Mole and Avogadro's number

Chemists usually deal with macroscopic quantities of various elements and compounds. It is therefore of particular interest to relate the actual number of atoms in an amount of an element to its mass in grams. For example, how many atoms are present in 12.01 grams of carbon, in 1.008 grams of hydrogen, or in 32.04 grams of sulfur? We know, of course, that the number of atoms in each of these quantities is the same. But what is the number? This number has been determined experimentally in a number of different ways and turns out to be an extremely large number-- 6.022 x 10²³. It is known as Avogadro's number (N_A), in honor of the Italian chemist.

Sample problem: How many atoms are present in 24 g of carbon?
Solution: 24 g of carbon is 2 moles or 1.2 x 10²⁴.

Sample problem: What mass of silver contains the same number of atoms as 12 g of carbon?
Solution: Since 12 g of carbon is one mole, we need one mole of silver or 107 g.

Atomic mass and weight

• Elements in the periodic table are generally identified by the atomic symbol (e.g., H for hydrogen) and by two numbers. The smaller number is the atomic number (Z) or the number of protons in the nucleus. The larger number is the mass number (A) or the total number of protons and neutrons in the nucleus.
• The difference between the mass number and the atomic number is the number of neutrons (N) in a given nucleus: N=A−Z.
• Atomic mass is the mass of a single atom. It is usually expressed in atomic mass units (amu). An atomic mass unit (amu) is defined as exactly 1/12th of the mass of an atom of carbon-12, the isotope of carbon with six protons and six neutrons in its nucleus. Since one mole of carbon-12 has a mass of 12 grams, one amu is approximately equal to 1/N_A=1.66 × 10 ^{- 24} grams.
• Most of the mass of an atom is concentrated in the protons and neutrons contained in the nucleus. Each nucleon (proton or neutron) has a mass of about 1 amu, and thus the atomic mass is always very close to the mass number. Atoms of an isotope of an element all have the same atomic mass. Atomic masses are usually determined by mass spectrography.
• Two or more atoms which have the same number of protons but differ in the number of neutrons are known as isotopes of each other. Isotopes of a given element have identical chemical properties but slightly different physical properties and very different half-lives, if they are radioactive. For most elements, both stable and radioactive isotopes are known.
• Radioactive isotopes of many common elements, such as carbon and phosphorus, are used as tracers in medical, biological, and industrial research. Their radioactive nature makes it possible to follow the substances in their paths through a plant or animal body and through many chemical and mechanical processes; thus a more exact knowledge of the processes under investigation can be obtained. The very slow and regular transmutations of certain radioactive substances, notably carbon-14, make them useful as "nuclear clocks" for dating archaeological and geological samples. By taking advantage of the slight differences in their physical properties, the isotopes may be separated. The mass spectrograph uses the slight difference in mass to separate different isotopes of the same element. Depending on their nuclear properties, the isotopes thus separated have important applications in nuclear energy. For example, the highly fissionable isotope uranium-235 must be separated from the more plentiful isotope uranium-238 before it can be used in a nuclear reactor or atomic bomb.

Molecular weight

• Formula weight is a quantity computed by multiplying the atomic weight (in atomic mass units) of each element in a formula by the number of atoms of that element present in the formula and then adding all of these products together. For example, the formula weight of water (H2O) is two times the atomic weight of hydrogen plus one times the atomic weight of oxygen. Numerically, this is (2×1.00797)+(1×15.9994) = 2.01594+15.9994 = 18.01534. If the formula used in computing the formula weight is the molecular formula, the formula weight computed is the molecular weight.
• The percentage by weight of any atom or group of atoms in a compound can be computed by dividing the total weight of the atom (or group of atoms) in the formula by the formula weight and multiplying by 100. For example, the weight percentage of hydrogen in water is determined by taking two times the atomic weight of hydrogen, dividing it by the formula weight of water, and multiplying by 100. Numerically, this is 100×(2×1.00797)/18.01534 = 11.19% hydrogen in water by weight.
• Formula weights are especially useful in determining the relative weights of reagents and products in a chemical reaction. For example, it is known that two molecules of hydrogen gas, H2, react with one molecule of oxygen gas, O2, to form two molecules of water, H2O. This reaction may be represented by the chemical equation 2H2+O2→2H2O. The formula weight of hydrogen gas is 2.01594, that of oxygen gas 31.9998, and that of water 18.01534. Our chemical equation is numerically equivalent to 2×2.01594+31.9998 = 2×18.01534 or 4.03188+31.9998 = 36.03068 if the formula weight of each reactant is substituted for the formula of that reactant. From this equation we know, for example, that 4.03188 grams of hydrogen gas will react with 31.9998 grams of oxygen gas to yield 36.03068 grams of water. The relative proportions by weight of these reactants is the same in any reaction of hydrogen and oxygen to form water. These relative weights computed from the chemical equation are sometimes called equation weights.

Periodic table

• The Periodic Table organizes the elements by order of increasing atomic number in a series of rows or periods so that those with similar properties appear in vertical columns or groups.
• Within each column or group there is also a steady change in properties. Groups include the halogens, the alkali metals, and the inert gases.
• Elements within a group will form ions of the same charge because they have the same number of valence electrons.
• Elements tend to gain or lose electrons in order to achieve a noble gas configuration.
  • Metals tend to lose electrons to achieve a noble gas configuration. For example, Li often loses 1 electron to achieve a configuration like that of He.
  • Nonmetals tend to gain electrons to achieve a noble gas configuration. For example, F tends to gain 1 electron to achieve a configuration like that of Ne.
• Across each period there is a steady decrease in metallic character left-to-right, ending on the very nonmetallic inert (noble) gases, and an increase top-to-down. Metals tend to give up electrons (and thus form positively charged ions) more easily than nonmetals.
  • Sn is more metallic than Te, according to the left-to-right trend in metallic character.
  • Sn is more metallic than Si, according to the top-down trend in metallic character.
  • Te is more metallic than Br, according to both the top-down and the left-to-right trend in metallic character.
  • For I vs Se, we can’t tell because of competing trends. I would be more metallic according to the top-down trend, but Se would be more
    metallic according to the left-right trend. The effects tend to cancel.
• Atomic size decreases along a period from left to right and increases as one moves down a group.
  • C has a greater atomic size than O, according to the left-to-right trend.
  • K has a greater atomic size than Li, according to the top-down trend.
  • Al has a greater atomic size than C, according to both the left-to-right trend and top-down trends.
  • For I vs Se, I would be greater according to the top-down trend, but Se would be greater according to the left-right trend. The effects tend to cancel and the two elements have roughly the same atomic size.

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