Avogadro constant using

Becker, P (2003), Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal. Metrologia, 40 (6), 366-75. 

In these problems we use the Avogadro constant and the fact that one mole of atoms of an element has a weight in grams equal to its atomic mass. 

Note that the Avogadro constant is al.so commonly given the symbol N/,. We will use L in this present text. 

A powder diffraction pattern establishes that silver crystallizes in a face-centred cubic unit cell. The 111 reflection is observed at 0=19.1°, using Cu-Ka radiation. Determine the unit cell length, a. If the density of silver is 10.5x10 kg m and Z=4, calculate the value of the Avogadro constant. (The atomic mass of silver is 107.9.)... 

The refractive index, nD, defined as the ratio of light speed at the sodium D-line in a vacuum to that in the medium, is used in obtaining the polarizability, a, of solvent molecules. The relationship between a and nD is given by a = (3Vm/ 4 rNA)( D-l)/(wD + 2), where NA is the Avogadro constant and Vm is the molar volume.4 Solvent molecules with high a-values tend to interact easily with one another or with other polarizable solute particles by dispersion forces.5 ... 

The number of objects per mole, 6.0221 X 1023 mol 1, is called the Avogadro constant, NA, in honor of the nineteenth-century Italian scientist Amedeo Avogadro (Fig. E.3), who helped to establish the existence of atoms. The Avogadro constant is used to convert between the number of moles and the number of atoms, ions, or molecules ... 

The molar masses of elements are determined by using mass spectrometry to measure the masses of the individual isotopes and their abundances. The mass per mole of atoms is the mass of an individual atom multiplied by the Avogadro constant (the number of atoms per mole). However, there is a complication. Most elements occur in nature as a mixture of isotopes we saw in Section B, for instance, that neon occurs as three isotopes, each with a different mass. In chemistry, we almost always deal with natural samples of elements, which have the natural abundance of isotopes. So, we need the average molar mass, the molar mass calculated by taking into account the masses of the isotopes and their relative abundances in typical samples. All molar masses quoted in this text refer to these average values. Their values are given in Appendix 2D. They are also included in the periodic table inside the front cover and in the alphabetical list of elements inside the back cover. 

Use the Avogadro constant to convert between number of moles and the number of atoms, molecules, or ions in a sample, Example E.l. 

In the last step, we used the relation In 2 = 1 - f + j — + . Finally, we multiply 1 by 2 to obtain the total energy arising from interactions on each side of the ion and then by the Avogadro constant, NA, to obtain an expression for the lattice energy per mole of ions ... 

We have used M = mNA in the last step. The molar kinetic energy of an ideal gas is the mean energy of a molecule (the quantity we have just calculated) multiplied by the number of molecules per mole (the Avogadro constant). Therefore,... 

A fundamental theorem of classical mechanics called the equipartition theorem (which we shall not derive here) states that the average energy of each degree of freedom of a molecule in a sample at a temperature T is equal to kT. In this simple expression, k is the Boltzmann constant, a fundamental constant with the value 1.380 66 X 10-21 J-K l. The Boltzmann constant is related to the gas constant by R = NAk, where NA is the Avogadro constant. The equipartition theorem is a result from classical mechanics, so we can use it for translational and rotational motion of molecules at room temperature and above, where quantization is unimportant, but we cannot use it safely for vibrational motion, except at high temperatures. The following remarks therefore apply only to translational and rotational motion. 

Determination of the amount of substance is thus in direct relation to basic units of the SI system and does not need a RM for comparison. The Faraday constant is one of the fundamental constants (it can be expressed as the product of the electron charge and the Avogadro constant). It enables the attainment of high precision and accuracy and is independent of the atomic weights of the elements in the sample. Its drawback is lower selectivity, a feature common to titration methods. This makes coulometry especially suitable for determination of relatively pure substances used as standards by other (relative) methods. The Faraday constant has been proposed as an ultimate standard in chemistry [3],... 

Chemists have devised various ways to determine the Avogadro constant. To learn more about how this constant has been found in the past and how it is found today, go to the web site above. Go to Science Resources, then to Chemistry 11 to find out where to go next. What are some methods that chemists have used to determine the number of particles in a mole How has the accepted value of the Avogadro constant changed over the years ... 

In the Thought Lab below, you can practise working with the mole by relating the Avogadro constant to familiar items. Normally the mole is used to group atoms and compounds. For example, chemists know that 1 mol of barium contains 6.02 x 1023 atoms of Ba. Similarly, 2 mol of barium sulfate contain 2 x (6.02 x 1023) = 12.0 x 1023 molecules of BaS04. 

The mole is used to help us count atoms and molecules. The relationship between moles, number of particles, and the Avogadro constant is... 

Think about your answer to Analysis question 5(a). Did you need to use the Avogadro constant in your calculation Explain why or why not. 

Chemists rarely use the Avogadro constant directly in their calculations. What relationship do they use to avoid working with such a large number ... 

You can use what you now know about the mole to carry out calculations involving molar mass and the Avogadro constant. One mole of any compound or element contains 6.02 x 1023 particles. The compound or element has a mass, in grams, that is determined from the periodic table. 

First convert the mass to moles, using the molar mass of iodine. Multiplying the number of moles by the Avogadro constant will yield the number of molecules. 

Use the Avogadro constant to convert between moles and particles. 

Use the definition of the Avogadro constant to explain why its value must be determined by experiment. 

The atomic contents of the unit cell give the composition of the material. The theoretical density of a crystal can be found by calculating the mass of all the atoms in the unit cell. (The mass of an atom is its molar mass divided by the Avogadro constant see Section Sl.l). The mass is divided by the unit cell volume. To count the number of atoms in a unit cell, we use the following information ... 

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