Law of simple ratios of volumes
TEC
Principle
According to Gay-Lussac’s law of chemical volumes, gases react in volume ratios which are
whole numbers. These values can be volumetrically determined.
Related topics
Law of constant proportions, Avogadro’s law, Gay-Lussac’s law of chemical volumes,
general equation of state for ideal gases, Gas-Lussac’s first law.
Tasks
Determine the volume ratio for the conversion of hydrogen and oxygen to water
experimentally by burning gas mixtures of different compositions and measuring the
resulting gas volume.
Fig 1: Experimental set-up
P3031401
PHYWE Systeme GmbH & Co. KG © All rights reserved
1
TEC
Law of simple ratios of volumes
Equipment
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
Slow eudiometer
Glass jacket
Heating apparatus
Power regulator
High voltage power supply, 0…10 kV
Connecting cord, 30 kV, l = 1000 mm
Digital thermometer
Immersion probe, NiCr-Ni
Glass tubes, straight, l = 80 mm
H-base -PASSSupport rod, l = 250 mm
Right angle clamp
Universal clamp
Magnet, l = 200 mm, d = 10 mm
Magnetic stirrer bar, l = 30 mm
Glass beaker, 250 ml, tall
Funnel, glass, do = 55 mm
Syringe, 50 ml
Cannula, 0.45×13 mm
Closure caps, GL18
Rubber caps
Rubber tubing, di = 6 mm
Silicone tubing, di = 7 mm
Gas bar
Graduated vessel, with handle
Reduction valve for hydrogen
Reduction valve for oxygen
Steel cylinder, hydrogen, 2 l, filled
Steel cylinder, oxygen, 2 l, filled
Table stand for 2 l steel cylinders
Wrench for steel cylinder
Silicone fluid for heating bath, 500 ml
Water
02612-00
02615-00
32246-93
32247-93
07367-00
07367-00
07050-00
13615-03
36701-65
02009-55
02031-00
37697-00
37715-00
06311-00
46299-02
36004-00
34457-00
02592-00
02598-04
41220-03
02615-03
39282-00
39296-00
40466-00
36640-00
33484-00
33482-00
41775-00
41778-00
41774-00
40322-00
31849-50
Set-up and procedure
Set up the experiment as shown in Fig. 1.
The gas supply for the experiment is stored in the small gasometers of the gas bar. When
assembling the gas bar, take care that the right-angled glass tubes which are inserted into
the holes of the rubber stoppers do not extend beyond the lower end of the stoppers. To
prepare the gas bar, fill the gasometers bubble-free with water so that the Erlenmeyer
flasks are completely filled. Attach one end of a tubing to one of the right angled glass
tubes and its other end to the reducing valve of the oxygen cylinder. Carefully let the gas
into the flask, whereby water is displaced into the plastic funnel. Seal the outlet tube with a
rubber cap and the upper opening of the funnel with a rubber stopper to prevent the gas
from being forced out by the water. This stopper must be removed when taking gas from
the gasometer. Fill the other gasometer with hydrogen in the same way.
Fit the slow eudiometer in the glass jacket according to the instruction manual. Ensure that
the screw caps are tight, so that the eudiometer is not able to shift its position. Mount the
2
PHYWE Systeme GmbH & Co. KG © All rights reserved
P3031401
Law of simple ratios of volumes
TEC
glass jacket on the support rods in such a manner that it rests lightly on the heating
apparatus. Use a funnel to fill silicone fluid in through one of the upper tubular sleeves, and
when it is full, drop a magnetic stirrer bar in. Close one tubular sleeve with a closure cap
and fix a short glass tube in the other one to hold the temperature probe, which must be
immersed in the bath fluid. Attach a piece of silicone hose to the hose connection of one
glass sleeve, so that the expanding bath fluid can drain through it into a beaker. Switch on
the heating apparatus and the power regulator, and heat the glass jacket to 110 – 120 °C.
During heating, mix the fluid by moving the stirrer bar with a bar magnet.
Connect the electrodes of the eudiometer lid to the power supply unit using high-voltage
connection cables. Before setting the lid on the device, switch on the unit and adjust the
voltage to 10 kV. Ensure that a continuous spark is generated between the electrodes. This
check is very important, as any intermittent sparking during the reaction would increase
the risk of the formation of explosive oxyhydrogen gas. Set the plunger of the eudiometer
to the zero scale graduation. Close the capillary tube on the lid of the eudiometer with a
rubber cap. Fill the syringe with the respective oxygen / hydrogen mixture (listed in
Table 1) by inserting the cannula in succession through the rubber caps of the two
gasometers and drawing the desired gas volume in. Slowly inject the gas mixture through
the rubber cap of the eudiometer lid and read the volume after the reaction (= V1). Record
the current temperature of the heating bath TB and the room temperature TR. After each
reaction, remove the lid of the eudiometer and press out evolved gas by pushing the
plunger.
V0 (H2) / ml
V0 (O2) / ml
0
40
5
35
10
30
15
25
20
20
25
15
30
10
35
5
40
0
Theory and evaluation
Gay-Lussac deduced from his observations of many different gas reactions, that gases
react in whole number volume relationships. Avogadro formulated the law that, at the
same temperature and pressure, the same volumes of ideal gases contain the same
number of molecules.
Consequently, at constant pressure p and constant temperature T, in accordance with the
reaction equation
2 H2 + O2 → 2 H2 O
two parts by volume of hydrogen react with one part by volume of oxygen to form two
parts by volume of water in the gas phase.
P3031401
PHYWE Systeme GmbH & Co. KG © All rights reserved
3
TEC
Law of simple ratios of volumes
V 0 (H2)−V 1( H2) V 0 (O2 )−V 1 (O2) V 1 (H2 O)
=
=
2
1
2
(1)
The initial (V0) and the end (V1) volumes result additively from the partial volumes of the
gases involved:
V 0 = V 0 (H2 ) + V 0 (O2)
(2.1)
V 1 = V 1( H2) + V 1 (O2 ) + V 1 (H2 O)
(2.2)
If there is a stoichiometric excess of oxygen ( V0 (H2) < 2/3 V0 ), then
V 1 (H2 ) = 0
V 1 (H2 O) = V 0 (H2)
V 1 (O2) = V 0 (O2)−1/2 V 1 (H2 O) = V 0 (O2)−1/2V 0 ( H2)
and equation (2.2) simplifies to
V 1 = V 0−1/2V 0 (H2)
(2.2.1)
Fig. 2: Dependence of the final volume V1 reduced to room
temperature from the initial volume V0 (H2) of hydrogen for
the combustion of hydrogen-oxygen mixtures of different
composition ( V0 = 40 ml, TR = 295.5 K)
4
PHYWE Systeme GmbH & Co. KG © All rights reserved
P3031401
Law of simple ratios of volumes
TEC
If there is an excess of hydrogen ( V0 (H2) > 2/3 V0 ), then
V 1 (O2) = 0
V 1 (H2 O) = 2V 0 ( O2 )
V 1 (H2 ) = V 0 ( H2)−V 1 ( H2 O) = V 0 ( H2)−2 V 0 (O2)
And equation (2.2) simplifies to
V 1 = V 0 (H2)
(2.2.2)
According to these relationships, the measured gas volume V1 first decreases linearly with
increasing initial volumes V0 (H2) of hydrogen (2.2.1), and then increases in the region of
excess hydrogen (2.2.2). The minimum value of the volume, which can be read from the
intersection of the two straight lines, is at exactly V0 (H2) = 2/3 V0. This corresponds to the
partial volume of hydrogen that is converted with a partial volume of oxygen at
V0 (O2) = 1/3 V0 quantitatively to water ( V1 = V1 (H2O); V1 (H2) = V1 (O2) = 0).
Any deviation from this stoichiometric composition results in an increase in the final volume
which is observed as compared to the stoichiometric mixture, due to excess oxygen or
hydrogen. For evaluation, we must correct the final volumes V1’ measured at heating-bath
temperature TB to the volumes V1 at room temperature TR using Gay-Lussac’s first law:
V 1 = V 1'
TR
TB
(3)
Data and Results
The plot of the final volume V1 against the initial volume V0 (H2) is shown in Fig. 2. From
the straight regression lines for both branches of the curve, V0 (H2) = 26.3 ml is obtained
as minimum volume. With equation (2.1) it follows that V0 (O2) = 13.7 ml.
These values confirm the conversion of the two gases in a volume ratio of 2:1.
P3031401
PHYWE Systeme GmbH & Co. KG © All rights reserved
5