Physical Properties of Solutions

Basics of Chemistry-Summary 1

Topics

1. Units of Measure 2. Uncertainty a. Measurements b. Calculations 3. Dimensional Analysis a. In formulas b. Conversions 4. Algebra and Math 5. Problem Solving 6. Temperature 7. Density 8. Miscellaneous Vocabulary 9. Other Things to Memorize a. Prefixes b. Scientific Variables

Topic 1: Units of Measure

All measurements in science consist of two parts: a number (or value), and a scale (or unit or dimension). Science uses SI units of measure for consistency. The fundamental units of measure are:

Fundamental Unit Quantity Abbreviation Mass kilogram kg Length meter m Time second s Temperature Kelvin K Amount of Substance mole mol Electric Current ampere A Luminous Intensity candela cd Memorize the first 5 rows of this table. Topic 2: Uncertainty

Measurements: All measurements are uncertain. No matter how good the instrument, there could always be a better one. All measurements must reflect this uncertainty, so scientists have agreed on a protocol for communicating measurements. First, we all agree that measurement will be reported with every known (certain) digit, plus one, and only one more estimated or uncertain digit. Thus the following thermometer reads 5.22º. We are certain it is between 5.2º and 5.3º and we estimate 5.22º.

If we all adhere to this system, then we can all reconstruct the measuring device, just by correctly interpreting the number of significant digits in the reported measurement. Thus, a reported measurement of 6.2º would have been produced by a thermometer just like the one above, but lacking the shorter lines between the longest, whole degree lines. We would be sure it is between 6º and 7º and add the .2º as an uncertain digit.

Calculations: When we calculate using measurements, our answer can never be better (more precise) than the worst of the measurements used in the calculation. In other words, our answer must have the same number of significant figures as the worst of our measurements. So, 11.11567 cm x 2 cm = 22.23134 ≈ 20 cm2. The first measurement has seven significant digits, but the second has only one, so the answer can have only one significant digit. It looks like we are saying 11.11567 x 2 = 20, but we are not. We are saying that 11.11567 x some measurement near 2 cm is near 20 cm.

Zeros cause a problem in counting significant figures, so we have to rely on some rules. They are: 1. All non-zero’s count 2. All TRAILING zero’s AFTER the decimal point count. 3. All zero’s SANDWICHed between significant digits count. 4. Forget all other zero’s.

So, 10 = 1 sig fig, 1.0 = 2 sig fig, 10.0 = 3 sig fig, 101 = 3 sig fig, 1010 = 3 sig fig, 0.001 = 1 sig fig.

In scientific notation, ALL DIGITS ARE SIGNIFICANT. Topic 3: Dimensional Analysis

Also known as the Factor-Label Method. This is a skill that you must acquire to be successful in chemistry. Fortunately, it will also make you more competent in virtually every other human endeavor that requires making calculations. Really.

In Formulas: When solving a formula there is a tendency to apply the units needed to the answer without checking to see if it is appropriate. This method REQUIRES you to make no assumptions about the final units of the answer. Rather, you are required to algebraically solve for the units that result from your expression, and only then compare them to the desired units. If they match, fine. You are probably going to get this one correct. If they don’t match, then you have made a mistake. Thus, using dimensional analysis in formula problems is like having someone standing behind you and saying, “Oooh, you made a mistake there. Better go back and fix it!”

Example 1: P=rt where P = Pay, R = rate, and t = hours worked. How many hours did Molly work if she is paid 205 dollars and earns 5.00 dollars per hour?

Label is correct when problem is solved correctly: P 205 dollars hour Solve for t : t  substitute known values : t   41.0 hours r 5.00 dollars

Label is wrong when mistake is made: 205 dollars 5.00 dollars Solve for t : t  P x r substitute known values : t   hour 1025 dollars 2  ?? hours

Conversions: Mistakes are often made in conversions, especially complicated ones, when applying conversion factors. A common question arises like, “Now wait, do I multiply by 1000 or divide by 1000 here?” The solution to this is easy: Start with the given, then move way to the right, place an equals sign, a space for the answer, and right the labels you intend to finish with. Now go back to the beginning and write as many fractions as you need, ignoring number at first, and only filling in labels such that the one you need to eliminate cancels-out and is replaced by the one you want. Like this: Example 2: Convert 4.04 g of H2 gas into moles of H atoms.

4.04 g H 2 x   mol H 1 Then,

4.04 g H mol H mol H 2 x 2 x  mol H 1 g H 2 mol H 2

Then, knowing 1 mol H2 = 2.02 g H2 and 1 mol H2 = 2 mol H,

4.04 g H 1 mol H 2 mol H 2 x 2 x  mol H 1 2.02 g H 2 1 mol H 2

and finally,

4.04 g H 1 mol H 2 mol H 2 x 2 x  4.00 mol H 1 2.02 g H 2 1 mol H 2

Topic 4: Algebra and Math

You should already know algebra, but here are a few time saving tricks and things to watch out for.

If you make lots of simple algebra mistakes, use the triangle trick on 3-variable problems:

A = B x C Note that the B and C are side-by-side. Put them side-by-side in a triangle, then place the A in the remaining space. Like this:

To solve the equation for B, cover it with your finger so B equals A over C. To solve the equation for C, cover it with your finger so C equals A over B. To solve the equation for A, cover it with your finger so A equals B times C. Very slick. It works for any three variable equation.

P1 P2 P1 1 P1 To solve  for V2, be careful you don’t accidentally do this: V2  instead of  V1 V2 V1P2 V2 V1P2

V1 V2 P2V1 The easiest way to avoid this is to invert the equation at the start:  then solve: V2  . P1 P2 P1 Remember that dividing by a fraction is the same as multiplying by its reciprocal. Your set-ups should never have more than one fraction line: 12.01 5 12.01 5 2 Don’t write 1 . Instead write . Dividing by ½ equals multiplying by 2. 8.315 8.315 2

5 miles 5 miles  hour Don’t write . Instead write . Dividing by 10 miles/hr equals multiplying 10 miles / hour 10 miles by 1 hour/10 miles.

Keep your calculator math simple. Avoid unnecessary key strokes. Every time you enter a key stroke, it is an opportunity to make a mistake. Avoid parentheses where possible. Use the exponential function.

2x3x4 This fraction is calculated: 234/5/6/7=. It is NOT 234/567=. 5x6x7 You could punch in 234/(567)=, but why waste the two extra key strokes?

To calculate (3 x 103) x (4 x 105) do not key in: 310^3410^5=. You will mess up scientific notation if you persist in doing this. You also waste key strokes and invite error. Instead punch in: 3E34E5=. Most calculators access the E by hitting 2nd EE. The E takes the place of “x 10”.

Learn not to calculate everything. It is a waste of time. 6.4 20.001 Don’t calculate . The answer is 4.0 without a calculator. 6.4 x 20 is the same as 64 x 2. 32 64/32 = 2 and 2 x 2 = 4. Two significant figures makes it 4.0. Mr. Calculator gives 4.0002 which you must round to 4.0. Be smart!

Topic 5: Problem Solving or “The Way”

You don’t have to learn The Way, you have to use The Way. Any fool can learn it. You must use this procedure to receive full credit on all of my tests and it will maximize your score on the AP test. For the rest of your life, people will think you are smarter than you really are if you use The Way. The Way.

1. Read the question and decide which of your many equations applies. Write it down at the top, center of the answer space. 2. On the far left, list ALL of the variables and constants necessary to solve the equation. a. If a value is given, write it down as is. This is also a good place to perform simple conversions. b. If you must calculate the value, treat it as a separate problem, using The Way in another location within the answer space. 3. When all values have been identified, solve the equation algebraically for the remaining unknown value. 4. Substitute the values, including all labels into the equation. 5. Cancel and collect the labels. Write the result in the answer space. Compare the result with the expected labels. Locate and repair your error now if it is different than expected. 6. Estimate the numerical answer. 7. Calculate the answer and compare to the estimate. 8. Write down the answer and round it to the appropriate number of significant figures. 9. Execute a reality check.

Example 3: At what pressure is a 4.00 g sample of 25ºC hydrogen gas that is stored in a 23 L container? PV = nRT P = ? nRT 1.98 mol .0821 L  atm 298 K V = 23 L P   V 23 L mol  K n = 1.98 mol R = 0.0821 L∙atm/mol∙K = 2.106186 atm = 2.1 atm T = 25 + 273 = 298 K

solve for n here: MM=m/n MM = 2.02 g/mol 4.00 g  mol m = 4.00 g n = m/MM = = 1.98 mol then insert 2.02 g Notes: list of variables on left; algebra before math; labels were canceled before math; easy temperature conversion in variable list; “difficult” calculation for moles of gas in separate calculation.

Reality check: The beach ball: 1 mole of ideal gas at 0 ºC and 1 atm has a volume of 22.4 L. This is 2 moles of gas at a bit above 0 ºC and a bit more than 22.4 L. That is, twice as much gas in the same container at the same temperature. Twice the pressure sounds about right! Topic 6: Temperature

The official SI unit of measure for temperature is Kelvins, not degrees Kelvin. Just Kelvins. However, we usually measure temperature in degrees Celsius. Go figure. The good news is that a degree of Celsius is equal in size to a Kelvin. Only the scales are offset. How do you convert? Easy, just add or subtract 273.15 so that the Kelvin temperature is bigger than the Celsius. Memorize 273.15!

Topic 7: Density

Density is given by the equation, d=m/V. Density does not depend on sample size. It is an intensive property of matter. Look up intensive and extensive properties.

Topic 8: Miscellaneous Vocabulary

Make a flash card of each of the following terms:

1. Matter 6. Phase 2. Solid, Liquid, Gas 7. Physical and Chemical Change 3. Pure Substance 8. Separation of Mixtures 4. Solution 9. Volatility 5. Homogeneous and Heterogeneous 10. Compound Mixtures 11. Element Topic 8: Other Things to Memorize

Metric Prefixes Chemical Prefixes nano n 10-9 mono- 1 micro μ 10-6 di- 2 milli m 10-3 tri- 3 centi c 10-2 tetra- 4 deci d 10-1 penta- 5 kilo k 103 hexa- 6 mega M 106 hepta- 7 octa- 8 nona- 9 deca- 10 unideca- 11 Scientific Variables dodeca- 12 m = mass and molality t = time T = temperature w = work q = heat V = volume n = number of moles MM = molar mass M = molarity [A] = concentration of A