### Richard A. Paselk

Chem 107

Fundamentals of Chemistry

Fall 2009

Lecture Notes: 3 September

© R. Paselk 2005

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# Dimensional (Unit) Analysis and Problem Solving

Memorize: 1 mL = 1 cm3; 1 inch = 2.54 cm; density of water = 1 g/mL; 1 liter is about 1 quart; 0° C = 32 °F, 100°C = 212 °F

Dimensional analysis can be convenient check on your work, or even a way to determine the best approach to a problem. This simply means to include all of the units for each factor in an equation, and then to check to see that the units on both sides of the equation are equal.

For example, how long is a one foot ruler? Know conversion for cm to inches: 2.54 cm = 1 inch (no sig figs, defined ) [ans. = 30.48 cm]

Let's try some density problems. First recall that the units of density are g/cm3 or g.cm-3.

• A student found that 20.0 mL of a liquid weighed 35.987 g. What is its density?
• Using a jewelers balance a student found that a coin weighed 2.34 carats in air. By weighing it again submerged in water she found it had a volume of 0.034 mL. What is its density? (1 carat = 200 mg, defined)

Let's look at a pressure problem. What I want to emphasis here is that you don't need to know what the units refer to, you only need to know the conversions.

• What is the force in Newtons on the surface of water in a 10.00 x 10.00 cm square container (area = 100.0 cm2) if the pressure is 754 mmHg?
• First we need to look up some units. Obviously Newtons are force, and pressure is force/area.
• So what are units of pressure
• We have 754 mmHg, whatever that is, but in the back of the text we see that 1 mmHg = 1 Torr, and 760 mmHg = 1.013 x 105 Pa
• and 1 pascal (Pa) = 1 Nm-2 = 1 N/m2 or 1 N = (Pa)(m2)
• So how do we set it up?
• Look at what we have and see how to convert it to what we need.
• Get rid of mmHg by canceling: (754 mmHg) / ([760 mmHg] / [1.013 x 105 Pa]) = 1.005 x 105 Pa
• Cancel out: (1.005 x 105Pa)(Nm-2/Pa) = 1.005 x 105 Nm-2
• Cancel out m: (1.005 x 105 Nm-2)(1 m2/104 cm2) = 10.05 Ncm-2
• Finally multiply by area: (100.0 cm2)(10.05 Ncm-2) = 1.005 x 103 N
• How about significant figure? Use multiplication rule, so count digits and use least.
• Least digits is original pressure, 754 mmHg, therefore: 1.005 x 103 N = 1.01 x 103 N

Heat and Specific Heat: Earlier we spoke of heat as a measure of energy transferred between objects of different temperatures. We are already familiar with the units of temperature, what are the units of heat?

• joule (SI unit): It takes 4.184 J to raise 1 g of water at 20 °C 1 °C.
• calorie (metric, non-SI unit): It takes 1 cal to raise 1 g of water at 20 °C 1°C. Thus 1 cal = 4.184 J (defined).
• Calorie (large Calorie = nutritional Calorie): 1 Calorie = kilocalorie.

Let's look at a specific heat problem. Specific heat is the amount of heat it takes to raise 1 g of a specific substance 1 °C. Specific heats for other substances are relative to water, so no units (comparing results in canceling out units).

The heat transferred in a process (q) is summarized in the equation:

Heat = q = mCspT

where m is the mass of substance and Csp is the specific heat of the substance.

Example: 750 calories of heat is transferred to 100.0 g of water at 20.00 °C. What will the new temperature of the water be assuming no heat is lost to the container of the surroundings?

# Atoms and Atomic Structure

## Atoms

Atoms are the smallest constituents of elements. The first successful atomic theory was that of John Dalton (1803).

### Dalton's atomic theory states:

1. All matter is composed of ultimately small particles, called atoms.
2. Atoms are permanent and indivisible - they can neither be created nor destroyed.
3. Elements are characterized by their atoms. All atoms of a given element are identical in all respects. Atoms of different elements have different properties.
4. Chemical change consists of a combination, separation, or rearrangement of atoms.
5. Chemical compounds are composed of atoms of two or more elements in fixed ratios.

All of these statements are close to reality, and nearly describe chemical behavior. But here are exceptions. Thus atoms can be created and destroyed via nuclear processes. They consist of different forms called isotopes. Atoms are not the smallest particles, etc.

Atoms are now known to consist of three different types of particles: electrons, protons and neutrons (the common form of one very important atom, hydrogen, has only two kinds: a proton and an electron). The protons and neutrons reside in a small inner portion called the nucleus while the electrons reside in a relatively large cloud centered on the nucleus. Important properties of these particles are listed in the table below:

 Particle Charge Relative Mass Mass Electron (e-) -1 1/1840 9.11 x 10-28g Proton (p or H+) +1 ª1 1.67 x 10-24g Neutron (n) 0 ª1 1.67 x 10-24g

Some important terms which you must know are:

• Atomic number (Z) - the number of protons in the nucleus. This number is characteristic of a given element.
• Atomic mass number (A) - the sum of the protons and neutrons in a given atom (p + n).
• Atomic mass - the actual mass of an average atom in a sample. The characteristic atomic masses for Earth are shown on periodic tables.
• Atomic Mass Unit: the atomic mass unit = amu is a unit of mass for atoms. It is defined as 1/12 the mass of one atom of 12C, where the mass of 12C is defined as 12 exactly.

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