Solubility of Oxygen

Apparatus as used by M.Arthurs (1916)

Oxygen is slightly soluble in water and in aqueous solutions. Several methods have been devised for estimating the dissolved oxygen, and of these that due to Winkler is regarded as one of the most convenient and trustworthy. As used by M'Arthur the method consists in pouring the solution containing dissolved oxygen into a flask graduated to 250 c.c. and 252 c.c. respectively, as shown in fig., until the former level is reached. One c.c. each of alkaline potassium iodide and manganous chloride solution are added, and the stopper inserted to the 252 c.c. level. On shaking, the manganous hydroxide liberated by the sodium hydroxide is oxidised by the dissolved oxygen. The stopper is removed and the whole acidified with 3 c.c. of concentrated hydrochloric acid and well shaken. Titration of the liberated iodine, preferably in another flask or dish, with thiosulphate gives the amount of oxygen.

Apparatus as used by Letts and Blake (1899).

Letts and Blake use a large separating funnel (fig.), graduated to hold exactly 350 c.c. of liquid. It is filled with water, 7 c.c. removed and replaced by 5 c,c. of ferrous sulphate solution and 2 c.c. of concentrated ammonia. The stopper is inserted, the whole well shaken and allowed to stand fifteen minutes. Upon inverting and filling the open tube with diluted sulphuric acid, the tap may be opened. The acid enters owing to contraction caused by chemical action within the bulb, and, when all the ferrous hydroxide has dissolved, the solution is titrated with permanganate.

Volumetric methods are frequently adopted, the volume of gas absorbed by a given volume of gas-free liquid, or, conversely, the volume expelled from the saturated solution being directly measured.

There are several ways in which the solubility of a gas may be expressed. By β' is meant the volume of gas reduced to 0° C. and 760 mm. which is absorbed by one volume of the liquid under a total pressure of 760 mm., which includes the vapour pressure of the solvent.

β is the volume of gas at N.T.P. absorbed by unit volume of the liquid under a partial pressure of the gas itself of 760 mm. irrespective of the vapour pressure of the liquid. It is known as Bunserts absorption coefficient. Hence if f is the vapour pressure of the solvent at any temperature

β' = β(760-f)/760

Ostwald's solubility product, I, represents the ratio of the volume of absorbed gas to that of the liquid at the temperature and partial pressure of measurement. It is not reduced to 0° C. and 760 mm. Hence, if the measurements are made at atmospheric pressure

l = β(l + 0.00367t).

In the following table are given the results obtained by different modern investigators for the absorption coefficient, β, of oxygen in distilled water.

Solubility of Oxygen in Water

Temperature, °C.	Winkler, 1891.	Bohr and Bock,1891.	Fox, 1909.	Adeney and Becker, 1919.
0	0.04890	0.04961	0.04924	0.04660
10	0.03802	0.03903	0.03837	0.03626
20	0.03102	0.03171	0.03144	0.02965
30	0.02608	0.02676	0.02665	0.02479
40	0.02306	0.02326	0.02330	. . .
50	0.02090	0.02070	0.02095	. . .

Several complicated empirical formulae have been given by means of which the solubility of oxygen may be calculated for any desired temperature. Winkler gives, for temperatures between 0° and 30° C., the formula

β = 0.04890 – 0.0013413t + 0.0000283t² - 0.00000029534t³.

Fox gives an analogous expression for a temperature interval of 0° to 50° C.:

β = 0.049239 – 0.0013440t + 0.000028752t² - 0.0000003024t³.

The solution of oxygen in water is accompanied by an expansion of the latter, 1 c.c. Becoming 1.00115 c.c. on the absorption of 1 c.c. of oxygen.

The Rate of Solution of Oxygen and Air in Water

Comparatively little work has been carried out on the velocity with which partially or completely de-aerated water reabsorbs oxygen and nitrogen from the atmosphere. Two cases merit consideration, namely:

1. When the water is subjected to agitation so that fresh surface layers are continually formed, the rate of gaseous absorption is then at its maximum.
2. When the water is quiescent. In this latter case the process is not purely one of absorption followed by diffusion into the body of the liquid from the surface layers, as has generally been supposed. It is considerably more rapid than this. Experiment shows that the gases do not remain concentrated in the surface layers, but tend to "stream" downwards under the influence of gravity, and thus to promote comparatively rapid mixing. This is a point of very great biological and economic importance.

Much of the modern research on the subject is due to Adeney and Becker, whose initial researches were concerned with the rate of absorption of air by water under gentle agitation. They begin with the assumption that, during the process of solution, the rate of passage, R, of gas into the liquid is proportional to the partial pressure of the gas, p, and the area, A, of the liquid exposed. Hence

R = uAp

where u is the velocity of solution per unit area. Simultaneously with absorption, however, evaporation of the gas into the air takes place, with a rapidity proportional to the area A, and to the concentration, w, of the gas in the upper layers. If the coefficient of escape of the gas per unit area and volume of the liquid is denoted by f, the rate of escape, R¹, of the gas from the liquid is given by the expression

R¹ = fwA,

w being expressed as grams of gas per c.c. of the upper layer. The net rate of solution of the gas, therefore, is

R - R¹ = uAp – fwA,

and the two latter terms become equal upon saturation, when

fw = up.

Denoting the volume of the liquid by V, it follows that the rate of solution



where a = uAp/V and b = fA/V, time being expressed as θ.

The above equation may, for the sake of convenience, be expressed somewhat differently. Writing

,

it follows that

;

whence

;

or, delogarising,

w – a/b = Ce^-bθ

C being a constant. When w = 0, θ = 0. Hence and

C = -a/b

and

.

For practical purposes it is most convenient to express the results in terms of the percentage of saturation. So that if w is the amount of gas in solution initially, expressed as a percentage of total saturation, the amount w dissolved after a given time θ is



Now f varies both with the temperature and the humidity. For an atmosphere saturated with moisture the following values for f have been determined, the water being gently agitated to ensure thorough mixing:

For oxygen	f = 0.0096 (T-237)
For nitrogen	f = 0.0103 (T-240)
For air	f = 0.0099 (T-239)

T being the absolute temperature, and θ expressed in minutes.

An example will make the value of the above equation quite clear. Consider a cubic decimetre of water at 2.5° C. and containing 40 per cent, of its total saturation capacity for oxygen. If it exposes one side (100 sq. cm.) to oxygen, how much gas will be dissolved in one hour under gentle agitation.

It is unnecessary to consider the pressure of the gas since Henry's Law is obeyed and the desired result is to be calculated in percentage of total saturation. Since θ = 60, w₁ = 40, f = 0.0096 (275.5 - 237), it is easy to calculate that

w = 11.8.

In other words, after an hour the oxygen content will have risen from 40 to 51.8 per cent, of saturation.

The foregoing values for f were determined experimentally for water under gentle agitation in an atmosphere saturated with moisture. Such conditions are largely artificial.

For quiescent bodies of water the following data have been obtained:

	Value of f at 15° C.
Air dried over calcium chloride	0.61
Air of average humidity	0.34
Air nearly saturated with moisture	0.23

These results are very striking, showing that dry air, is much more rapidly absorbed than moist. This is interpreted as meaning that the process by which the dissolved gas is carried down into the body of the liquid is influenced by the rate of evaporation of the liquid surface, this being at a maximum when the air is dry. In the case of pure water this is merely a temperature effect, the evaporation causing a cooling of the surface layers and, at temperatures above 4° C., a gravitational circulation. In the case of solutions, such as sea-water, density changes, consequent upon variation in superficial concentration, are superimposed on the temperature effect, so that more rapid mixing is likely to occur. This is confirmed by experiments which yielded the following values for f at 15° C. under similar conditions of average humidity:

Tap-water	f = 0.388
Sea-water	f = 0.509

The rate of solution of oxygen in water does not appear to be appreciably retarded by a thin layer of petroleum.

As a general rule the presence of dissolved salts, chemically neutral towards oxygen, reduces the solubility of the gas. Thus, in the case of sea-water, the value for β falls with rising chlorine content, as indicated in the following table:

Solubility of Oxygen in sea-water from a free, dry atmosphere, at 760 mm.

Parts of Chlorine per 1000	Temperature, ° C.
	0	4	8	12	16	20
0	10.29	9.26	8.40	7.68	7.08	6.57
4	9.83	8.85	8.04	7.36	6.80	6.33
8	9.36	8.45	7.68	7.04	6.52	6.07
12	8.90	8.04	7.33	6.74	6.24	5.82
16	8.43	7.64	6.97	6.43	5.96	5.56
20	7.97	7.23	6.62	6.11	5.69	5.31

These results may be expressed mathematically by the equation

1000β'' = 10.291 – 0.2809t + 0.006009t² + 0.0000632t³ – Cl(0.1161 – 0.003922t + 0.0000631t²),

the chlorine being expressed as grams per litre.

The foregoing data have been recalculated to parts per million by Whipple. Earlier data are those of Clowes and Biggs, who show that the solubility of atmospheric oxygen in diluted sea-water falls regularly with the amount of sea-water present; the sodium chloride, as the predominant salt, has a determining effect upon the quantity of gas dissolved.

The following data, based on the results of M'Arthur, give the actual and relative solubilities of oxygen in solutions of various salts at 25° C.

Solubility of Oxygen in Aqueous solutions

Salt.	Molecular Concentration.	Grams per Litre.	Relative Density at 25° C.	c.c. Oxygen per Litre.	Relative Solubility.
Water only	. . .	. . .	1.0000	5.78	100
NaCl	m/8	7.31	1.0022	5.52	95.5
	m/4	14.62	1.0067	5.30	91.7
	m/2	29.23	1.017	4.92	85.5
	m	58.46	1.038	4.20	72.7
	2m	117.0	1.075	3.05	52.8
	3m	175.5	1.112	2.24	38.8
	4m	234.0	1.149	1.62	28.1
KCl	m/8	9.32	1.003	5.52	95.5
	m/4	18.64	1.0086	5.30	91.7
	m/2	37 28	1.020	4.98	86.2
	m	74.56	1.042	4.26	73.7
	2m	149.1	1.086	3.21	55.5
	3m	223.7	1.134	2.36	40.8
	4m	298.2	1.170	1.86	32.2
KI	m/8	20.75	1.013	5.65	97.8
	m/4	41.50	1.027	5.49	95.0
	m/2	83.0	1.056	5.20	90.0
	m	166.0	1.116	4.75	82.2
	2m	332.0	1.230	3.77	65.2
	5m	830.0	1.460	1.81	31.3
NH4Cl	m/8	6.69	1.0015	2.31	40.0
	m/4	13.37	1.0025	1.16	20.1
	m	53.47	1.0014	0.07	0.1
KNO3	m/4	25.28	1.015	5.49	95.0
	m/2	50.56	1.029	5.11	88.4
	m	101.11	1.059	4.61	79.8
	2m	202.22	1.110	3.65	63.1
Na2SO4	m/8	17.76	1.014	5.04	87.2
	m/4	35.52	1.032	4.60	79.6
	m/2	71.03	1.063	3.97	68.7
	m	142.06	1.13	3.00	51.9
K2SO4	m/8	21.78	1.016	5.11	88.4
	m/4	43.57	1.032	4.66	80.6
	m/2	87.13	1.060	3.89	67.3
MgCl2	m/8	11.91	1.011	5.35	92.6
	m/4	23.81	1.022	5.04	87.2
	m/2	47.62	1.044	4.37	75.6
	m	95.24	1.085	3.18	55.0
	2m	190.48	1.160	2.22	38.4
	4m	381.0	1.284	0.78	13.5
	5m	476.2	1.343	0.54	9.3
BaCl2	m/8	26.04	1.019	5.40	93.4
	m/4	52 08	1.042	5.04	87.2
	m/2	104.15	1.082	4.27	73.8
	m	208.29	1.177	3.10	53.6
CaCl2	m/4	27.75	1.022	5.08	87.9
	m	111.0	1.084	3.71	64.2
	5m	555.0	1.340	2.14	37.0

The solubility of oxygen in aqueous solutions of acids and alkalies is given by Geffcken as follows:

Solubility of Oxygen in dilute acids and alkalies

Solution.	Molecular Concentration	Grams per Litre.	c.c. Oxygen per c.c. at
			l (15° C.).	l (25° C.).
Water only	. . .	. . .	0.0363	0.0308
H2SO4	m/4	24.52	0.0338	0.0288
	m/2	49.04	0.0319	0.0275
	m	98.08	0.0285	0.0251
	3m/2	147.12	0.0256	0.0229
	2m	196.16	0.0233	0.0209
	5m/2	245.20	0.0213	0.0194
HCl	m/2	18.22	0.0344	0.0296
	m	36.45	0.0327	0.0287
	2m	72.90	0.0299	0.0267
HNO3	m/2	36.52	0.0348	0.0302
	m	63.05	0.0336	0.0295
	2m	126.10	0.0315	0.0284
NaOH	m/2	20.03	0.0288	0.0250
	m	40.06	0.0231	0.0204
	2m	80.12	0.0152	0.0133
KOH	m/2	28.08	0.0291	0.0252
	m	56.16	0.0234	0.0206

Oxygen is much more readily soluble in blood than in water; 100 c.c. of average human blood is able, when fully saturated in contact with air, to hold between 18 and 19 c.c. of oxygen measured at N.T.P. In ethyl alcohol, oxygen is several times more soluble than in water. Its solubility at any temperature may be calculated from the following equation:

β = 0.2337 – 0.00074688t + 0.000003288t₂.

The solubility of oxygen in aqueous solutions of ethyl alcohol at 20° C. is as follows:

Alcohol per cent, by weight	9.09	16.67	23.08	28.57	33.33	50.00	66.67	80.00
l	2.78	2.63	2.52	2.49	2.67	3.50	4.95	5.66

It will be observed that there is a decided minimum solubility at about 30 per cent, of alcohol.

These data refer to an atmosphere of oxygen of partial pressure, 760 mm.

Oxygen is also soluble in certain molten metals, e.g. platinum and silver, more than twenty times its own volume of the gas being absorbed in the case of the latter metal; the dissolved gas is largely, but not completely, restored at the moment of solidification of the metal, and the phenomenon of "spitting" is thus produced. The power of oxygen to diffuse through heated silver, whereas glass is impervious, is probably due to this solubility of oxygen in the metal.

Certain finely divided metals, especially platinum black and palladium black, can absorb many times their own volume of oxygen. In the case of the latter metal absorption is probably attended by the formation of an oxide or mixture of oxides, but in the case of the former, although the product may include an unstable oxide, the oxygen can be entirely recovered by reducing the pressure.

Wood charcoal can absorb eighteen times its own volume of oxygen at 0° C. and more than two hundred times its bulk at -185° C.; the absorbed gas is liberated if the charcoal is heated.

By thermal conductivity is understood the quantity of heat that would pass between the opposite faces of a unit cube with unit temperature difference between the faces. The value found for oxygen at a mean temperature of 55° C. is 0.0000593. According to the kinetic theory of gases the thermal conductivity, k, is given by the expression

k = fηC_v

where η is the viscosity of the gas and C_v the specific heat at constant volume. f is a constant, apparently depending on the ratio of the specific heats, and in the case of diatomic gases has the value 1.603.

The viscosity of oxygen at 23.00° C. and 760 mm. pressure is 2042.35×10^-7. The viscosity rises with the temperature. Its mean specific heat at constant pressure rises with temperature as indicated in the following table:

Specific heat of oxygen

Temperature Interval, °C.	Mean Specific Heat at Constant Pressure.
20 to 440	0.2240
20 to 630	0.2300

The ratio of the specific heat at constant pressure to that at constant volume is

γ = C_p/C_v = 1.899

- a value to be expected for a diatomic gas.

The molecular specific heat at constant volume is given by the expression

C_v = 4.900 + 0.00045t

and at constant pressure by

C_v = 6.50 + 0.0010T

where t and T are on the centigrade and absolute scales respectively. The molecular specific heat at constant pressure at 20° C. is calculated as 6.924 from the velocity of sound in oxygen by Kundt's method.

The coefficient of expansion per degree centigrade rise in temperature between 0° and 100° C., measured at constant pressure of one atmosphere, was determined by Jolly as 0.0036743, and found to be constant for a temperature ranging up to 1600° C.

For a gas that obeys Boyle's Law the coefficient of expansion at constant pressure is numerically the same as the coefficient of increase of pressure with rise of temperature at constant volume. This has been determined for a temperature interval of 0° to 1067° C. and has the value 0.0036652 in the case of oxygen.

The refractive index of oxygen is 1.000272 at 0° C. and 760 mm. for the sodium D line (λ = 5893×10^-8 cm.); the indices for other wavelengths not widely removed may be calculated from Cauchy's equation



where μ and λ represent the refractive index and wave-length respectively, whilst A and B are constants; the latter constant, B, is the coefficient of dispersion. For oxygen gas, A = 26.63×10^-5, and B = 5.07×10^-11. According to Cuthbertson, the refractive index, n, of oxygen for any incident light of frequency, f, is given by the expression



Examination of long layers of the gas shows oxygen to exert a selective absorption for light in certain parts of the spectrum.

The emission spectra obtained by an electric discharge through the gas under a reduced pressure and by the spark discharge are of a complex nature.

Both the magnetic susceptibility and the magnetic rotatory power of gaseous oxygen have been subjected to investigation.