/(mol*K). There is an error of 18%. Possible
sources of error could have been having air trapped in the eudiometer tube would have increased
the measured gas volume, reading the eudiometer scale wrong, inaccurate measurement of the
water column height, or incomplete reaction of the magnesium. To improve this experiment,
multiple trials could have been conducted which would have given a more precise measurement
of gas volume, ensuring complete reaction of the magnesium.
Conclusion
From this experiment, the determined experimental value of the ideal gas law constant, R,
to be 0.0673 L*atm/(mol*K), compared to the accepted value of 0.0821 L*atm/(mol*K). While
result differed from the expected value by 18%, it still demonstrated that the ideal gas law can be
used to model the behavior of real gas, such as hydrogen. The discrepancy was most likely due,
as mentioned previously, air trapped in the eudiometer, inaccurate measurements of the water
column height, or incomplete reaction of the magnesium ribbon which would affect the
calculated pressure or volume of the gas. From this lab, practical experiences in collecting gas by
water displacement, correcting gas pressure for water vapor and column height, and applying
stoichiometry. Additionally though this lab, it reinforced the importance of precise technique
when measuring small quantities and how multiple sources of measurement error can compound
together affecting the final calculated result.