Math in ChemistryUnit 1B

What is it? Anything that has ______ and ____________

What is volume? _______________________________________

What tools are used to measure volume? For liquids – ____________________________ For solids – ______________________________

Matter

What is mass? ___________________________________

Measured in ___________, usually with a balance Related to, but not the same as ________________

What is weight? _________________________________________

Most properties of matter are best described in quantitative terms A quantitative measurement has

___________________ There are __________ associated with

quantitative measurements

Units of measurement

What is the SI system? A subset of the metric system adopted in 1960

as the standard system of measurement units The most common units used in chemistry:

_______ length __ _______ mass __ _______ time __ _______ temperature __ _______ amount of substance __

Systeme Internationale (SI)

Based on ________ Prefixes identify the factor of 10

Kilo = ______ (k) Hecta = ______ (h) Deka = ______ (dk) Deci = ______ (d) Centi = ______ (c) Milli = ______ (m)

SI Prefixes

This pneumonic device should help you remember the basic metric prefixes:

__________________________________________________________________________

(kilo, hecta, deka, unit, deci, centi, milli)

Remembering Prefixes

Metric conversions

What is scientific notation? _______________________________________________

_______________________________________________ M x 10x

When moving the decimal left, the exponent is ____

When moving the decimal right, the exponent is ____

Scientific notation

100 = ___ 101 = ___

102 = ___ 103 = ___ + exp. =

__________

Large #’s > 1

o 10-1 = ___ = ___o 10-2 = ___ = ___o 10-3 = ___ = ___o - exp. =

___________

o Very small #’s < 1

1. Before +/-, make sure all #’s have the same exponent:

1. Ex. 9.9 x 102 0.099 x 104

+ 6.2 x 104 + 6.2 x 104

6.299 x 104

2. M1 x 10x

+/- M2 x 10x

M1 +/- M2 x 10x

Using scientific Notation

2. Multiplication:1. Add exponents after multiplying M values2. M1 x 10x x M2 x 10y

1. __________________________________

Division:1. Subtract exponents after dividing M values2. M1 x 10x d M2 x 10y

1. ________________________________________

1. Exact numbers1. Counting2. Results of definitions (1 hour = 60 minutes)

2. Measurements – are never exact. These are limited by the instrument used.

1. BR scale – nearest lb (2 lbs)2. Food scale – nearest ounce (2.25 lbs)

Significant Figures

Significant figures in measurements include __________________________________________________________________________________________

Ex. 6.35 m 6 and 3 are certain, 5 is uncertain, so there are ___ significant figures.

Scientists agree +/- 1 in last sig. fig.

1. ALL _________ digits are significant (1234 has ___ sig. figs.)

2. “_____________” (those zeroes before a non-zero digit) are ______ significant. They are used only to locate the decimal. (0.000005 has _____ sig. fig.)

Rules for determining how many significant figures

3. “____________” (those zeroes between two non-zero digits) are _______ sig. (50005 has _ sig. figs.)

4. “_____________” that follow a non-zero digit and are not followed by a decimal are _____ significant. (50000 has __ sig. fig)

5. “______________” that follow a non-zero digit and ARE followed by a decimal ____ significant. (50000. has __ sig. figs.)

1. In addition and subtraction:1. Round answer to the part of the equation

with the fewest significant figures.1. 22.567 + 5.4 = ___________

Using Significant Figures

1. In multiplication and division:1. Round your answer to the same # of

significant figures as your factor having the least # of sig. figs. If a factor is an exact number, do not include it in your sig. figs.1. If a factor is a conversion factor (1 hr = 60

min), do not include it in your sig. figs.

2 x 237 = 474 = _______ (w/ sig figs)

If, however, 2 is an exact number, then your answer would be _______.

1. Precision – _________________________________ (a precise measurement should be measured +/- 1 digit each time)

2. Accuracy – ____________________________________________________________________________________

(again, this should be +/- 1 digit)

Why use significant figures?

What is a conversion factor? A mathematical expression that

______________________________________________________________________________________________ Based on statements of ________________________ Ex. _________________________________ Can be written as:

Conversion Factors

1. ALWAYS write both the ______________________ ( ex. ________, NOT ___)

2. Units act like _____________________in solving equations.

a. Cannot ______ unlike units1. 3x + 4y = ___________2. 3cm + 4 dm = __________3. 3 cm + 40 cm = _________

Using conversion factors in Dimensional Analysis

3. CAN ___ units1. a. X x Y = ____2. b. cm x cm = ________3. g x cm2/sec = _________

4. CAN ___ and ______ units

1. Study the problem (highlight key info)2. Write down all data with label and units

1. Ex. Mass = 3 g1. (label) amt. unit

2. Write down what you are asked to find1. V = ? L

Problem-solving strategies

3. Find a __________ that connects the given data to the information you’re trying to find.

4. Use ____________________________________________________________________________________

5. Check your result (_________________________)

If a person drives 88 km/hr for 2 hours, how far will they have traveled?speed = _____ time = __________distance = ?

Example 1

Convert the mass of a 180 lb person to appropriate metric units.

Example 2

How many minutes are there in 2 weeks?1. Realize that you will need more than 1

conversion factor to get from minutes to weeks.

2. What conversion factors do we know?1. 1 week = ___ days2. 1 day = ___ hours3. 1 hour = ___ minutes

Example 3

What is a derived unit? A unit _________ from a combination of the

seven base units: Ex. _______ is derived by multiplying the

length, width and height of an object. 1 cm3 = ____ (where mL is our derived unit)

Derived units