Molar volume mole concept

Figure 6.1 illustrates the concept of the apparent molar volume. AB is the portion of the total volume AC for n2 moles of solute that is attributed to the pure solvent. Then, the volume BC is apparently due to the solute. The slope of the line passing through point C and V is the apparent molar volume. The slope of the curve of the total volume at point C is the partial molar volume of component 2. Indeed, the slope of the total volume curve at any point is the partial molar volume of component 2 at that concentration. It is obvious that partial molar properties and apparent molar properties are both functions of concentration. 

Avogadro s principle tells us that equal volumes of gases, at equal temperatures and pressures, contain an equal number of particles. It is from this principle that chemists have developed the concept of the molar volume of gases. It has been determined that one mole of any gas at standard temperature and pressure (a temperature of 273 K and 101.3 kPa of pressure) will occupy 22.4 dm3 of volume. This allows us to determine the number of moles in a gas, provided we know the volume, temperature, and pressure of the sample. 

One closely related concept to 5 is the cohesive energy E, which is defined as the increase in the internal energy per mole of the system upon removal of all intermolecular interactions. When E is divided by the molar volume V, we obtain the cohesive energy density (ced), ElV, of the system. The solubility parameter is simply the square root of this cohesive energy density. A thorough discussion of the defliution of 5 and its relation to internal pressure may be found in the comprehensive review by Barton. ... 

The mole concept is useful in expressing concentrations of solutions, especially in analytical chemistry, where we need to know the volume ratios in which solutions of different materials will react. A one-molar solution is defined as one that contains one mole of substance in each liter of a solution. It is prepared by dissolving one mole of the substance in the solvent and diluting to a final volume of one liter in a volumetric flask or a faction or multiple of the mole may be dissolved and diluted to the corresponding fraction or multiple of a hter (e.g., 0.01 mol in 10 mL). More generally, the molarity of a solution is expressed as moles per liter or as millimoles per milliliter. Molar is abbreviated as M, and we talk of the molarity of a solution when we speak of its concentration. A one-molar solution of silver nitrate and a one-molar solution of sodium chloride will react on an equal-volume basis, since they react in a 1 1 ratio Ag + Cl —> AgCl. We can be more general and calculate the moles of substance in any volume of the solution. 

Molality, abbreviated molal or m, is useful for colligative properties because it is a more direct ratio of molecules of solute to molecules of solvent. The unit molarity automatically includes the concept of partial molar volumes because it is defined in terms of liters of solution, not liters of solvent. It is also dependent on the amounts of solvent and solute (in mole and kilogram units), but independent of volume or temperature. Thus, as T changes, the concentration in molality units remains constant while the concentration in molarity units varies due to expansion or contraction of the solutions volume. 

In the models discussed hitherto, we have always assumed that the molar volumes of the two components of the solution were very similar, so that the imperfection of the solution was attributed solely to interactions between the molecules. This hypothesis, though, is clearly not true in all cases -particularly in solutions of a polymer in a solvent - e.g. a solution of polystyrene in acetone, where the difference between the molar volumes is very significant acetone has a molar volume of 73 cm /mole, whilst that of polystyrene is, on average, 3333 cmVmole. In order to take account of this fact, we introduce the concept of combinatorial excess entropy, which is linked to the distributions of the molecules in the space. 

Background This experiment uses the concept of continuous variation to determine mass and mole relationships. Continuous variation keeps the total volume of two reactants constant, but varies the ratios in which they combine. The optimum ratio would be the one in which the maximum amount of both reactants of known concentration are consumed and the maximum amount of product(s) is produced. Since the reaction is exothermic, and heat is therefore a product, the ratio of the two reactants that produces the greatest amount of heat is a function of the actual stoichiometric relationship. Other products that could be used to determine actual molar relationships might include color intensity, mass of precipitate formed, amount of gas evolved, and so on. 

The number of molecules passing in each direction from vapour to liquid and in reverse is approximately the same since the heat given out by one mole of the vapour on condensing is approximately equal to the heat required to vaporise one mole of the liquid. The problem is thus one of equimolecular counterdiffusion, described in Volume 1, Chapter 10. If the molar heats of vaporisation are approximately constant, the flows of liquid and vapour in each part of the column will not vary from tray to tray. This is the concept of constant molar overflow which is discussed under the heat balance heading in Section 11.4.2. Conditions of varying molar overflow, arising from unequal molar latent heats of the components, are discussed in Section 11.5. 

Section 12.1 introduces the concept of pressure and describes a simple way of measuring gas pressures, as well as the customary units used for pressure. Section 12.2 discusses Boyle s law, which describes the effect of the pressure of a gas on its volume. Section 12.3 examines the effect of temperature on volume and introduces a new temperature scale that makes the effect easy to understand. Section 12.4 covers the combined gas law, which describes the effect of changes in both temperature and pressure on the volume of a gas. The ideal gas law, introduced in Section 12.5, describes how to calculate the number of moles in a sample of gas from its temperature, volume, and pressure. Dalton s law, presented in Section 12.6, enables the calculation of the pressure of an individual gas—for example, water vapor— in a mixture of gases. The number of moles present in any gas can be used in related calculations—for example, to obtain the molar mass of the gas (Section 12.7). Section 12.8 extends the concept of the number of moles of a gas to the stoichiometry of reactions in which at least one gas is involved. Section 12.9 enables us to calculate the volume of any gas in a chemical reaction from the volume of any other separate gas (not in a mixture of gases) in the reaction if their temperatures as well as their pressures are the same. Section 12.10 presents the kinetic molecular theory of gases, the accepted explanation of why gases behave as they do, which is based on the behavior of their individual molecules. 

Many substances do not react on a 1 1 mole basis, and so solutions of equal molar concentration do not react on a 1 1 volume basis. By introducing the concepts of equivalents and nonnality, we can make calculations in these cases that are similar to molar calculations for 1 1 mole reactions. To do so, we define a new unit of concentration called normality. The symbol iV stands for normal, just as M stands for molar. The normality of a solution is equal to the number of equivalents of material per liter of solution ... 

Let s introduce the concept of surface concentration of surfactant (measured in g mole/m ) [2]. If the environment is a binary solution with the volume molar concentration C of surfactant dissolved in it, then the quantities F and C are related by the Gibbs equation (aka the Gibbs isotherm) ... 

First we need to recognize that this is the dilution of the concentrated solution to prepare the desired one. The underlying concept we must use is that the number of moles of HCl will be the same before and after dilution, and this means we can use Equation 3.3. We know the desired final molarity and final volume, as well as the initial molarity. So we can solve for the needed initial volume. 

We apply the concept of the representative elementary volume (REV) within a volume AE for averaging variables, which will be discussed in Sect. 5.1. Suppose that for a mixture solution with -components of species, an amount of substance of species a is given as ria mole. Then the volume molar fraction coa and the mass density are defined as follows ... 

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