Page 1 After studying this Unit, you will be able to • describe the formation of different types of solutions; • express concentration of solution in different units; • state and explain Henry’s law and Raoult’s law; • distinguish between ideal and non-ideal solutions; • explain deviations of real solutions from Raoult’s law; • describe colligative properties of solutions and correlate these with molar masses of the solutes; • explain abnormal colligative properties exhibited by some solutes in solutions. In normal life we rarely come across pure substances. Most of these are mixtures containing two or more pure substances. Their utility or importance in life depends on their composition. For example, the properties of brass (mixture of copper and zinc) are quite different from those of German silver (mixture of copper, zinc and nickel) or bronze (mixture of copper and tin); 1 part per million (ppm) of fluoride ions in water prevents tooth decay, while 1.5 ppm causes the tooth to become mottled and high concentrations of fluoride ions can be poisonous (for example, sodium fluoride is used in rat poison); intravenous injections are always dissolved in water containing salts at particular ionic concentrations that match with blood plasma concentrations and so on. In this Unit, we will consider mostly liquid solutions and their formation. This will be followed by studying the properties of the solutions, like vapour pressure and colligative properties. We will begin with types of solutions and then various alternatives in which concentrations of a solute can be expressed in liquid solution. Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Almost all processes in body occur in some kind of liquid solutions. Objectives 2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of Solutions Solutions Solutions Solutions Solutions 2 Unit Unit Unit Unit Unit 2 Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture. Generally, the component that is present in the largest quantity is known as solvent. Solvent determines the physical state in which solution exists. One or more components present in the solution other than solvent are called solutes. In this Unit we shall consider only binary solutions (i.e., Page 2 After studying this Unit, you will be able to • describe the formation of different types of solutions; • express concentration of solution in different units; • state and explain Henry’s law and Raoult’s law; • distinguish between ideal and non-ideal solutions; • explain deviations of real solutions from Raoult’s law; • describe colligative properties of solutions and correlate these with molar masses of the solutes; • explain abnormal colligative properties exhibited by some solutes in solutions. In normal life we rarely come across pure substances. Most of these are mixtures containing two or more pure substances. Their utility or importance in life depends on their composition. For example, the properties of brass (mixture of copper and zinc) are quite different from those of German silver (mixture of copper, zinc and nickel) or bronze (mixture of copper and tin); 1 part per million (ppm) of fluoride ions in water prevents tooth decay, while 1.5 ppm causes the tooth to become mottled and high concentrations of fluoride ions can be poisonous (for example, sodium fluoride is used in rat poison); intravenous injections are always dissolved in water containing salts at particular ionic concentrations that match with blood plasma concentrations and so on. In this Unit, we will consider mostly liquid solutions and their formation. This will be followed by studying the properties of the solutions, like vapour pressure and colligative properties. We will begin with types of solutions and then various alternatives in which concentrations of a solute can be expressed in liquid solution. Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Almost all processes in body occur in some kind of liquid solutions. Objectives 2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of Solutions Solutions Solutions Solutions Solutions 2 Unit Unit Unit Unit Unit 2 Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture. Generally, the component that is present in the largest quantity is known as solvent. Solvent determines the physical state in which solution exists. One or more components present in the solution other than solvent are called solutes. In this Unit we shall consider only binary solutions (i.e., 34 Chemistry Type of Solution Solute Solvent Common Examples Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases Liquid Gas Chloroform mixed with nitrogen gas Solid Gas Camphor in nitrogen gas Liquid Solutions Gas Liquid Oxygen dissolved in water Liquid Liquid Ethanol dissolved in water Solid Liquid Glucose dissolved in water Solid Solutions Gas Solid Solution of hydrogen in palladium Liquid Solid Amalgam of mercury with sodium Solid Solid Copper dissolved in gold Table 2.1: Types of Solutions consisting of two components). Here each component may be solid, liquid or in gaseous state and are summarised in Table 2.1. Composition of a solution can be described by expressing its concentration. The latter can be expressed either qualitatively or quantitatively. For example, qualitatively we can say that the solution is dilute (i.e., relatively very small quantity of solute) or it is concentrated (i.e., relatively very large quantity of solute). But in real life these kinds of description can add to lot of confusion and thus the need for a quantitative description of the solution. There are several ways by which we can describe the concentration of the solution quantitatively. (i) Mass percentage (w/w): The mass percentage of a component of a solution is defined as: Mass % of a component = ? Mass of the component in the solution 100 Total mass of the solution (2.1) For example, if a solution is described by 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water resulting in a 100 g solution. Concentration described by mass percentage is commonly used in industrial chemical applications. For example, commercial bleaching solution contains 3.62 mass percentage of sodium hypochlorite in water. (ii) Volume percentage (V/V): The volume percentage is defined as: Volume % of a component = ? Volume of the component 100 Total volume of solution (2.2) 2.2 2.2 2.2 2.2 2.2 Expressing Expressing Expressing Expressing Expressing Concentration Concentration Concentration Concentration Concentration of Solutions of Solutions of Solutions of Solutions of Solutions Page 3 After studying this Unit, you will be able to • describe the formation of different types of solutions; • express concentration of solution in different units; • state and explain Henry’s law and Raoult’s law; • distinguish between ideal and non-ideal solutions; • explain deviations of real solutions from Raoult’s law; • describe colligative properties of solutions and correlate these with molar masses of the solutes; • explain abnormal colligative properties exhibited by some solutes in solutions. In normal life we rarely come across pure substances. Most of these are mixtures containing two or more pure substances. Their utility or importance in life depends on their composition. For example, the properties of brass (mixture of copper and zinc) are quite different from those of German silver (mixture of copper, zinc and nickel) or bronze (mixture of copper and tin); 1 part per million (ppm) of fluoride ions in water prevents tooth decay, while 1.5 ppm causes the tooth to become mottled and high concentrations of fluoride ions can be poisonous (for example, sodium fluoride is used in rat poison); intravenous injections are always dissolved in water containing salts at particular ionic concentrations that match with blood plasma concentrations and so on. In this Unit, we will consider mostly liquid solutions and their formation. This will be followed by studying the properties of the solutions, like vapour pressure and colligative properties. We will begin with types of solutions and then various alternatives in which concentrations of a solute can be expressed in liquid solution. Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Almost all processes in body occur in some kind of liquid solutions. Objectives 2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of Solutions Solutions Solutions Solutions Solutions 2 Unit Unit Unit Unit Unit 2 Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture. Generally, the component that is present in the largest quantity is known as solvent. Solvent determines the physical state in which solution exists. One or more components present in the solution other than solvent are called solutes. In this Unit we shall consider only binary solutions (i.e., 34 Chemistry Type of Solution Solute Solvent Common Examples Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases Liquid Gas Chloroform mixed with nitrogen gas Solid Gas Camphor in nitrogen gas Liquid Solutions Gas Liquid Oxygen dissolved in water Liquid Liquid Ethanol dissolved in water Solid Liquid Glucose dissolved in water Solid Solutions Gas Solid Solution of hydrogen in palladium Liquid Solid Amalgam of mercury with sodium Solid Solid Copper dissolved in gold Table 2.1: Types of Solutions consisting of two components). Here each component may be solid, liquid or in gaseous state and are summarised in Table 2.1. Composition of a solution can be described by expressing its concentration. The latter can be expressed either qualitatively or quantitatively. For example, qualitatively we can say that the solution is dilute (i.e., relatively very small quantity of solute) or it is concentrated (i.e., relatively very large quantity of solute). But in real life these kinds of description can add to lot of confusion and thus the need for a quantitative description of the solution. There are several ways by which we can describe the concentration of the solution quantitatively. (i) Mass percentage (w/w): The mass percentage of a component of a solution is defined as: Mass % of a component = ? Mass of the component in the solution 100 Total mass of the solution (2.1) For example, if a solution is described by 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water resulting in a 100 g solution. Concentration described by mass percentage is commonly used in industrial chemical applications. For example, commercial bleaching solution contains 3.62 mass percentage of sodium hypochlorite in water. (ii) Volume percentage (V/V): The volume percentage is defined as: Volume % of a component = ? Volume of the component 100 Total volume of solution (2.2) 2.2 2.2 2.2 2.2 2.2 Expressing Expressing Expressing Expressing Expressing Concentration Concentration Concentration Concentration Concentration of Solutions of Solutions of Solutions of Solutions of Solutions 35 Solutions For example, 10% ethanol solution in water means that 10 mL of ethanol is dissolved in water such that the total volume of the solution is 100 mL. Solutions coxntaining liquids are commonly expressed in this unit. For example, a 35% (v/v) solution of ethylene glycol, an antifreeze, is used in cars for cooling the engine. At this concentration the antifreeze lowers the freezing point of water to 255.4K (–17.6°C). (iii) Mass by volume percentage (w/V): Another unit which is commonly used in medicine and pharmacy is mass by volume percentage. It is the mass of solute dissolved in 100 mL of the solution. (iv) Parts per million: When a solute is present in trace quantities, it is convenient to express concentration in parts per million (ppm) and is defined as: Parts per million = = 6 Number of parts of the component ×10 Total number of parts of all components of the solution (2.3) As in the case of percentage, concentration in parts per million can also be expressed as mass to mass, volume to volume and mass to volume. A litre of sea water (which weighs 1030 g) contains about 6 × 10 –3 g of dissolved oxygen (O 2 ). Such a small concentration is also expressed as 5.8 g per 10 6 g (5.8 ppm) of sea water. The concentration of pollutants in water or atmosphere is often expressed in terms of µg mL –1 or ppm. (v) Mole fraction: Commonly used symbol for mole fraction is x and subscript used on the right hand side of x denotes the component. It is defined as: Mole fraction of a component = Number of moles of the component Total number of moles of all the components (2.4) For example, in a binary mixture, if the number of moles of A and B are n A and n B respectively, the mole fraction of A will be x A = ? A A B n nn (2.5) For a solution containing i number of components, we have: x i = ?? ? i 12 i ....... n nn n = ? i i n n (2.6) It can be shown that in a given solution sum of all the mole fractions is unity, i.e. x 1 + x 2 + .................. + x i = 1 (2.7) Mole fraction unit is very useful in relating some physical properties of solutions, say vapour pressure with the concentration of the solution and quite useful in describing the calculations involving gas mixtures. Page 4 After studying this Unit, you will be able to • describe the formation of different types of solutions; • express concentration of solution in different units; • state and explain Henry’s law and Raoult’s law; • distinguish between ideal and non-ideal solutions; • explain deviations of real solutions from Raoult’s law; • describe colligative properties of solutions and correlate these with molar masses of the solutes; • explain abnormal colligative properties exhibited by some solutes in solutions. In normal life we rarely come across pure substances. Most of these are mixtures containing two or more pure substances. Their utility or importance in life depends on their composition. For example, the properties of brass (mixture of copper and zinc) are quite different from those of German silver (mixture of copper, zinc and nickel) or bronze (mixture of copper and tin); 1 part per million (ppm) of fluoride ions in water prevents tooth decay, while 1.5 ppm causes the tooth to become mottled and high concentrations of fluoride ions can be poisonous (for example, sodium fluoride is used in rat poison); intravenous injections are always dissolved in water containing salts at particular ionic concentrations that match with blood plasma concentrations and so on. In this Unit, we will consider mostly liquid solutions and their formation. This will be followed by studying the properties of the solutions, like vapour pressure and colligative properties. We will begin with types of solutions and then various alternatives in which concentrations of a solute can be expressed in liquid solution. Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Almost all processes in body occur in some kind of liquid solutions. Objectives 2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of Solutions Solutions Solutions Solutions Solutions 2 Unit Unit Unit Unit Unit 2 Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture. Generally, the component that is present in the largest quantity is known as solvent. Solvent determines the physical state in which solution exists. One or more components present in the solution other than solvent are called solutes. In this Unit we shall consider only binary solutions (i.e., 34 Chemistry Type of Solution Solute Solvent Common Examples Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases Liquid Gas Chloroform mixed with nitrogen gas Solid Gas Camphor in nitrogen gas Liquid Solutions Gas Liquid Oxygen dissolved in water Liquid Liquid Ethanol dissolved in water Solid Liquid Glucose dissolved in water Solid Solutions Gas Solid Solution of hydrogen in palladium Liquid Solid Amalgam of mercury with sodium Solid Solid Copper dissolved in gold Table 2.1: Types of Solutions consisting of two components). Here each component may be solid, liquid or in gaseous state and are summarised in Table 2.1. Composition of a solution can be described by expressing its concentration. The latter can be expressed either qualitatively or quantitatively. For example, qualitatively we can say that the solution is dilute (i.e., relatively very small quantity of solute) or it is concentrated (i.e., relatively very large quantity of solute). But in real life these kinds of description can add to lot of confusion and thus the need for a quantitative description of the solution. There are several ways by which we can describe the concentration of the solution quantitatively. (i) Mass percentage (w/w): The mass percentage of a component of a solution is defined as: Mass % of a component = ? Mass of the component in the solution 100 Total mass of the solution (2.1) For example, if a solution is described by 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water resulting in a 100 g solution. Concentration described by mass percentage is commonly used in industrial chemical applications. For example, commercial bleaching solution contains 3.62 mass percentage of sodium hypochlorite in water. (ii) Volume percentage (V/V): The volume percentage is defined as: Volume % of a component = ? Volume of the component 100 Total volume of solution (2.2) 2.2 2.2 2.2 2.2 2.2 Expressing Expressing Expressing Expressing Expressing Concentration Concentration Concentration Concentration Concentration of Solutions of Solutions of Solutions of Solutions of Solutions 35 Solutions For example, 10% ethanol solution in water means that 10 mL of ethanol is dissolved in water such that the total volume of the solution is 100 mL. Solutions coxntaining liquids are commonly expressed in this unit. For example, a 35% (v/v) solution of ethylene glycol, an antifreeze, is used in cars for cooling the engine. At this concentration the antifreeze lowers the freezing point of water to 255.4K (–17.6°C). (iii) Mass by volume percentage (w/V): Another unit which is commonly used in medicine and pharmacy is mass by volume percentage. It is the mass of solute dissolved in 100 mL of the solution. (iv) Parts per million: When a solute is present in trace quantities, it is convenient to express concentration in parts per million (ppm) and is defined as: Parts per million = = 6 Number of parts of the component ×10 Total number of parts of all components of the solution (2.3) As in the case of percentage, concentration in parts per million can also be expressed as mass to mass, volume to volume and mass to volume. A litre of sea water (which weighs 1030 g) contains about 6 × 10 –3 g of dissolved oxygen (O 2 ). Such a small concentration is also expressed as 5.8 g per 10 6 g (5.8 ppm) of sea water. The concentration of pollutants in water or atmosphere is often expressed in terms of µg mL –1 or ppm. (v) Mole fraction: Commonly used symbol for mole fraction is x and subscript used on the right hand side of x denotes the component. It is defined as: Mole fraction of a component = Number of moles of the component Total number of moles of all the components (2.4) For example, in a binary mixture, if the number of moles of A and B are n A and n B respectively, the mole fraction of A will be x A = ? A A B n nn (2.5) For a solution containing i number of components, we have: x i = ?? ? i 12 i ....... n nn n = ? i i n n (2.6) It can be shown that in a given solution sum of all the mole fractions is unity, i.e. x 1 + x 2 + .................. + x i = 1 (2.7) Mole fraction unit is very useful in relating some physical properties of solutions, say vapour pressure with the concentration of the solution and quite useful in describing the calculations involving gas mixtures. 36 Chemistry Calculate the mole fraction of ethylene glycol (C 2 H 6 O 2 ) in a solution containing 20% of C 2 H 6 O 2 by mass. Assume that we have 100 g of solution (one can start with any amount of solution because the results obtained will be the same). Solution will contain 20 g of ethylene glycol and 80 g of water. Molar mass of C 2 H 6 O 2 = 12 × 2 + 1 × 6 + 16 × 2 = 62 g mol –1 . Moles of C 2 H 6 O 2 = ?1 20 g 62 g mol = 0.322 mol Moles of water = -1 80 g 18 g mol = 4.444 mol ? ? 262 glycol 262 2 moles of C H O x moles of C H O moles of H O ? ? 0.322mol 0.322mol 4.444 mol = 0.068 Similarly, ?? ? water 4.444 mol 0.932 0.322 mol 4.444 mol x Mole fraction of water can also be calculated as: 1 – 0.068 = 0.932 Example 2.1 Example 2.1 Example 2.1 Example 2.1 Example 2.1 (vi) Molarity: Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimetre) of solution, ? Moles of solute Molarity Volume of solution in litre (2.8) For example, 0.25 mol L –1 (or 0.25 M) solution of NaOH means that 0.25 mol of NaOH has been dissolved in one litre (or one cubic decimetre). Example 2.2 Example 2.2 Example 2.2 Example 2.2 Example 2.2 Calculate the molarity of a solution containing 5 g of NaOH in 450 mL solution. Moles of NaOH = -1 5 g 40 g mol = 0.125 mol Volume of the solution in litres = 450 mL / 1000 mL L -1 Using equation (2.8), Molarity = –1 0.125 mol × 1000 mL L 450 mL = 0.278 M = 0.278 mol L –1 = 0.278 mol dm –3 Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution Page 5 After studying this Unit, you will be able to • describe the formation of different types of solutions; • express concentration of solution in different units; • state and explain Henry’s law and Raoult’s law; • distinguish between ideal and non-ideal solutions; • explain deviations of real solutions from Raoult’s law; • describe colligative properties of solutions and correlate these with molar masses of the solutes; • explain abnormal colligative properties exhibited by some solutes in solutions. In normal life we rarely come across pure substances. Most of these are mixtures containing two or more pure substances. Their utility or importance in life depends on their composition. For example, the properties of brass (mixture of copper and zinc) are quite different from those of German silver (mixture of copper, zinc and nickel) or bronze (mixture of copper and tin); 1 part per million (ppm) of fluoride ions in water prevents tooth decay, while 1.5 ppm causes the tooth to become mottled and high concentrations of fluoride ions can be poisonous (for example, sodium fluoride is used in rat poison); intravenous injections are always dissolved in water containing salts at particular ionic concentrations that match with blood plasma concentrations and so on. In this Unit, we will consider mostly liquid solutions and their formation. This will be followed by studying the properties of the solutions, like vapour pressure and colligative properties. We will begin with types of solutions and then various alternatives in which concentrations of a solute can be expressed in liquid solution. Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Almost all processes in body occur in some kind of liquid solutions. Objectives 2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of Solutions Solutions Solutions Solutions Solutions 2 Unit Unit Unit Unit Unit 2 Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture. Generally, the component that is present in the largest quantity is known as solvent. Solvent determines the physical state in which solution exists. One or more components present in the solution other than solvent are called solutes. In this Unit we shall consider only binary solutions (i.e., 34 Chemistry Type of Solution Solute Solvent Common Examples Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases Liquid Gas Chloroform mixed with nitrogen gas Solid Gas Camphor in nitrogen gas Liquid Solutions Gas Liquid Oxygen dissolved in water Liquid Liquid Ethanol dissolved in water Solid Liquid Glucose dissolved in water Solid Solutions Gas Solid Solution of hydrogen in palladium Liquid Solid Amalgam of mercury with sodium Solid Solid Copper dissolved in gold Table 2.1: Types of Solutions consisting of two components). Here each component may be solid, liquid or in gaseous state and are summarised in Table 2.1. Composition of a solution can be described by expressing its concentration. The latter can be expressed either qualitatively or quantitatively. For example, qualitatively we can say that the solution is dilute (i.e., relatively very small quantity of solute) or it is concentrated (i.e., relatively very large quantity of solute). But in real life these kinds of description can add to lot of confusion and thus the need for a quantitative description of the solution. There are several ways by which we can describe the concentration of the solution quantitatively. (i) Mass percentage (w/w): The mass percentage of a component of a solution is defined as: Mass % of a component = ? Mass of the component in the solution 100 Total mass of the solution (2.1) For example, if a solution is described by 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water resulting in a 100 g solution. Concentration described by mass percentage is commonly used in industrial chemical applications. For example, commercial bleaching solution contains 3.62 mass percentage of sodium hypochlorite in water. (ii) Volume percentage (V/V): The volume percentage is defined as: Volume % of a component = ? Volume of the component 100 Total volume of solution (2.2) 2.2 2.2 2.2 2.2 2.2 Expressing Expressing Expressing Expressing Expressing Concentration Concentration Concentration Concentration Concentration of Solutions of Solutions of Solutions of Solutions of Solutions 35 Solutions For example, 10% ethanol solution in water means that 10 mL of ethanol is dissolved in water such that the total volume of the solution is 100 mL. Solutions coxntaining liquids are commonly expressed in this unit. For example, a 35% (v/v) solution of ethylene glycol, an antifreeze, is used in cars for cooling the engine. At this concentration the antifreeze lowers the freezing point of water to 255.4K (–17.6°C). (iii) Mass by volume percentage (w/V): Another unit which is commonly used in medicine and pharmacy is mass by volume percentage. It is the mass of solute dissolved in 100 mL of the solution. (iv) Parts per million: When a solute is present in trace quantities, it is convenient to express concentration in parts per million (ppm) and is defined as: Parts per million = = 6 Number of parts of the component ×10 Total number of parts of all components of the solution (2.3) As in the case of percentage, concentration in parts per million can also be expressed as mass to mass, volume to volume and mass to volume. A litre of sea water (which weighs 1030 g) contains about 6 × 10 –3 g of dissolved oxygen (O 2 ). Such a small concentration is also expressed as 5.8 g per 10 6 g (5.8 ppm) of sea water. The concentration of pollutants in water or atmosphere is often expressed in terms of µg mL –1 or ppm. (v) Mole fraction: Commonly used symbol for mole fraction is x and subscript used on the right hand side of x denotes the component. It is defined as: Mole fraction of a component = Number of moles of the component Total number of moles of all the components (2.4) For example, in a binary mixture, if the number of moles of A and B are n A and n B respectively, the mole fraction of A will be x A = ? A A B n nn (2.5) For a solution containing i number of components, we have: x i = ?? ? i 12 i ....... n nn n = ? i i n n (2.6) It can be shown that in a given solution sum of all the mole fractions is unity, i.e. x 1 + x 2 + .................. + x i = 1 (2.7) Mole fraction unit is very useful in relating some physical properties of solutions, say vapour pressure with the concentration of the solution and quite useful in describing the calculations involving gas mixtures. 36 Chemistry Calculate the mole fraction of ethylene glycol (C 2 H 6 O 2 ) in a solution containing 20% of C 2 H 6 O 2 by mass. Assume that we have 100 g of solution (one can start with any amount of solution because the results obtained will be the same). Solution will contain 20 g of ethylene glycol and 80 g of water. Molar mass of C 2 H 6 O 2 = 12 × 2 + 1 × 6 + 16 × 2 = 62 g mol –1 . Moles of C 2 H 6 O 2 = ?1 20 g 62 g mol = 0.322 mol Moles of water = -1 80 g 18 g mol = 4.444 mol ? ? 262 glycol 262 2 moles of C H O x moles of C H O moles of H O ? ? 0.322mol 0.322mol 4.444 mol = 0.068 Similarly, ?? ? water 4.444 mol 0.932 0.322 mol 4.444 mol x Mole fraction of water can also be calculated as: 1 – 0.068 = 0.932 Example 2.1 Example 2.1 Example 2.1 Example 2.1 Example 2.1 (vi) Molarity: Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimetre) of solution, ? Moles of solute Molarity Volume of solution in litre (2.8) For example, 0.25 mol L –1 (or 0.25 M) solution of NaOH means that 0.25 mol of NaOH has been dissolved in one litre (or one cubic decimetre). Example 2.2 Example 2.2 Example 2.2 Example 2.2 Example 2.2 Calculate the molarity of a solution containing 5 g of NaOH in 450 mL solution. Moles of NaOH = -1 5 g 40 g mol = 0.125 mol Volume of the solution in litres = 450 mL / 1000 mL L -1 Using equation (2.8), Molarity = –1 0.125 mol × 1000 mL L 450 mL = 0.278 M = 0.278 mol L –1 = 0.278 mol dm –3 Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution 37 Solutions Example 2.3 Example 2.3 Example 2.3 Example 2.3 Example 2.3 Solution Solution Solution Solution Solution (vii) Molality: Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as: Molality (m) = Moles of solute Mass of solvent in kg (2.9) For example, 1.00 mol kg –1 (or 1.00 m) solution of KCl means that 1 mol (74.5 g) of KCl is dissolved in 1 kg of water. Each method of expressing concentration of the solutions has its own merits and demerits. Mass %, ppm, mole fraction and molality are independent of temperature, whereas molarity is a function of temperature. This is because volume depends on temperature and the mass does not. Solubility of a substance is its maximum amount that can be dissolved in a specified amount of solvent at a specified temperature. It depends upon the nature of solute and solvent as well as temperature and pressure. Let us consider the effect of these factors in solution of a solid or a gas in a liquid. 2.3 Solubility 2.3 Solubility 2.3 Solubility 2.3 Solubility 2.3 Solubility Calculate molality of 2.5 g of ethanoic acid (CH 3 COOH) in 75 g of benzene. Molar mass of C 2 H 4 O 2 : 12 × 2 + 1 × 4 + 16 × 2 = 60 g mol –1 Moles of C 2 H 4 O 2 = 1 2.5 g 60 g mol = 0.0417 mol Mass of benzene in kg = 75 g/1000 g kg –1 = 75 × 10 –3 kg Molality of C 2 H 4 O 2 = 24 2 Moles of C H O kg of benzene = 1 0.0417 mol 1000 g kg 75 g = 0.556 mol kg –1 Intext Questions Intext Questions Intext Questions Intext Questions Intext Questions 2.1 Calculate the mass percentage of benzene (C 6 H 6 ) and carbon tetrachloride (CCl 4 ) if 22 g of benzene is dissolved in 122 g of carbon tetrachloride. 2.2 Calculate the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride. 2.3 Calculate the molarity of each of the following solutions: (a) 30 g of Co(NO 3 ) 2 . 6H 2 O in 4.3 L of solution (b) 30 mL of 0.5 M H 2 SO 4 diluted to 500 mL. 2.4 Calculate the mass of urea (NH 2 CONH 2 ) required in making 2.5 kg of 0.25 molal aqueous solution. 2.5 Calculate (a) molality (b) molarity and (c) mole fraction of KI if the density of 20% (mass/mass) aqueous KI is 1.202 g mL -1 .Read More

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