EXPERIMENT 9
Evaluation of the Universal Gas Constant, R
Outcomes
After completing this experiment, the student should be able to:
1. Determine universal gas constant using reaction of an acid with a metal.
2. Demonstrate understanding of universal gas constant.
3. Show accuracy and precision of their results using average and standard deviation of their
results.
Introduction
The ideal gas law gives the relation between the pressure (P), volume (V), temperature (T), and the
number of moles of gas (n) in volume V:
PV = nRT
(1)
R is called the universal gas constant. Eq. 1 is called the ideal gas law because it assumes that there
are no attractive or repulsive forces between the gas molecules. For this reason, it can be applied to
any gas or gas mixture, independent of the nature of the gas. “Real” gases will show deviations from
the ideal gas law, but for most applications such deviations become important only at high pressures
or low temperatures. At atmospheric pressure and room temperature deviations from the ideal gas law
typically are only 1 to 2%.
In this experiment we will assume that the ideal gas law can be applied to hydrogen gas (H2), and we
will determine the value of R by measuring the volume of H2 gas evolved in the reaction of a known
mass of Magnesium metal, Mg, with excess hydrochloric acid, HCl.
In the L.atm system, pressure has the units of atmosphere (atm), volume is in L, n in moles and T in
Kelvin (K). If we write these units in the gas law:
P(atm).V(L) = n(mol).R.T(K)
We see that the units for the gas constant R are L.atm/mol.K.
In the SI system, pressure has the units of pascal (Pa), volume is in m3, n in moles and T in Kelvin
(K). The pressure unit Pa equals N.m−2 (force/area). R will then have the units J/mol.K.
L.atm.system:
SI system:
R = 0.08206
R = 8.314
L.atm/mol.K
J/mol.K
In the calculations for this experiment we will use the L.atm system. You will be able to calculate the
value of R from your own experimentation, by measuring the values of P and V for a known number
of moles of gas evolved, n, in three separate trials, then calculating the value of R as determined in
each trial. Obviously, in your final calculation of R, it is important to use consistent units.
The procedure uses the reaction between magnesium metal and hydrochloric acid, resulting in the
formation of hydrogen gas:
Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)
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The hydrogen gas evolved will be collected over the dilute HCl solution in an inverted buret. This
means that the gas collected will contain H2 but also water vapours, which has a “vapour pressure”,
PH2O. The pressure exerted by the H2 will be the atmospheric pressure Patm minus the vapour pressure
of water:
PH2 = Patm − PH2O
(2)
The vapour pressure of water, PH2O, is given in mm Hg (see the following table).
Table 1. Vapour pressure of water, PH2O, at different temperatures.
T (oC)
15
16
17
18
19
20
21
PH2O (mm Hg)
12.8
13.6
14.5
15.5
16.5
17.5
18.7
T (oC)
23
24
25
26
27
28
29
PH2O (mm Hg)
21.1
22.4
23.8
25.2
26.7
28.3
30.0
22
19.8
30
31.8
The atmospheric pressure may be assumed to be 1 atm (760 mm Hg) or can be read on a barometer.
The temperature T will be the temperature in the laboratory.
A further correction to Patm is needed to correct for the final liquid level in the buret after the reaction
is complete. The correction for the difference in water level between inside the buret and the beaker
must be measured in order to correct for the pressure difference. Since the density of mercury (Hg) is
13.6 g/mL, and for water it is 1.0 g/mL, we can directly convert the level difference in mm water to
mm Hg:
ΔPlevel correction (mm Hg) =
mm level difference
13.6
(3)
Of course this ΔP may be positive (when the level of water in the burette is above the level in the
beaker) or negative (when the level in the buret is below the level in the beaker). The final result is:
PH2 = Patm − PH2O − ΔPlevel correction
(4)
To convert mm Hg to atm or Pa, and oC to K you need the following conversions:
1 atm = 760 mm Hg
K = oC + 273.15
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Measurement versus Numbers: There is an important conceptual distinction between measurements
and numbers. It is important to note that “measurements” are not simply just numbers, rather
measurements are obtained by comparing an object with a standard "unit." On the other hand,
“numbers” are obtained by counting or by definition. Numbers are “exact” values of expression
whereas measurements are intrinsically “inexact”. Finally, arithmetic is based on manipulating
numbers, whereas the sciences such as chemistry, are based on “measurements”.
Uncertainty: There is no such thing as a perfect measurement with no associated error. In fact, every
measurement has an inherent degree of uncertainty which is referred to as associated uncertainty. This
uncertainty comes from a combination of factors including the instrument, the experimental method,
and the person making the measurement. In fact, each time a repetitive measurement is made, it is
possible that a slightly different measured value can be recorded.
Average Value: Since it is impossible to determine any measured value with absolute certainty, we
are often confined to using mathematical expressions that define the accuracy and precision of the
measurement(s). An average value calculated by using the numerical values for the measurements
reflects the accuracy of a given set of measurements. An average, , is mathematically expressed as
the sum of all the values divided by the total number of measurements (values) made. This can
symbolically be written as,
wherex is the average of n different number of measured values.
Standard Deviation: The precision of a set of measurements is reflected in the statistical expression
called the standard deviation (σ). The standard deviation reflects the ‘spread’ in the measured data
points. It is symbolically written as,
Note: Any scientific calculator has built in functions that determine the average and standard
deviation of a series of values.
When making a measurement, the right-most quoted digit provides the last degree of precision for that
measurement. Figure 1.2 gives two examples of this statement. For the ruler, the measurement is only
precise to the hundredths place. For the analytical balance, the measurement is only precise to the
ten-thousandth place. It is important to realize that instruments that provide greater precision come at
a higher cost and maintenance. A typical bathroom scale that has precision to the ‘ones’ place costs
approximately fifteen dollars. An analytical balance in the chemistry lab which has precision to the
‘ten-thousandths’ place, costs several thousands of dollars.
Example. You repetitively weigh a penny three times and find the masses to be,
1.
2.
3.
1.259 g
1.273 g
1.280 g
The average mass:
x
1.259  1.273  1.280
 1.271
3
The standard deviation for this set of n=3 measurements is,
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In this experiment, you will do three separate trials to find the value of R as determined in each trial.
The SD can be expressed as absolute value or as a relative value (%):
SD(%) = {SD(absolute)/Rave}x100%
Sample calculations:
a) PH2 = Patm − PH2O − ΔP
with ΔP = mm level difference/13.6 (mm Hg)
Patm = _______________
(mm Hg)
PH2O = _______________
(mm Hg)
ΔP =
(mmHg)
_______________
PH2 = _______________
VH2 =
___________ mL
(mm Hg) = __________________ atm
= ____________ L
b) n = mass Mg (g)/atomic mass Mg =__________ moles Mg = __________ moles H2 (n in
gas equation)
c) R = PV/nT
R = ___________ L.atm/mol.K
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Safety Precautions
Handle concentrated HCl in the fumehood only, wear gloves and safety glasses (as always!). Rinse
any spills immediately.
Hydrogen is highly flammable, so don’t keep any open flames or electrical sparks close to your
experiment. The amount of gas evolved is relatively small and causes no danger once released in the
laboratory.
Materials and Equipment
Balance, 500 mL beaker, 50 mL buret, 10 mL graduated cylinder, conc. HCl, Mg ribbon, funnel, ruler
(mm scale).
Procedure
1. Weigh approximately 25 mg (0.0250 mg) Mg ribbon to the nearest 0.001 g on a top-loading
balance.
2. Bend the piece of ribbon to make a ring so that it will fit tightly into neck (open end) of the
buret (check with your instructor if you are not sure).
3. Obtain a 500 mL beaker and fill it with water to almost full.
4. Obtain a 50 mL buret. Make sure the stopcock is tightly closed. Measure the volume at the
bottom of the buret between the stopcock and the 50 mL mark by adding water from a 10 mL
graduated cylinder. Record this volume in your datasheet (it will be approximately 4-5 ml).
Empty the buret.
5. In the fumehood, pour approximately 10 mL 6M. HCl (provided) into the buret. Wash down
with water any acid drops that may stick to the buret wall.
6. Push the Mg ribbon into the open end of the buret, to approximately 5 cm from the top. Fill the
buret to the top with water.
7. Close the buret with your figure and invert it in the 500 mL beaker, making sure the Mg stays in
place. The open end of the buret should be close to the bottom of the beaker but should not be
touching it.
8. The HCl in the buret will gradually sink and diffuse to reach the Mg and start to react. If the Mg
breaks free make sure that all will still react. This may be a slow process but you will have to
wait until all Mg is reacted. Once all Mg has reacted, make sure that the buret is in an
accurately vertical position and record the solution level. Also record the level difference (in
mm, not mL!) between the water level in buret and top of the water in the beaker.
9. Calculate the value of R using eq. 4, of course with correct units!
10. Repeat this complete procedure two times.
11. Calculate the average value and the standard deviation of R from your three experiments.
Disposal
The only reaction products are MgCl2 and the remaining excess HCl. Dispose as instructed by your
Instructor/Teaching Assistant. Rinse out the buret and beaker with distilled water.
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Experimental General Chemistry 1
Experiment 9: Evaluation of the universal gas constant, R
Laboratory Data Sheet
Name: ______________________________________________ Section:
________
1. Experimental results and calculation of the gas law constant
Trial 1
Trial 2
Trial 3
1. Mass of Mg
2. Moles Mg = mass/24.3 (g/mol)
3. Mol of Mg = mol of H2
4. Buret volume above 50 mL mark
5. Final buret reading (mL)
6. 50 mL - #5 above
7. Volume of gas (mL) = (4) + (6)
8. Volume of gas (L) = (7)/1000
9. Barometric pressure (mm Hg) of lab
10. Level difference: (H2O level in
buret− H2O level in beaker) (mm)
11. ΔP use equation 3 (mm Hg)
12. Room temperature (K)
13. PH2O (mm Hg) – see Table 1
14. PH2 (eq. 4) (mm Hg)
760 – (11) – (13)
15. PH2 (atm) = (mmHg/760)
16. R (L.atm/mol.K: (8)*(15)/(3)*(12)
Calculations:
Average value of R
Calculations next page
Standard deviation (SD) of R for 3 trials
Calculations next page
Relative SD of R, % = (SD/Rave)x100%
Calculations next page
Difference with literature value for R (%)
Calculations next page
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Show calculations:
R average
SD for R
RSD for R
Difference (%) from literature value (R = 0.08206 L.atm/(mol.K)
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