Chemistry 103A; Sections 5, 6, 7, 8; Lecture 32, 8 Nov 00

Recall:

We were talking about:

Hybrid Orbitals

A hybrid orbital comes about from "mixing" two or more of the familiar s, p, and d orbitals we know.

Principle: The number of orbitals is conserved. You get the same number of orbitals out that you put in. If we "mix" the s orbital with one of the p orbitals we get two so-called sp hybrid orbitals. Molecules that use sp hybrid orbitals are CO2, HCN, C2H2, and so on.

sp hybridization leaves two unhybridized p orbitals on the central atom which are available to be involved in bonding in other ways. For example they can form the p molecular orbitals we discussed earlier.

 If we mix the s orbital with two of the p orbitals we get three so-called sp2 hybrid orbitals. The sp2 hybrid orbitals point in just the proper direction to give us BCl3, SO2, SO3, H2CO, and many more trigonal planar arrangements of electron pairs. Mixing the s orbital with all three p orbitals gives four sp3 hybrid orbitals. sp3 hybrid orbitals have their electron density pointing towards the corners of a tetrahedron. This is just the right set of directions to give us CH4, NH3, H2O. and related molecules.

sp3 hybridization does not leave any unhybridized p orbitals to form p bonds.

 To get the trigonal bipyramidal and octahedral shapes of the 10 and 12 electron expanded octets requires additional orbitals. All of the molecules with expanded octets that we have studied were compounds of second row, third row, and higher elements. These elements have nearby (in energy) d orbitals available.

The trigonal bipyramidal shape requires the addition of one d orbital to give sp3d hybrid orbitals.

The octahedral shape requires an additional two d orbitals to give sp3d2 hybrid orbitals.
 
 

 Molecular Orbitals

We will not do much with molecular orbitals in this course. The only things you should know are:

Molecular orbitals are a very useful way to describe what the electrons are doing in molecules.

A molecular orbital is a charge cloud distribution that encompasses more than one nucleus. (Recall that atomic orbitals are charge cloud distributions that encompass only one nucleus.)

The elementary types of molecular orbitals are the s orbitals (which form s -bonds) and p orbitals which form p -bonds.

In a s -bond (an electron pair in a s orbital) the electron density is between the nuclei of the two atoms involved in the bond.

In a p -bond (using p orbitals) the electron density is not on the axis connecting the nuclei involved in the bond.
 
 

 States of Matter

We learned back in Chapter 1 that the three common stable states of matter on the surface of our planet are gas, liquid, and solid.

Gases are the easiest substances to describe theoretically and they were studied first historically. There are some relatively simple equations, called the gas laws, which describe the behavior of gases.

In a gas the molecules are moving at random. That is, the molecules move in random directions and with random speeds.

The molecules in a gas are, on the average, very far apart compared to the diameter of one of the molecules.

 Solids are the next easiest to describe and there are extensive and detailed theories which describe the properties of solids. (The theory of solids was once called "solid state physics", but now solids are most often lumped together with liquids into what is called "the physics of condensed matter.") In a solid the average distance between the molecules is about the same as the diameter of one of the molecules. The molecules are still moving randomly, but they cannot move freely in space. They are limited to small excursions about one point, called the equilibrium position. Liquids are the most difficult to describe theoretically. There are many different theoretical models for the properties of different types of liquids, but there is no one simple equation which describes well the properties of all liquids. In liquids the average distance between molecules is about the same as the diameter of one of the molecules so that the densities of liquids are close to the densities of solids. But, unlike solids, the molecules are free to move around in random directions. The molecules can tumble over each other and move about in the liquid. In this course we will study the properties of gases first in some detail. Then, later, we will look at the properties of solids and liquids in much less detail.
 

Properties of Gases

There are a number of so called "gas laws" which describe the properties of gases. But before we can talk about these gas laws we must review the variables which are used to describe the properties of gases.

The state of a gas sample is entirely characterized by specifying its pressure, p, its volume, V, its Kelvin temperature, T, and the amount of gas in the sample. Usually we describe the amount of gas in the sample by giving the number of moles, n, of gas in the sample.

If we know the values of these four variables we say that we know the "state" of the gas. These variables are called "state variables" or "state functions" because if we know the values of these four variables we know the state of the system.

The state of a system is unique. That is, each set of values of p, V, T, and n corresponds to only one state of the gas. There can be no other state of the gas with these same values of p, V, T, and n. Historically there were a number of gas laws discovered empirically (that is, by experiment). The gas laws are equations which relate these variables to each other for a sample of gas.

Before we look at the gas laws we must think a little about how some of these variables, p, V, T, and n are measured.
 

Pressure

The pressure of a gas is cause by the collision of gas molecules with a surface. Molecules colliding with a surface produce a force against the surface. Pressure is the force per unit area,

.
The SI unit of pressure is the Paschal (Pa), but we commonly use other units. The most common pressure unit is the atmosphere (atm).
1 atm = 101325 Pa.

(This, by the way, is the definition of the atmosphere.)

A pressure unit related to the SI unit is the bar,
1 bar = 105 Pa.
It is easy to show that
1 atm = 1.01325 bar.
Another common unit is the Torr or mm of Hg. One Torr is the pressure generated by the pull of gravity on a column of Hg which is one mm high. It is related to the atmosphere by
1 atm = 760 Torr.
The many devices used to measure pressure all take advantage of the fact that the gas pressure exerts a force on anything the gas comes in contact with.

We will describe two devices for measuring pressure. Absolute pressures can be measured by a mercury barometer. Absolute and relative pressures can be measured by a related device called a manometer.

To make a mercury barometer, take a glass tube about 80 cm long, closed at one end, and fill it with mercury. Now invert the tube with its open end in a bowl of mercury so that the end of the tube is below the surface of the mercury in the bowl and no air bubbles get into the tube. The height of the column of mercury in the tube (in mm) measured from the surface of the liquid in the bowl is the pressure in mm of Hg.

(You could make a similar device out of water, but the tube would have to be over 34 feet long. There would also be another complication which we will talk about later)

 A manometer is similar, except the glass tube is in the shape of a "U." The pressure on one arm of the U-tube can be compared to the pressure on the other side of the other arm by measuring the difference in height of the liquid in the two arms of the tube.
 

Volume

Volume is relatively easy to measure by any number of mechanical methods. The SI unit of volume is the m3. We will usually use the metric unit of volume, the liter (L),

1 L = 10-3 m3.


Temperature

The SI unit of temperature is the Kelvin. The Kelvin has the same size "degree" as the Celsius scale, but the origin of the Kelvin scale is at absolute zero. The size of the degree is defined such that,

0o C = 273.15 K.
(The actual formal definition of the Kelvin scale is that the "triple point" of water is at 273.16 K = 0.01 oC. We will talk about the triple point in chapter 13. For now suffice it to say that the triple point is the freezing point of water when the only gas in contact with the water is water vapor.) Temperature measurements for use in the gas laws will always be in Kelvin (K).
 

The Gas Laws

Beginning in the middle 17th century many scientists were experimenting to determine the properties of gases. These experiments spanned nearly 200 years and resulted in a set of equations (gas laws) which describe to good accuracy the properties of gases. Mainly these gas laws showed how the variables, p, V, T, and n, were related to each other in the description of gases.
 

Boyles Law

Around 1660 Robert Boyle was experimenting with the properties of gases under conditions where the temperature was held constants. He would take a sample of gas and measure the volume of the gas at different pressures (without changing the temperature).

Boyle found that, at constant temperature, the volume of the gas was inversely proportional to the pressure on the gas. That is, at constant T,

.
We usually write Boyles law in the form,
The latter form is useful when we think of p1 and V1 as the initial pressure and volume in an experiment and p2 and V2 as the final pressure and volume. Example calculation: A sample of gas has a volume of 4.60 L at sea level where the pressure is 1.00 atm. What would be the volume of the gas at an altitude of 20.0 km (about 12.4 miles) where the pressure is 0.0553 atm if we keep the two temperatures the same?