Avogadro s number

Avogadro s number, L The number of particles (atoms or molecules) in one mole of any pure substance. L = 6 023 x 10. It has been determined by many methods including measurements of Brownian movement, electronic charge and the counting of a-particles. 

Boltzmann constanty k A fundamental constant. It is the gas constant per molecule, equal to R divided by Avogadro s number L. 

Brownian movement The rapid and random movement of particles of a colloidal sol, observed brightly lit against a dark ground. First observed with a pollen suspension. The Brownian movement is due to the impact on the dispersed particles of the molecules of the dispersion medium. As the particles increase in size, the probability of unequal bombardment from different sides decreases, and eventually collisions from all sides cancel out and the Brownian movement becomes imperceptible at a particle size of about 3-4/z. From the characteristics of the movement, Perrin calculated Avogadro s number L. 

Benjamin Franklin s experiment is mentioned in the opening paragraphs of this chapter. Estimate, from his results, an approximate value for Avogadro s number make your calculation clear. The answer is a little off explain whether more accurate measurements on Franklin s part would have helped. 

Avogadro s number and n = n, then tire above relationship becomes... 

Tlie molecular volume Vm can in turn be obtained by dividing the molecular weight by density or from refractivity measurements is Avogadro s number. The cavity radius (... 

Having detemiined A b and knowing that the gas constant R = 8.314JK from macroscopic measurements on gases, determine Avogadro s number L from the relationship... 

Multiplying and dividing the right-hand side of this expression by N converts the Nj s to mole fractions, and, if N is taken to be N, Avogadro s number, kN becomes R. Accordingly, we write for 1 mol of mixture... 

Multiplying and dividing the right-hand side by Ni -t- N2 and letting this sum equal Avogadro s number of molecules gives per mole of solution ... 

We can shift from numbers of molecules to numbers of moles of solute by dividing by Avogadro s number and changing k to R. Also, recalling that V = SjnjVj, we write... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

An important historic application of this relationship was the determination of Avogadro s number from measurements of light scattered by the atmosphere (see Problem 3). 

Prepare a log-log plot of rx versus X and evaluate the slope as a test of the Rayleigh theory applied to air. The factor M/pN in Eq. (10.36) becomes 6.55 X 10 /No, where Nq is the number of gas molecules per cubic centimeter at STP and the numerical factor is the thickness of the atmosphere corrected to STP conditions. Use a selection of the above data to determine several estimates of Nq, and from the average, calculate Avogadro s number. The average value of n - 1 is 2.97 X 10" over the range of wavelengths which are most useful for the evaluation of N. ... 

In principle, one molecule of a chemiluminescent reactant can react to form one electronically excited molecule, which in turn can emit one photon of light. Thus one mole of reactant can generate Avogadro s number of photons defined as one einstein (ein). Light yields can therefore be defined in the same terms as chemical product yields, in units of einsteins of light emitted per mole of chemiluminescent reactant. This is the chemiluminescence quantum yield which can be as high as 1 ein/mol or 100%. 

Concentration. The basis unit of concentration in chemistry is the mole which is the amount of substance that contains as many entities, eg, atoms, molecules, ions, electrons, protons, etc, as there are atoms in 12 g of ie, Avogadro s number = 6.0221367 x 10. Solution concentrations are expressed on either a weight or volume basis. MolaUty is the concentration of a solution in terms of the number of moles of solute per kilogram of solvent. Molarity is the concentration of a solution in terms of the number of moles of solute per Hter of solution. 

Particle Motion. AH suspended micrometer-si2e particles are in motion due to the thermal energy they possess. At any given temperature, the average kinetic energy due to thermal motion of an individual particle is equal to kP where k is the Bolt2maim constant (k = the gas constant, R, divided by Avogadro s number) ... 

AB and ABC are the products of the principal moments of inertia. Moments of inertia are calculated from bond angles and bond lengths. Many values are given by Landolt-Bornsteiu. is Avogadro s number, and M is the molecular weight of the molecule. Stuper et al. give a computerized method for prediction of the radius of gyration. 

---