### Richard A. Paselk

VUB Biology

Fall 2001

Lecture Notes:: 17 September

# Introduction to Chemistry, cont.

## The Mole

This is the SI (International Metric system) unit of amount of substance. 1 mole = the number of carbon atoms in 12 g of 12C. This number, called Avogadro's Number, has been measured as 6.022 x 1023 mol-1 (current value: 6.022 141 99 x 1023mol-1). Notice that this number can refer to anything (a mole of eagles, a mole of pennies, etc.). In each case we are talking about 6.022 x 1023 items or entities.

For chemists, biologists, etc. a mole has two common uses:

• It refers to Avogadro's Number of entities.
• It refers to the atomic weight (or formula weight or molecular weight) of a substance expressed in grams. Thus a mole of sodium is 22.99 g of sodium (which contains 6.022 x 1023 atoms of sodium!).

Note that Avogadro's number, 6.022 x 1023 is thus the conversion factor from amu's to grams!

Atomic Mass:

• At the microscopic scale (atoms, ions and molecules) it is the mass in amu's of a single atom etc.
• At the macroscopic scale (visible amounts of stuff) it is the mass in grams of a mole of atoms etc.

Examples:

• What is the mass of 27 atoms of oxygen
• in amu's? (432.0 amu)
• in grams? (7.174 x 10-22g)
• Given 3.45 grams of copper
• how many moles of copper is this? (0.0543 mole)
• how many atoms of copper are there in this sample? (3.27 x 1022)
• A 2.34 mole sample of sulfur contains
• how many grams of sulfur? (75.0 g)
• how many atoms of sulfur? (1.41 x 1024)

# Weak Bonds

Weak bonds range from about 10% as strong as a covalent or ionic bond to <1% as strong.

The van der Waals bonds refers strictly to the dipole-induced dipole and dispersion types (attractions due to "momentary" dipoles in non-polar atoms or molecules occuring because of the radom nature of electron movement about the nucleus), but is also often used to refer to other weak bonds other than hydrogen bonds. Notice that the bonds are not only very weak (about 0.1 - 0.3% as strong as a covalent bond), they also do not act at a distance. Essentially they are contact bonds - they sort of act like a weak tape. The corollary is that they increase in importance with increases in molecular size (and thus contact surface).

Thus for hydrocarbons, which are essentially completely non-polar, we see a very low boiling point for methane (CH4) of - 161°C and a fairly regular increase in boiling point as carbons are added (ethane, C2H6 - 88°C; butane, C4H10 - 0.5°C; hexane, C6H14 69°C; octane, C8H18 126°C; etc.) until very large molecules such as paraffin (about 100 C's) and polyethylene (>1,000 C's) are essentially non-volatile. Note also though, in these very large molecules the forces holding the substance together have become significant due to the very large contact areas.

Hydrogen bonds are a special case of weak bonds. Note that they are significantly stronger (>100 fold) than the other weak bonds at about 4-10% as strong as a covalent bond. Hydrogen bonds only occur when a hydrogen bound to a small, very electronegative atom is brought close to another small, very electronegative atom. Essentially this means that we only see hydrogen bonds between hydrogens bound to N, O, or F (second Period electronegative elements) and N, O, or F. So we can have O-H O, O-H N, O-H F, N-H O, N-H N etc. hydrogen bonds. This is because hydrogen bonds involve dipole-dipole interactions, but they also have covalent character (about 10% of the sharing we see in true covalent bonds) which requires that the participating atoms be small enough to get close enough to allow such partial sharing.

Hydrogen bonding accounts for much of the special properties of water, such as its very high boiling point (261°C higher than methane with only a 10% increase in MW), high viscosity, high heat capacity etc. which in turn are due to the strong bonds between the individual molecules so they stick together.

# Water

Water: water is so ubiquitous, and has so many important and even special properties, that we will talk a bit more about it.

Water is a very unusual, even incredible substance whose amazing properties are often unappreciated because of its ubiquitousness. Water's special properties include extremely high mp and bp (0 °C & 100 °C, compare to methane, -183 °C & -161 °C, with a MW of 16 vs. water's 18); a high heat capacity (18 cal/°C mol vs. 8 cal/°C mol for methane); it has a high viscosity; its solid form is less dense than the liquid form at the same temperature (ice floats on water - very rare), and it has a high dielectric constant (78.5 vs. 1.9 for hexane).

The high mp, bp, and heat capacity all predict relatively strong bonding between water molecules, H-bonding. Note environmental consequences - Earth's weather is much more pleasant because it is moderated by water, especially along coasts. Ice floating prevents "solid" seas, definitely a downer in environmental terms.

We've looked at some gee whiz properties of water. Now let's look at water in more detail.

Water of course is a covalent structure: H-O-H. But what gives it its special properties is the polarity of its O-H bonds and the resultant dipole moments of the bonds and the molecule itself.

The water molecule itself is bent, with an angle of 104.5° between the hydrogens (compare to 109.5° for the sp3 tetrahedron of methane) as seen in Figure 2.15 p 32 of your text. Because of the very strong dipole moments of these bonds and the very small size of the hydrogen substituents on water, a slight degree of orbital overlap occurs between adjacent water oxygens and hydrogens to give partial covalent bonds known as H-bonds (effectively, can only form with O, N, & F). Note that the partial covalent character means that they are directional!

Within solid bulk water (ice) every water molecule is bonded to 4 others. [overhead 2.3, VV] In liquid water the molecules are still bonded to a large degree (the heat of fusion for ice is only 13% of the heat of vaporization for ice, thus most of the H-bonds must survive melting). Of course in liquid water the bonds are very unstable (average lifetime about 10 psec = 10-11 sec), exchanging constantly to give a "flickering cluster" structure. The various properties of water arise from this structure. (Note hi bp & mp, heat cap., viscosity, and, less obviously, that ice floats. This is because the molecules are in an open lattice rather than close-packed. G&G note that close-packed molecules would only occupy about 57% of volume. This would lead one to expect that ice would float "high." It doesn't because most of the structure remains in the liquid phase at 0° C.)

Aqueous Solutions - Definitions:

• Solution - a homogeneous mixture of substances.
• The major component is known as the solvent.
• The substances dissolved in it (by definition minor components) are solutes.
• Solubility - a measure of how much solute will dissolve in a given solvent under given conditions (default = 20 °C, 1 atm).

As a general rule for solubility we can say that "Like dissolves like."

Water is an excellent solvent for polar substances since its own polar dipole structure enables it to insulate them from each other and it can make good dipole-dipole and dipole-charge bonds. Figure 3.7 on p 42 shows the hexavalent liganding of water to sodium and chloride ions to form hydration shells (For sodium ions, the waters in the inner hydration-shell exchange every 2-4 nsec.). We say that substances dissolved in water are hydrated. (More generally, solvents solvate, with hydration being the special case for aqueous solvation.) Anything which can H-bond (such as alcohol or acetic acid) will also of course be quite soluble.

# Ionization of Water, pH & Buffers

Dissociation of water molecules: One aspect of water we have yet to talk about is its dissociation or ionization. In normal aqueous solution there is a certain probability that a hydrogen nucleus (a proton) can exchange between two hydrogen bonded molecules:

(Of course the hydronium ion, H3O+, will be associated with additional water molecules as well through H-bonding. For simplicity we will just write H+, with the understanding that it refers in fact to hydrated hydronium ions in aqueous solution. ) Note the reaction is not highly favored, in neutral solution (no excess H+) there will only be 10-7 molar hydronium ions, in other words only about 2 of every billion water molecules will be protonated!

For aqueous solution [H+][OH-]= 10-14;

• Brönsted acid: we will be using the Brönsted definition for acids and bases­an acid is a proton donor, while a base is a proton acceptor. Recall the corollary that acids and bases therefore exist as conjugate acid base pairs. Note that when an acid by this definition gives up a proton it becomes a base, since the reverse reaction would be accepting a proton:
Thus the acetic acid in the first reaction becomes its conjugate base acetate ion, while the base, hydroxide ion, becomes its conjugate acid, water. In the reverse reaction the nomenclature also reverses. Note that a molecule such as water can be both an acid, donating a proton to become its conjugate base hydroxide ion, or it can be a base, accepting a proton to become its conjugate acid, a hydronium ion.

Let's look at the pH scale for a moment:

• pH = -log [H+]. Remember that a lo pH means a high concentration of protons.
• Range: pH = -1 to pH = 15 (10M -10-15M)
• for 1 M HCl, pH = 0
• for 1 M NaOH, pH = 14
• At midrange [H+] = [OH-] = 10-7M. The solution is said to be "neutral."
• This follows in aqueous solution from Kw = 1.0 x 10-14 = [H+] [OH-], thus if [H+] = [OH-], then [H+] = (1.0 x 10-14)1/2= 1.0 x 10-7

Examples:

• What is the pH of a solution of 0.015 M HCl?
Strong acid, so [H+] = 0.015 M
pH = - log [H+]
pH = - log 0.015 = - (- 1.824)
pH = 1.82

Note that the significant figures are correct, 1 is the power of ten, only the figures to the right are significant.

• What is the pH of a solution of 0.067 M NaOH
Strong base, so [OH-] = 0.067 M
Recall that [H+][OH-] = 1.0 x 10-14
Substituting, [H+][0.067] = 1.0 x 10-14
Rearranging, [H+] = (1.0 x 10-14) / 0.067 = 1.493 x 10-13
pH = - log (1.493 x 10-13) = - (- 12.83)
pH = 12.83
Again note the significant figures - 12 corresponds to the power of ten, only the figures to the right are significant.

Note that the "p" has the more general meaning of "-log[]". Thus pOH is -log [OH-], pCa = -log [Ca2+], etc.

Buffers: What is a buffer?

• A buffer is a solution which resists changes in pH. Essentially it consists of an acid and its salt (a Brönsted acid and its conjugate base) in solution together. Thus the solution has a proton donor and a proton acceptor, so pH is stabilized.
• A buffer is simply an acid equilibrium system with significant amounts of both the acid and its conjugate base.

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