Numbers Avogadro’s number

A mole of a substance is the number of elementary particles (atoms, molecules) found in the mass (in grams) of that substance that corresponds to its atomic or molecular weight. In molar volumes, which amount to 22.4 L for gases and are different from solid to solid, there are always the same number of atoms or molecules. This "magic number", Avogadro s number, is 6.022xl023 mol-1. 

Avogadro s number Avogadro s number is the number of particles (atoms or molecules or ions) in a mole and is numerically equal to 6.022 x 1023 particles. 

The basic unit of electrical charge used by chemists is appropriately called a Faraday, which is defined as the charge on one mole of electrons (6 X 10 electrons). Incidentally, note that chemists have extended the original definition of the mole as a unit of mass to a corresponding number (Avogadro s number) of particles. Use the electrolysis of molten sodium chloride to see the relationship between Faradays of electricity and moles of decomposition products. 

Remember that kinetic energy is 1/2mv1. The Boltzmann constant k is equal to the ideal gas constant R divided by Avogadro s number. Avogadro s number is the number of molecules in a mole, so the Boltzmann constant treats individual molecules, while the ideal gas constant deals with moles of molecules. So, if we use the molecular mass (M), we need to use the ideal gas constant. Also, we re always safest in physics when we stick to SI units, so let s express the molecular mass in units of kg/mol and R in units of J/mol/K. So, on a molar scale, we can recast the relationship between kinetic energy and temperature as ... 

Quantity that contains the same number of entities (atoms, molecules, etc.) as there are atoms in 12g of carbon-12. This number - Avogadro s number... 

A mole is a fixed number (Avogadro s number) of molecules therefore, a mole haction is a number fraction—the mole fraction of B is the fraction of all the molecules in the solution that are B molecules. It follows from the definition that a + Xb = 1 or, for more than two components, Xa + Xb + Xc + = 1. If we have 3.42 g of sucrose (CiaHiaOu, 342 g/mole) dissolved in 18.0 g of water (18.0 g/mole), then we have 0.0100 mole sucrose and 1.00 mole water. The mole fractions are... 

Avogadro s number is defined with respect to carbon-12—it is the number equal to the number of atoms in exactly 12 g of carbon-12. If Avogadro s number was defined as 1.00 X 10 (a nice round number), it would correspond to 1.99 g of carbon-12 atoms (an inconvenient number). Avogadro s number is defined with respect to carbon-12 because, as you recall from Section 2.6, the amu (the basic mass unit used for all atoms) is defined relative to carbon-12. Therefore, the mass in grams of 1 mol of any element is equal to its atomic mass. As we have seen, these two definitions together make it possible to determine the number of atoms in a known mass of any element. 

If you wanted to carry out this reaction, how could you measure the correct numbers of particles of aluminum and iodine Fortunately, you can count particles by measuring mass. Suppose you have a sample of an element, and the mass of the sample in grams is numerically equal to the atomic mass of the element. Scientists have discovered that this mass of an element contains 6.02 X 10 atoms of that element. This number is called Avogadro s number. Avogadro s number of particles is called a mole of particles. The mole is the SI base unit used to measure the amount of a substance and is defined as the number of particles in exactly 12 g of pure carbon-12. For the purpose of dealing with moles, the simplest unit of any substance is called a representative particle. The particle may be an atom, a molecule, a formula unit, or an ion. 

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... 

In terms of moles, Avogadro s hypothesis can be stated The same volume is occupied by one mole of any gas at a given temperature and pressure. The number of molecules in one mole is known as the Avogadro number constant. ... 

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. 

---