5 Environmental Aqueous Solutions of Gases, Acids and Bases, and pH

Prof. K.S. Gupta

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Contents

  1. Introduction
  2. Solubility
  3. Solutions of Gases in Water: Henry’s Law
  4. Temperature Dependence of KH
  5. Dissolution of O2, SO2,NH3 in Water
  6. Dissolution of Strong Acids HCl, HNO3, etc
  7. pH of Aqueous Solutions
  8. Solutions of Strong Acids and Strong Bases
  9. pH of Solutions of Weak Acids and Weak Bases
  10. Solubility of Solids in Aqueous Solutions
  11. Lowering of Vapor Pressure of the Solutions: Raolt’s Law
  12. Suggested Reading

Introduction

   A solution is a homogeneous mixture of two or more substances. The solutions can be made by mixing substances in any physical state, for example, gas in a gas, a solid in a solid or liquid in a liquid, in addition to a solid in a liquid, and gas in a liquid. Since in environmental chemistry, we generally encounter solutions of solid in a liquid, gas in a gas, or a gas in a liquid, the discussion shall be limited to these types of systems only.

 

   A substance, which is present in large amount, is called a solvent and the other a solute. For example in a solution of sodium chloride in water, sodium chloride is the solute and water is the solvent. In the solutions, which we encounter in environment, water is mostly the solvent. These solutions are generally dilute. In the subsequent discussion, the solutions shall be assumed to be dilute, unless stated otherwise. The thermodynamic criteria of for a dilute solution require: the heat of mixing, Hmixing = 0, and volume of mixing, Vmixing = 0.

 

Solubility

   The maximum amount of a substance, which can be dissolved per unit volume of the solution in a solvent at a given temperature, is known as the solubility of the substance at that temperature. The solutions having amount of a substance less than its solubility are called unsaturated solutions, and having more amount than its solubility are called super saturated solutions. The solubility can be expressed in the units of mole per liter (molarity) or mole per kg of solvent (molality) as discussed in Module 1. Some of the other units used to express solubility are as follows.

 

Concentration of solute in mass percent (w/w) is the mass of the solute divided by the total mass of the solution, multiplied by 100.

Problem 1. What is concentration of NaCl in mass percent (w/w), if 5 g NaCl is dissolved in 75 g water?

Solution . From Eq 1.,     mass percent of NaCl = 5 g x100/ ( 5 + 75) g     = 6.25%

 

Problem 2. If 4 g CaCl2 is dissolved in water and solution made up to 50 mL, calculate the concentration of CaCl2 in mass by volume percent.

 

 

Problem 3. If 2.2 mL ethyl alcohol is mixed with water and the solution made up to 50 mL, calculate the percent composition of ethyl alcohol in percent (v/v).

Solution . From Eq 3., ethyl alcohol in volume Percent (v/v)= 2.2                                                                ×100 = 4.4%(v/v)

 

Solutions of Gases in Water: Henry’s Law

   The dissolution of gases in liquids is governed by Henry’s law, which states that ‘at a given temperature, at equilibrium the amount of the gas dissolved in a liquid is proportional to the partial pressure of the gas above the liquid surface’. Consider the dissolution of a gas X(gas) in water. The gas is in equilibrium with the gas dissolved, X(aq), as shown in Eq. 4.

the Henry’s law constant. The value of KH is temperature – dependent. It also depends up on the nature of the gas and the nature of the solvent.

Table 1. Henry’s law constant values* of selected gases in water at 25oC.

Gas KH, mol L-1/atm
O2 1.3×10−3
H2 7.8×10−4
H2O2 7.1×104
NH3 5.9×101
NO2 3.4×10−2
NO 1.9×10−3
HNO3 2.6×106
HCl 2.5×103
SO2 1.2
CH3COOH 3.4×103
HCOOH 6.0×103

*From’ Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry http://www.mpch-mainz.mpg.de/~sander/res/henry.html Rolf Sander, Air Chemistry Department, Max-Planck Institute of Chemistry, Germany’

   The KH values of some gases are high and this generally happens when the gas forms a compound with the solvent and/or undergoes dissociation. The solubility of some gases, which are environmentally important, are discussed hereinafter.

 

Temperature Dependence of KH

It is given by the well known Eq. 6.

where KH1 and KH2 are Henry’s law constants at temperatures, T1 and T2, respectively. is heat of reaction.

 

Dissolution of O2 in Water

   From ecological point of view, the presence of dissolved oxygen is very important for the survival of aquatic species and other life forms. When O2 dissolves in water, its physical state remains unchanged, it neither forms a compound with water nor undergoes any other reaction. The dissolution equilibrium is Eq. 7.

According to Henry’s law:

where [O2(aq)] is concentration of dissolved O2  and pO2  is its partial pressure.

   At 25oC, KH = 1.3× 10-3 mol L-1 atm. Corresponding to partial pressure of 0.21% in dry air, the solubility of O2 at 25oC in water is calculated to be 0.273 × 10-3 mol L-1. The molecular weight of O2 is 32. So the solubility of O2 is 8.7 mg L-1 or 8.7 ppm at 25oC. With decrease in temperature, as in case of other gases, the solubility of O2 increases and becomes 14.7 ppm at 0oC. The decrease in solubility with increase in temperature causes the depletion in O2 concentration in rivers/lakes/water bodies, when their temperature becomes high due to the thermal pollution. The latter is an outcome of the release of hot water by thermal power plants and other industrial units. This makes the survival of aquatic species difficult.

 

Dissolution of SO2 in Water

   Sulfur dioxide is the key trace atmospheric gas responsible for acid rain. It gets dissolved in cloud water or in falling raindrops and its oxidation causes an increase in rainwater acidity. It is, therefore, necessary to consider its dissolution in water, governed by Henry’s law.

KH

SO2(gas)  + H2O   SO2.H2O(aq) (or H2SO3)                                                                                              (9)

The SO2.H2O undergoes dissociation to form bisulfite (or hydrogensulfite), HSO3-, and sulfite ions, SO32-.


 

Equation 17 shows the increase in pH to increase the solubility of SO2 in water. Indeed an increase in pH from 1-8, increases the concentration of dissolved SO2 in water by ~ 107 times. Thus, in Indian conditions, where rainwater pH is high and lies in the range 6 – 8.5, dissolution of SO2 would be very high.

 

Dissolution of NH3.

   It is one of the important trace atmospheric gases and its salts ammonium sulfate and ammonium nitrate are found as aerosols. In India, ammonia is reported to be in the range 7 – 56 µg m-3. Its dissolution equilibrium is Eq. 18. Its aquated form NH4OH dissociates to form NH4+ and OH-ions.

   The formation of hydroxyl ions makes the solution alkaline and so pH of the solution increases. Ammonia reacts with hydrogen ions and neutralizes acidity. If total dissolved ammonia concentration be [NH3]T, it can be shown as in case of SO2, that,

Value of K1(1.8 × 10-5) shows the solubility of ammonia to increase with decrease in pH.

 

Dissolution of Strong Acids HCl, HNO3, etc

   Trace amounts of HCl, HNO3 and other strong acids are found in atmosphere. On dissolution in water, these acids fully dissociate in to ions. The dissolution equilibrium of these acids may be written as in Eq. 21, and the value of KH by Eq. 22.

   Since the KH values of strong acids are high(Table 1), so the dissociation of these acids on dissolution in water would be very high and almost complete. Even a small concentration of HNO3 would lead to a relatively high solubility in aqueous atmospheric media.

 

On assuming: dissolved [HNO3] = [H+ (aq)] = [ NO3- (aq)], Eq. 22 leads to the following equation for the concentration of dissolved HNO3.

   The concept of pH is applicable to aqueous solutions and particularly in those solutions, which are dilute. In environmental chemistry, the solutions mostly encountered have the pH range 3- 10. pH is, therefore, very useful in expressing the acidity of cloud water, rainwater, fog water, sea water and of other water bodies oceans, lake, rivers, etc. In aqueous solutions, OH- ion concentration is expressed as pOH as in Eq. 25.

Dissociation of Water – The equilibrium for the dissociation of water is written as in Eq. 26. The value of equilibrium constant is expressed by Eq. 27.

In pure water, pH =7 and pOH = 7. Kw is also written as pKw. The value of pKw is equal to 14 at 25oC.

 

Solutions of Strong Acids and Strong Bases

   In aqueous solutions, strong acids such as, HCl, HNO3, H2SO4, HBr and strong bases such as, NaOH and KOH, which are all strong electrolytes, dissociate fully in to ions.

 

pH of Solutions of Weak Acids and Weak Bases

   The weak electrolytes dissociate only partially. Since formic acid, acetic acid, hydrogen cyanide, ammonium hydroxide are all weak electrolytes, they dissociate only partially.

   Consider the dissociation of a weak acid HA. Let the initial concentration of te acid in solution be a mol L-1 and its degree of dissociation be α(alpha). Then amount of acid dissociated would be aα.. The dissociation equilibrium may be written as in Eq. 31. On applying law of mass action to Eq. 31,we get expression(32) for dissociation constant of HA, Ka.

Ka is known as acid dissociation constant. It is also written as pKa , where pKa = – log Ka

On substituting the values of [H+], [A-] and [HA] at equilibrium in Eq. (32), it can be shown that

Likewise, for the dissociation of weak base, for example NH4OH(Eq. 34), it can be shown that

   It must be pointed out higher the value of Ka is stronger the acid and lower the value of pKa , stronger is the acid. The same is true for Kb and pKb.

 

Solubility of Solids in Aqueous Solutions

   In a saturated solution of an electrolyte, there would be an equilibrium between undissolved solid and the ions formed as result of dissolution(Eq. 35).

   On applying law of mass action and remembering that the activity of pure solids is taken as one, we obtain an expression (Eq. 36) for Ks, commonly known as solubility product of the electrolyte. The Eq. (36) applies to only sparingly soluble electrolytes.

Table 2 Solubility products of some electrolytes at 25oC

Compound pKs Compound pKs
Cu(OH)2 19.32 Fe(OH)3 38.8
Al(OH)3 32 – 36 Mn(OH)2 12.8
CdCO3 13.74 CaCO3 8.35

 

   The solubility of hydroxides is pH dependent. At higher pH, solubility shall be low. In environmental conditions, at high pH, Fe3+, Cu2+, etc. precipitate as hydroxides and their catalytic activity is diminished. It may be pointed out that these ions play a major role in the oxidation of dissolved SO2 in cloud/rain/fog water. Further, decrease in pH increases the concentration of Cu, Al and Cd in drinking water. The equilibrium applies to those compounds also, which dissolve without dissociation, e.g., urea.

 

Lowering of Vapor Pressure of the Solutions: Raolt’s Law

   Every solvent has a definite vapor pressure at a given temperature. Addition of a non-volatile solute, e. g., sugar, NaCl, urea and CaCl2 lowers the vapor pressure of the solvent and so solution has lower vapor pressure than the pure solvent. According to Raolt’s law, the vapor pressure of the solution is proportional to the mole fraction of the solvent.

   where pi is the vapor pressure of the solution, pio is the vapor pressure of the pure solvent and xi is the mole fraction of the solvent, i. Because of the lowering of vapor pressure, the freezing point of water is lowered and the boiling point elevated.

 

   Solubility of aerosol particles is of great importance in cloud condensation. The water-soluble particles lower the value of super-saturation required for the particles to serve as cloud condensation nuclei. This aspect is helpful in inducing rainfall and in artificial rainfall.

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Reference

  1. P. V. Hobbs(2000), Basic Physical Chemistry for the Atmospheric Sciences, Cambridge, UK
  2. Philip Mathews(2013), Advanced Chemistry, Cambridge, New Delhi
  3. Chemistry Part I for Class XII, NCERT, New Delhi
  4. Thomas Engel and Philip Reid(2013), Physical Chemistry, Pearson, New Delhi
  5. A Bahl, B. S. Bahl and G. D. Tuli(2012), Essentials of Physical Chemistry, S. Chand, New Delhi