How much solute is dissolved in how much solvent or solution? It is one of the most important question for every solution. We have studied various ways to express the concentration of solution in the previous post of Solutions. If you want to prepare a solution, you need to understand the process of dissolution of solute and learn about the factors affecting the process of dissolution. This can help us to prepare the solution of desired properties.
Let’s check solubility of few solutes. Why does table salt get dissolved in water but not in oil? Why does water and ethanol are miscible but water and oil are immiscible? Why is carbon dioxide more soluble in water as compared to the oxygen?
‘Like dissolves like’, you can take it as a slogan for dissolution. Table salt (Na+Cl-) is an ionic compound and water is a polar molecule, that’s why water is a suitable solvent for salt. On the other hand, oil is non-polar unsaturated hydrocarbon and so it doesn't dissolve salt readily. Similarly ethanol is a polar molecule like water so they have affinity for each other in contrast to water and oil.
Now you can guess the reason of higher solubility of CO2in water as compared to that of O2. Now you can predict the solubility if you know the chemistry of solute and solvent. It isn’t all about solubility though, there is some more chemistry behind it. Can you compare the solubility of O2 and N2 in water? Let’s see which factors decide the solubility of gases in liquids.
We have learnt the process of dissolution in the post of Solubility and Common ion Effect under chemical equilibrium. When a solute is dissolved in a solvent, an equilibrium is established between dissolved and undissolved solute molecules.
Gas molecules are much more mobile and free than the solid or liquid molecules. Therefore, when you dissolve a gas in a solvent, its molecules continually come in and out of the solvent and an equilibrium is established at the surface of the solvent between the gas molecules entering and leaving the solvent. It means that you can’t stop the exchange of molecules at the surface. There is an open gate for gas molecules. if it is crowded out there, more molecules will come inside, and if it is crowed inside, more molecules will move out, which means exchange rate will increase in either case. Is there any relation between crowding and exchange rate? Crowding shows the concentration of gas molecules and when it is outside the surface it is defined as vapour pressure, and when it is inside the surface it is defined by mole fraction. Mole fraction ultimately defines the solubility of gas.
William Henry gave the quantitative relation between pressure and solubility of a gas. This law states that at constant temperature, solubility of a gas in a liquid is directly proportional to the pressure of the gas.
pressure = KH. solubility
KH is the Henry’s constant. It is a function of temperature and its unit depends on the units used for pressure and solubility. Its value is different for different gases in different solvents.
Solubility of a gas is the concentration of the gas molecules in the solvent and you can express it in terms of mole fraction or molar concentration (mol/L).
If solubility is expressed by mole fraction and pressure by partial pressure of gas then you will find a relation:
p = KH. x
where p is the partial pressure of gas
xis the mole fraction of gas
KH = p / x
You must have noticed in the equation that x is inversely proportional to KH , which means that the gas which has lower value of Henry’s constant is more soluble. Value of KH at 298K for O2 is 34.86kbar and for CO2 its value is 1.67kbar. So, CO2 is more soluble than O2.
Partial pressure is the pressure exerted by molecules present above the surface of liquid. It gives an idea about the number of molecules present in gaseous phase. It can be defined in terms of concentration (moles/L) as well as pressure (kbar or atm).
If pressure is defined in terms of concentration and solubility is also expressed in moles/L then equation for Henry’s law will be modified as,
cg = KH. caq
where
cg = concentration in gaseous phase
caq = concentration in aqueous phase
In this case the KH will be unit less.
If pressure is defined in terms of partial pressure and solubility is expressed in moles/L, then equation for Henry’s law will be modified as,
p = KH. caq
In this case, the unit of KHwill depend on the unit used for pressure and concentration.
The value of Henry’s constant for oxygen dissolved in water at 298K can be defined in different units like 770 atm L/mol or 3.2×10−2 (KH unit less) or 34.86kbar.
We have studied earlier that the enthalpy of solution is always exothermic since energy is released in this process. That’s why on increasing the temperature, the equilibrium shifts backward and more molecules start leaving the solvent. It means that the solubility of a gas decreases with the increase in temperature.
Let’s practice a few problems based on Henry’s law
given,
p = 0.987 bar
KH= 76.48 kbar = 76.48 × 103 bar
Concentration = ? mmole/L
Partial pressure and value of KHis given in the question and units of both are the same which means that the solubility term must be unit less and that will be mole fraction. so we will use following formula:
p = KH. x
0.987 bar = 76.48 × 103 bar . x
x = 1.29× 10-5
N2(g) is dissolved in water so we need to calculate the number of mols of N2.
Mole fraction of a component = Number of moles of the component in the solution
Total number of moles of all components of the solution
let suppose number of moles of N2 is = n
number of moles of water in 1 L = weight of 1L water/ molecular weight of water
= 1000g/18g =55.5 mol
1.29× 10-5 = n
n+ 55.5
n+ 55.5 ⋍ 55.5
1.29× 10-5 = n/55.5
n = 7.16 × 10-4 mol
since 1mol = 1000ml
so 7.16 × 10-4 mol = 7.16 × 10-4 × 103 = 0.0716mmol
Answer is 0.0716mmol
Q2. How many grams of carbon dioxide gas are dissolved in a 1 L bottle of carbonated water if the manufacturer uses a pressure of 2.4 atm in the bottling process at 25 °C?
if: KH of CO2 in water = 29.76 atm/(mol/L) at 25 °C
if: KH of CO2 in water = 29.76 atm/(mol/L) at 25 °C
given,
p = 2.4 atm
KH= 29.76 atm/(mol/L)
Concentration = ? g
Here partial pressure and constant both have different units.
p / KH = concentration
concentration = 2.4 atm
29.76 atm/(mol/L)
concentration = 0.08 mol/L
1 mol of CO2 = 44g
0.08 mole = 44 × 0.08 = 3.52g
1 L solution contains 0.08 mols of CO2that is equal to 3.52g.
Answer is 3.52g.
Q3. The partial pressure of O2(g) in equilibrium with 6.87 × 10-4 mol/ L O2(aq) is 16.8 kPa.
If the partial pressure of O2(g) drops to 3.46 kPa, what is the final concentration of O2(aq) in mol/ L?
given,
p initial = p1 = 16.8 kPa
p final = p2 = 3.46 kPa
Concentration initial = c1= 6.87 × 10-4 mol/ L
Concentration initial = c2= ? mol/ L
Henry’s law is
partial pressure = KH . solubility
p1 = KH. c1 …..(1)
p2 = KH. c2 ….. (2)
on dividing equation 2 by equation 1 we get
p2 = KH. c2
p1 KH. c1
p2 = c2 ….. (3)
p1 c1
Since our calculation is for the same gas under same temperature, the value of KH will be the same on initial and final stages.
on putting the values in equation 3 we get the value of C2
3.46 kPa = c2 ….. (4)
16.8 kPa 6.87 × 10-4 mol/ L
c2 = 1.41× 10-4 mol/ L
Answer is 1.41× 10-4 mol/ L
Applications of Henry’s Law
You must have heard the popping sound on opening the bottle of a carbonated drink. As you open the cap, the pressure decreases and CO2 molecules start escaping from the liquid due to decrease in solubility (p∝x) and if you leave the cap open, the drink doesn't remain fizzy for long because the partial pressure of CO2in open atmosphere is very small which allows the soluble CO2molecules to escape.
At higher altitude climbers have trouble in breathing and sometimes they have anoxia, which is a clinical condition when brain becomes unable to work properly due to lack of oxygen. At high altitude, the atmospheric pressure decreases and so does the concentration of oxygen. The decrease in partial pressure of oxygen decreases the solubility of it in blood.
In contrast to higher altitude, atmospheric pressure increases in deep sea and this increased pressure also increases solubility of available gases in the blood. When divers come towards the surface, pressure suddenly decreases and the dissolved gases try to escape from the blood due to decreased solubility. Escaping gases form bubbles which can migrate to any part or joint of the body to find the way out. This causes severe pain in different joints. This condition is known as diver’s disease or Decompression sickness or bends or caisson disease. You might have read about this under the applications of boyels law.
You know that life on the earth was first started in the sea. You might be interested to find out why? Let’s try to calculate the concentration of oxygen in sea water which supports life under the sea.
By the Dalton's law of partial pressures we know that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. if we know the mole fraction or percent composition of gas we can calculate the partial pressure of particular gas if total pressure is given.
Total pressure = p1 + p2 + p3+ p4 ….
Atmospheric pressure = poxygen + pnitrogen+ pcarbondioxide + phydrogen ….
Partial pressure of gas 1 (p1 ) = pressure × mole fraction x1
or,
Partial pressure of gas 1 (p1 ) = pressure × percentage composition of gas1
Atmospheric pressure at sea level is 760mm Hg = 1atm = 1.01325 bar
Percentage of oxygen in air is 21%
So, the partial pressure of oxygen will be = (21 × 1)/ 100 = 0.21atm
Henry’s constant for O2 in water at 298K is 770 atm L/mol.
p = KH . Concentration
0.21atm = 770 atm L/mol . concentration
concentration of O2 = 2.7 × 10-4 mol/L
Pressure in the sea increases by approximately 1 atm for every 10m depth. Higher pressure and lower temperature at deep sea allow more oxygen to stay in water which supports giant aquatic creatures like sharks.
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