# Mathematical Relationships in Chemistry

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Mathematical Relationships in Chemistry
CP Chemistry

What You’ll Learn in this Unit
Measurement Dimensional Analysis Scientific Notation Significant Figures Error Density

Measurement Every measurement has two parts
Number with the correct sig - figs Scale (unit) SI system (le Systeme International) based on the metric system Prefix + base unit Prefix tells you the power of 10 to multiply by - decimal system -easy conversions

Measurement COMMON SI UNITS Symbol   Unit Name   Quantity   Definition    m meter length base unit    kg kilogram mass    s second time    K kelvin temperature       °C degree Celsius**   temperature    m3 cubic meter volume m3    L liter** dm3 = m3    N newton force kg·m/s2    J joule energy N·m    W watt power J/s    Pa pascal pressure N/m2    Hz hertz frequency 1/s We use the SI (not the Sports Illustrated) It is called the Systeme Internationale.

Metric SI Units Mass - kilogram (kg) Length- meter (m)
Time - second (s) Temperature - Kelvin (K) Electric current - ampere (amp, A) Amount of substance - mole (mol)

Prefix Symbol Magnitude Giga G 1,000,000,000 (109) Mega M 1,000,000 (106) Kilo K 1,000(103) Hecto H 100 (102) Deca da 10 (101) base unit g, L, m 1 (100) Deci d 0.1 (10-1) Centi c 0.01 (10-2) Milli m 0.001 (10-3) Micro μ (10-6) Nano n (10-9) Pico p (10-12)

Using Units to solve problems
Dimensional Analysis Using Units to solve problems

Dimensional Analysis Use conversion factors to change the units
1 foot = 12 inches (equivalence statement) 12 in = = 1 ft ft in 2 conversion factors multiply by the one that will give you the correct units in your answer.

Example Problem There are 2.2 lb in 1 kg
If you weigh 158 lbs, how many kg do you weigh?

Example Problems 11 yards = 2 rod 40 rods = 1 furlong
8 furlongs = 1 mile 1 mile = 1.6 km The Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers?

Example Problems Convert: 475m to km 35daL to mm

Scientific Notation 100 = 1.0 x 102 0.001 = 1.0 x 10-3
-- This provides a way to show significant figures.

TOO QUICK FOR YOU! So here are the rules.. slowly!
Place decimal point after 1st real non-zero integer. (ex) 1.0 NOT 10.0 Raise 10 to the exponential which equals the number of places you moved.

Sample Problems 2387

Answers 2.387 x 103 7.031 X 10-5 2.9 x 109 8.900 X 10-3 9.01 X 107 2.10 X 10-6

Uncertainty Basis for significant figures
All measurements are uncertain to some degree Precision- how repeatable Accuracy- how correct - closeness to true value. Random error - equal chance of being high or low- addressed by averaging measurements - expected

Uncertainty Systematic error- same direction each time
Want to avoid this Better precision implies better accuracy You can have precision without accuracy, and vice versa

Precision vs. Accuracy Precision- the degree of agreement among several measurements of the same quantity. Accuracy- the agreement of a particular value with the true value

Significant Figures Meaningful digits in a MEASUREMENT
The number of significant figures in your measurement will tell the reader how exact the instrumentation is If it is measured or estimated, it has sig figs. If not, it is exact.

Significant Figures All numbers except zero are significant.
Some zeros are, some aren’t

Which Zeros Count? In between other sig figs does
Before the first number doesn’t After the last number counts if it is after the decimal point the decimal point is written in sig figs sig figs

Doing the Math Multiplication and division, same number of sig figs in answer as the least in the problem Addition and subtraction, same number of decimal places in answer as least in problem.

Volume The space occupied by any sample of matter
Calculated for a solid by multiplying the length x width x height SI derived unit = cubic meter (m3) Everyday unit = Liter (L), which is non-SI

Units of Mass Mass is a measure of the quantity of matter
Weight is a force that measures the pull by gravity- it changes with location Mass is constant, regardless of location

Working with Mass The SI unit of mass is the kilogram (kg), even though a more convenient unit is the gram Measuring instrument is the balance scale

Density Which is heavier- lead or feathers?
It depends upon the amount of the material A truckload of feathers is heavier than a small pellet of lead The relationship here is between mass and volume- called Density

Density The formula for density is: mass volume
Common units are g/mL, or possibly g/cm3, (or g/L for gas) Density =

Density Useful for identifying a compound Useful for predicting weight
An intrinsic property- does not depend on what the material is Intensive Property Density is a physical property, and does not depend upon sample size

Things related to density
Corn oil density – 0.921g/mL Water density – 1.000g/mL What happens when corn oil and water are mixed? Why? Will lead float in water?

Example Problem An empty container weighs g. Filled with carbon tetrachloride (density=1.53 g/cm3), the full container weighs g. What is the volume of the container?

Density and Temperature
What happens to density as the temperature increases? Mass remains the same Most substances increase in volume as temperature increases Thus, density generally decreases as the temperature increases

Density and water Water is an important exception
Over certain temperatures, the volume of water increases as the temperature decreases Does ice float in liquid water? Why?

Specific Gravity A comparison of the density of an object to a reference standard (which is usually water) at the same temperature Water density at 4 oC = 1 g/cm3

Specific Gravity Formula
D of substance (g/cm3) D of water (g/cm3) Note there are no units left, since they cancel each other Measured with a hydrometer Uses? Tests urine, antifreeze, battery SG =

Temperature A measure of the average kinetic energy
Different temperature scales, all are talking about the same height of mercury. In lab take the reading in ºC then convert to our SI unit Kelvin ºC = K

Temperature Heat moves from warmer object to the cooler object
Glass of iced tea gets colder? Remember that most substances expand with a temp. increase? Basis for thermometers

Temperature scales Celsius scale- named after a Swedish astronomer
Uses the freezing point(0 oC) and boiling point (100 oC) of water as references Divided into 100 equal intervals, or degrees Celsius

Temperature scales Kelvin scale (or absolute scale)
Named after Lord Kelvin K = oC + 273 A change of one degree Kelvin is the same as a change of one degree Celsius No degree sign is used

Temperature scales Water freezes at 273 K Water boils at 373 K
0 K is called absolute zero, and equals –273 oC

100ºC = 212ºF 0ºC = 32ºF 100ºC = 180ºF 1ºC = (180/100)ºF 1ºC = 9/5ºF
For Calculations: °F = 9/5 (°C) + 32 °C = 5/9 (°F - 32)

Error Calculations X 100 accepted value
Error = Experimental value - accepted value % error = [error] accepted value X 100