Mathematical Relationships in Chemistry CP Chemistry.

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

• We use the SI (not the Sports Illustrated) It is called the Systeme Internationale.

COMMON SI UNITS

Symbol  Unit Name  

Quantity   Definition

   m meter length base unit

   kg kilogram mass base unit

   s second time base unit

   K kelvintemperature   

base unit

   °Cdegree Celsius**  

temperature

   m3 cubic meter volume m3

   L liter** volumedm3 = 0.001 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

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 0.000001 (10-6)

Nano n 0.000000001 (10-9)

Pico p 0.000000000001 (10-12)

Dimensional Analysis

Using Units to solve problems

Dimensional Analysis

• Use conversion factors to change the units• Conversion factors = 1• 1 foot = 12 inches (equivalence statement)

• 12 in = 1 = 1 ft. 1 ft.

12 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!1. Place decimal point after 1st real non-zero

integer. (ex) 1.0 NOT 10.0

2. Raise 10 to the exponential which equals the number of places you moved.

Sample Problems

• 2387• 0.00007031• 2900000000• 0.008900• 90100000• 0.00000210

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• 3200 2 sig figs

• 3200. 4 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 121.3 g. Filled with carbon tetrachloride (density=1.53

g/cm3), the full container weighs 283.2 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 + 273 = 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 = 212ºF0ºC = 32ºF

100ºC = 180ºF1ºC =

(180/100)ºF1ºC = 9/5ºFFor Calculations:

°F = 9/5 (°C) + 32°C = 5/9 (°F - 32)

Error Calculations

Error = Experimental value - accepted value

% error = [error] accepted value X 100