15Solutions

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SOLUTION
▢ Definition: Homogeneous mixture of two or more components.
▢ Single Phase Mixture: Mixture where two phases give single phase after mixing = homogeneous mixture = solution.
▢ Components:
  • •
    Solute
  • •
    Solvent
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SOLUBILITY
▢ Definition: Amount of solute in grams dissolved at particular temperature in \(100\,g\) solvent to form saturated solution.
▢ Formula: \(\text{Solubility}=\dfrac{\text{mass of solute}}{\text{mass of solvent}}\times100\)
▢ Example: Solubility of \(KNO_3\) at \(25^\circ C = 50.2\); i.e. \(50.2\,g\ KNO_3\) dissolves in \(100\,g\) water to form \(150.2\,g\) saturated solution.
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SOLUBILITY OF GAS IN LIQUID
▢ General:
  • •
    Solubility of gas generally decreases with rise in temperature.
  • •
    Solubility of gas increases with increase in pressure.
▢ Henry's Law:
❖ Statement: Mass of gas dissolved per unit volume of solvent is directly proportional to pressure of gas at given temperature.
❖ Formula: \(m=KP\)
❖ Terms:
  • •
    \(m=\) mass of gas dissolved per unit volume of solvent
  • •
    \(P=\) pressure of gas in equilibrium with solution
  • •
    \(K=\) proportionality constant
▢ Modified Henry's Law:
❖ Formulae:
  • •
    \(p=K_HX\)
  • •
    \(X=\dfrac{p}{K_H}\)
❖ Terms:
  • •
    \(p=\) partial pressure of gas
  • •
    \(X=\) solubility of gas in liquid / mole fraction of gas in liquid
  • •
    \(K_H=\) Henry's law constant
❖ Temperature Effect:
  • •
    Temperature \(\uparrow\) → \(K_H\uparrow\)
  • •
    \(K_H\uparrow\) → gas solubility in liquid \(\downarrow\)
  • •
    Gas solubility in liquid decreases with rise in temperature
❖ Pressure Effect: Gas solubility in liquid increases with increase of pressure.
▢ Applications of Henry's Law:
  • •
    Sea divers / scuba divers use gas diluted with He to prevent painful medical condition called bends.
  • •
    High altitude person suffers from anoxia due to deficiency of \(O_2\).
  • •
    Soft drink bottles are sealed under high pressure so that more \(CO_2\) dissolves in liquid.
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SOLUTIONS OF LIQUIDS IN LIQUIDS
▢ Miscible Liquids: Form ideal or non-ideal solutions.
▢ Ideal Solution:
❖ Definition: Attractive forces among solute-solvent molecules are of same order as solute-solute and solvent-solvent forces.
❖ Examples:
  • •
    Benzene + toluene
  • •
    Hexane + heptane
  • •
    Methanol + ethanol
❖ Characters:
  • •
    Formed by limited type of compounds
  • •
    \(\Delta H_{mix}=0\)
  • •
    \(\Delta V_{mix}=0\)
  • •
    Obeys Raoult's law
▢ Non-Ideal Solution:
❖ Definition: Solute-solvent interaction differs from solute-solute and solvent-solvent interactions.
❖ Characters:
  • •
    Does not obey Raoult's law for all concentrations
  • •
    \(\Delta H_{mix}\ne0\)
  • •
    \(\Delta V_{mix}\ne0\)
❖ Positive Deviation:
  • •
    \(\Delta V_{mix}>0\)
  • •
    \(\Delta H_{mix}>0\)
  • •
    Solute-solvent interaction weaker than solute-solute and solvent-solvent interactions
  • •
    Forms constant-boiling azeotropic mixture with boiling point less than either liquid
  • •
    Examples: acetone + ethyl alcohol, water + ethyl alcohol, \(CCl_4\) + chloroform, ethanol + chloroform, acetone + \(CS_2\), benzene + methanol
❖ Negative Deviation:
  • •
    \(\Delta V_{mix}<0\)
  • •
    \(\Delta H_{mix}<0\)
  • •
    Solute-solvent interaction stronger than solute-solute and solvent-solvent interactions
  • •
    Forms azeotropic mixture with boiling point higher than either liquid
  • •
    Examples: acetone + aniline, \(HCl\) + water, \(HNO_3\) + water, water + \(H_2SO_4\), acetone + chloroform
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CONCENTRATION OF SOLUTION

Table 1: Methods of expressing concentration

Name
Symbol
Formula
Definition
Temperature effect
Mass percent
\((W/W)\)
\(\dfrac{\text{mass of solute}}{\text{mass of solution}}\times100\)
Parts by mass of solute per 100 parts of solution
No effect
Gram per litre
\(g/L\)
\(\dfrac{\text{mass of solute in g}}{\text{volume of solution in L}}\)
Amount of solute in grams present in solution
Changes with temperature
Parts per million
ppm
\(\dfrac{\text{mass of solute}}{\text{mass of solution}}\times10^6\)
Parts by mass of solute per \(10^6\) parts of solution
No effect
Molarity
\(M\)
\(\dfrac{\text{number of moles of solute}}{\text{number of litres of solution}}\)
Moles of solute present in 1 litre solution
Changes with temperature
Molality
\(m\)
\(\dfrac{\text{number of moles of solute}}{\text{number of kg of solvent}}\)
Moles of solute present in 1000 g solvent
No effect [MOE]
Normality
\(N\)
\(\dfrac{\text{number of gram equivalents of solute}}{\text{number of litres of solution}}\)
Gram equivalents of solute present in 1 litre solution
Changes with temperature
Mole fraction
\(X\)
\(\dfrac{n_A}{n_A+n_B}\)
Moles of one component / total moles of solution
No effect
Formality
\(f\)
\(\dfrac{\text{number of formula masses}}{\text{number of litres of solution}}\)
Formula mass in grams present per litre solution
Changes with temperature
Most commonly used concentration term = molarity.
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RAOULT'S LAW
▢ Statement: Partial pressure of volatile constituent of solution at constant temperature equals vapour pressure of pure constituent multiplied by mole fraction of that constituent.
▢ Formula: \(P_A=X_A\times P_A^0\)
▢ Binary Volatile Liquid Solution:
  • •
    \(P_A=P_A^0X_A\)
  • •
    \(P_B=P_B^0X_B\)
  • •
    \(P_{total}=P_A+P_B=P_A^0X_A+P_B^0X_B\)
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COLLIGATIVE PROPERTIES
▢ Definition: Properties of dilute solutions containing non-volatile solutes depending on number of solute particles, not on nature of solute or solvent.
▢ Depend On: Concentration of solute particles in solution.
▢ Types:
  1. Relative lowering in vapour pressure
  2. Elevation in boiling point
  3. Depression in freezing point
  4. Osmotic pressure
Validity
Relations for colligative properties are strictly valid for dilute solutions of non-volatile solutes which are non-electrolytes.
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RELATIVE LOWERING IN VAPOUR PRESSURE
▢ Concept:
  • •
    Non-volatile solute dissolved in solvent → vapour pressure decreases.
  • •
    \(P_0=\) vapour pressure of pure solvent at \(T^\circ C\)
  • •
    \(P=\) vapour pressure of dilute solution at \(T^\circ C\)
  • •
    \(\Delta P=P_0-P\)
  • •
    Relative lowering in vapour pressure \(=\dfrac{\Delta P}{P_0}\)
▢ Raoult's Law: \(\dfrac{\Delta P}{P_0}=X_{solute}\)
▢ Formulae:
  • •
    \(\dfrac{\Delta P}{P_0}=\dfrac{n}{n+N}\)
  • •
    If \(n\ll N\), \(\dfrac{\Delta P}{P_0}=\dfrac{n}{N}\)
  • •
    \(\dfrac{\Delta P}{P_0}=\dfrac{w/m}{W/M}=\dfrac{wM}{mW}\)
  • •
    \(\Delta P=\dfrac{P_0wM}{mW}\)
  • •
    \(\Delta P=K_m\times m^_\)
  • •
    \(\Delta P\propto m^_\)
▢ Terms:
  • •
    \(n=\) moles of solute
  • •
    \(N=\) moles of solvent
  • •
    \(w=\) weight of solute
  • •
    \(W=\) weight of solvent
  • •
    \(m=\) molecular weight of solute
  • •
    \(M=\) molecular weight of solvent
  • •
    \(m^_=\) molality
  • •
    \(K_m=\) molal lowering constant
▢ Determination Method: Ostwald and Walker method.
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ELEVATION IN BOILING POINT
▢ Definition: Increase in boiling point of solution compared with pure solvent.
▢ Symbols:
  • •
    \(T_0=\) boiling point of pure solvent
  • •
    \(T=\) boiling point of dilute solution
  • •
    \(\Delta T_b=T-T_0\)
▢ Raoult's Law: Elevation in boiling point is directly proportional to molality of solution.
▢ Formulae:
  • •
    \(\Delta T_b\propto m^_\)
  • •
    \(\Delta T_b=K_bm^_\)
  • •
    \(\Delta T_b=K_b\dfrac{w\times1000}{mW}\)
▢ Molal Elevation Constant:
  • •
    \(K_b=\) molal elevation constant / ebullioscopic constant
  • •
    Depends on number of particles only
  • •
    Each solvent has characteristic value of \(K_b\)
  • •
    For water, \(K_b=0.52\,K\,kg\,mol^{-1}\)
  • •
    Unit of \(K_b\): \(K\,kg\,mol^{-1}\)
▢ Thermodynamic Formula:
  • •
    \(K_b=\dfrac{RT^2}{1000L_v}\)
  • •
    \(T=\) boiling point of solvent in absolute scale
  • •
    \(L_v=\) latent heat of vapourisation
▢ Methods: Landsberger's method and Cottrell's method.
▢ Study: Ebullioscopy.
▢ Numerical:
❖ Problem: Boiling point of \(2.5\) molal urea at sea level.
❖ Calculation: \(\Delta T_b=K_bm^_=0.52\times2.5=1.3\)
❖ Answer: Boiling point \(=100+1.3=101.3^\circ C\)
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DEPRESSION IN FREEZING POINT
▢ Definition: Decrease in freezing point of solution compared with pure solvent.
▢ Formulae:
  • •
    \(\Delta T_f=K_fm^_\)
  • •
    \(\Delta T_f=K_f\dfrac{w\times1000}{mW}\)
▢ Raoult's Law: Depression in freezing point is directly proportional to molality of solution.
▢ Molal Depression Constant:
  • •
    \(K_f=\) molal depression constant / cryoscopic constant
  • •
    Does not depend on nature of solute
  • •
    For water, \(K_f=1.86\,K\,kg\,mol^{-1}\)
▢ Thermodynamic Formula:
  • •
    \(K_f=\dfrac{RT^2}{1000L_f}\)
  • •
    \(L_f=\) latent heat of fusion
▢ Methods: Beckmann's method and Rast's camphor method.
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OSMOTIC PRESSURE
▢ Definition: Pressure required to prevent osmosis.
▢ Van't Hoff Equation:
  • •
    \(\pi=CRT\)
  • •
    \(C=\) molar concentration
  • •
    \(R=\) gas constant
  • •
    \(T=\) absolute temperature
  • •
    \(\pi=\dfrac{n}{V}RT\)
  • •
    \(\pi=\dfrac{w}{mV}RT\)
▢ Isotonic Solution:
  • •
    For same solute nature: \(C_1=C_2\)
  • •
    \(\dfrac{w_1}{m_1V_1}=\dfrac{w_2}{m_2V_2}\)
▢ Method: Best method for determination of osmotic pressure = Berkeley and Hartley's method.

Table 1: Types according to osmotic pressure

Solution
Meaning
Hypotonic
Low osmotic pressure
Hypertonic
High osmotic pressure
Isotonic
Same osmotic pressure
▢ Saline Water:
  • •
    Saline = \(0.9\%\ NaCl\) solution
  • •
    Osmotic pressure of blood cells = osmotic pressure of \(0.9\%\ NaCl\)
  • •
    Injected intravenously
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VAN'T HOFF FACTOR
▢ Definition: Ratio of observed colligative property to calculated colligative property.
▢ Formula: \(i=\dfrac{\text{colligative property observed}}{\text{colligative property calculated}}\)
▢ Modified Colligative Formulae:
  • •
    \(\Delta T_b=iK_bm^_\)
  • •
    \(\Delta T_f=iK_fm^_\)
  • •
    \(\pi=iCRT\)
▢ Values:
  • •
    \(i=1\) for non-electrolyte
  • •
    \(i<1\) for association in non-polar solvent, e.g. acetic acid in benzene
  • •
    \(i>1\) for dissociation in polar solvent
▢ Complete Dissociation:

Table 1: Van't Hoff factor for 100% dissociation

\(i\)
Examples
2
\(NaCl\), \(KBr\), \(KClO_3\), \(KNO_3\)
3
\(Na_2CO_3\), \(CaCl_2\), \(MgCl_2\)
4
\(AlCl_3\), \(K_3[Fe(CN)_6]\)
5
\(K_4[Fe(CN)_6]\), \(Al_2(SO_4)_3\)
▢ Degree of Dissociation:
  • •
    \(\alpha_d=\dfrac{i-1}{n-1}\)
  • •
    \(\alpha_d=\) degree of dissociation
  • •
    \(n=\) number of particles formed after dissociation
  • •
    For \(NaCl\), \(n=2\)
  • •
    For \(CaCl_2\), \(n=3\)
▢ Degree of Association:
  • •
    \(\alpha_a=\dfrac{i-1}{\frac{1}{n}-1}\)
  • •
    \(\alpha_a=\) degree of association
▢ Effective Concentration:
  • •
    \(\text{Effective concentration}=i\times c\)
  • •
    \(0.1\,M\) glucose solution \(=1\times0.1=0.1\)
  • •
    \(0.01\,M\ Al_2(SO_4)_3\) solution \(=0.01\times5=0.05\)
▢ Molecular Formula: \(\text{Molecular formula}=(\text{Empirical formula})_x\)
▢ Numerical:
❖ Problem: Freezing point of \(2\) molal \(CaCl_2\) solution, if 100% ionized; \(i=3\), \(K_f=1.86\).
❖ Calculation: \(\Delta T_f=iK_fm^_=3\times1.86\times2=11.16^\circ C\)
❖ Answer: Freezing point \(=-11.16^\circ C\)
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REVERSE OSMOSIS
▢ Definition: If pressure higher than osmotic pressure is applied to solution, solvent flows from solution into pure solvent through semipermeable membrane.
▢ Direction: Reverse of osmosis.
▢ Use: Desalination of sea water to obtain pure water.
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AZEOTROPIC MIXTURE
▢ Definition: Constant boiling mixture of definite composition.
▢ Positive Deviation: Boiling point lower than either component.
▢ Negative Deviation: Boiling point higher than either component.
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IMPORTANT RELATIONS
▢ Molarity on Mixing: \(M_1V_1+M_2V_2=M_3(V_1+V_2)\)
▢ Normality on Mixing: \(N_1V_1+N_2V_2=N_3(V_1+V_2)\)
▢ Molarity and Percentage Strength: \(M=\dfrac{\%\times10}{\text{molar mass of solute}}\)
▢ Normality and Percentage Strength: \(N=\dfrac{\%\times10}{\text{equivalent mass of solute}}\)
▢ Percentage and g/L: \(\%=\dfrac{g/L}{10}\)
▢ Molarity and Density: \(M=\dfrac{\text{percentage strength}\times\text{density}\times10}{\text{molar mass of solute}}\)
▢ Normality and Density: \(N=\dfrac{\text{percentage strength}\times\text{density}\times10}{\text{equivalent mass of solute}}\)
▢ Molarity and Molality: \(\dfrac{\text{Molarity}}{\text{Molality}}=\dfrac{\text{density of solution}\times\text{volume of solution}-\text{moles of solute}\times\text{molar mass of solute}}{\text{volume of solution in litres}}\)
▢ Normality and Molarity:
  • •
    \(\text{Normality}=n\times\text{Molarity}\)
  • •
    \(n=\) valency
  • •
    \(\text{Normality}\times\text{Eq. wt.}=\text{Molarity}\times\text{Mol. wt.}\)
▢ Normality of Mixture: \(N_m=\dfrac{N_1V_1+N_2V_2+N_3V_3+\cdots}{V_1+V_2+V_3+\cdots}\)
▢ Acid-Base Mixture:
❖ Formula: \(N_m=\dfrac{(N_1V_1+N_2V_2+\cdots)_{acid}-(N_1V_1+N_2V_2+\cdots)_{base}}{V_m}\)

Table 1: Result of acid-base mixture

Case
Condition
Result
I
\(N_m=0\)
Neutral solution
II
\(N_m>0\)
Acidic solution; acid > base
III
\(N_m<0\)
Alkaline solution; acid < base
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READ & DIGEST
▢ Important Points:
  • •
    Among \(6\%\) urea solution and \(6\%\) glucose solution, urea solution is hypertonic.
  • •
    For iso-osmotic solutions: molar concentration should be same and nature of solute should be same.
  • •
    Best semipermeable membrane = copper ferrocyanide, \(Cu_2[Fe(CN)_6]\), not ferricyanide.
  • •
    Semipermeable membranes: cellophane, parchment paper, copper ferrocyanide, silicates of Fe and Co.
  • •
    RBC is isotonic to \(0.9\%\ NaCl\).
  • •
    Saline contains \(0.9\%\ NaCl\).
  • •
    At freezing point, vapour pressure of ice = vapour pressure of water; ice and water coexist in equilibrium.
  • •
    Vapour pressure of liquid equals atmospheric pressure at boiling point.
  • •
    If liquid is in equilibrium with vapour at boiling point, molecules in both phases have equal total energy.
  • •
    Molecular weight of acetic acid \((CH_3COOH)\) is \(120\) due to dimerization.
  • •
    Azeotropic solution has definite composition and constant boiling point.
  • •
    Water is amphiprotic solvent.
  • •
    Molarity of pure water = \(55.56\,M\).
  • •
    Temperature of liquid \(\uparrow\) → vapour pressure \(\uparrow\).
  • •
    Acetone + chloroform → hydrogen bonding → negative deviation from Raoult's law.
  • •
    Positive deviation → azeotrope boiling point lower than either component.
  • •
    Negative deviation → azeotrope boiling point higher than either component.
  • •
    Dissolving substance in solvent decreases vapour pressure of solvent and increases boiling point.
  • •
    Van't Hoff received Nobel Prize in chemistry for laws of osmotic pressure of solutions.
  • •
    Townsend method measures osmotic pressure of non-aqueous solution without semipermeable membrane.
  • •
    During freezing point depression, solution, liquid solvent and solid solvent are in equilibrium.
  • •
    Van't Hoff factor for urea and glucose = 1 because they neither dissociate nor associate.
  • •
    Among \(K_2SO_4\), \(NaCl\), urea and glucose, freezing point is lowest for \(K_2SO_4\) because it gives more particles.
  • •
    Boiling point is highest for \(K_2SO_4\) because it gives more particles.
  • •
    Osmotic pressure of equimolar solutions: \(BaCl_2>NaCl>Sucrose\), because number of particles are 3, 2 and 1 respectively.
  • •
    \(NaCl>Sucrose\) due to number of particles.
  • •
    Dissociation of non-volatile solute lowers vapour pressure of solvent.
  • •
    A sublimable substance has vapour pressure less than water vapour in air.
Q1.
For a 1 molar solution of NaCl in water at 25°C and 1 atm pressure
Q2.
Which of the following modes of expressing concentration is independent of temperature?
Q3.
Molarity is expressed as
Q4.
A molal solution is one that contains one mole of a solute in
Q5.
The solubility of a gas in water depends on
Q6.
The volume of a 0.2 N base required to completely react with 0.5 litre of an 0.1 N acid is
Q7.
How many grams of CH3OH would have to be added to water to prepare 150 mL of a solution that is 2.0 M CH3OH?
Q8.
Which one of the following gases contains least number of molecules?
Q9.
5.85 g of NaCl is dissolved in H2O and solution made upto 500 mL. The molarity is
Q10.
What is the molarity of H2SO4 solution that has a density of 1.84 g/cc at 35°C and contains 98% by weight?
Q11.
An aqueous solution of glucose is 10% in strength. The volume in which 1 gm mole of it is dissolved will be
Q12.
A 500 g tooth paste sample has 0.2 g fluoride concentration. What is the concentration of F in terms of ppm level?
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Q13.
Increasing the temperature of an aqueous solution will cause
Q14.
10 mL of N-HCl, 20 mL of N/2 H2SO4, and 30 mL of N/3 HNO3 are mixed together and volume made to one litre. The normality of the resulting solution is
Q15.
What is the normality of 1 M solution of H3PO4?
Q16.
Normality of 2 M sulphuric acid is
Q17.
How many grams of dibasic acid (Mol. wt 200) should be present in 100 mL of its aqueous solution to give decinormal strength?
Q18.
Sum of mole fractions of the two components of a binary solution is always
Q19.
The molarity of pure water is
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Q20.
The number of moles in 180 g of water is
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Q21.
If we take 44 g of CO2 and 14 g of N2, what will be mole fraction of CO2 in the mixture?
Q22.
Which is heaviest?
Q23.
The temperature at which the vapour pressure is equal to the external pressure is called the
Q24.
A substance will be deliquescent if its vapour pressure is
Q25.
Azeotropic mixtures are
Q26.
Colligative properties of the solution depend on
Q27.
Identify the mixture that shows positive deviation from Raoult's law
Q28.
Which of the following is not a colligative property?
Q29.
Which is not a colligative property?
Q30.
Which of the following is a colligative property?
Q31.
For a dilute solution, Raoult's law states that
Q32.
A solution that obeys Raoult's law is
Q33.
A mixture of benzene and toluene forms
Q34.
Which of the following liquid pairs shows a positive deviation from Raoult's law?
Q35.
Which of the following pairs shows a negative deviation from Raoult's law?
Q36.
If liquid A and B form an ideal solution
Q37.
Which one of the following solutions would produce maximum elevation in B.P.?
Q38.
Which of the following solutions will have the highest boiling point?
Q39.
Semipermeable membrane is that which permits the passage of
Q40.
Which inorganic precipitate acts as semipermeable membrane?
Q41.
When a few typical solutes are separated by a particular selective membrane such as protein particles, blood corpuscles, this process is called
Q42.
As a result of osmosis the volume of the solution
Q43.
Osmotic pressure is measured quickly and accurately by
Q44.
The osmotic pressure of a solution is given by the relation
Q45.
The osmotic pressure of solution increases if
Q46.
Osmotic pressure of a sugar solution at 24°C is 2.5 atmosphere. The concentration of the solution in gm mole per litre is
Q47.
The osmotic pressures of equimolar solutions of BaCl2, NaCl and sucrose will be in the order
Q48.
Solutions with same osmotic pressure are called
Q49.
Van't Hoff factor for an electrolyte is
Q50.
Acetic acid dissolved in benzene shows a molecular mass of
Q51.
Pressure cooker reduces cooking time because
Q52.
Maximum freezing point falls in
Q53.
The molality of a solution having 18 g of glucose (mol. wt. = 180) dissolved in 500 g of water will be
Q54.
Which one of the following is not an ideal solution?
Q55.
Dialysis can separate
Q56.
Number of moles of a solute per kilogram of a solvent is called
Q57.
Units of mole fraction are
Q58.
Calculate the normality of 10 volume H2O2
Q59.
Which of the following colligative properties can provide molar mass of proteins with greatest precision?
Q60.
Camphor is often used in molecular mass determination because
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Q61.
Which of the following concentration terms is/are independent of temperature:
Q62.
Which has the minimum freezing point?
Q63.
Which one of the following is not correct for an ideal solution?
Q64.
Which of the following solutions will exhibit highest boiling point?
Q65.
Which of the following is not a non-electrolyte?
Q66.
During depression of freezing point in a solution which of the following are in equilibrium
Q67.
A solution of sodium metal in liquid NH3 gets reduced due to presence of: