Essential Math of Chemistry

Scientific Notation-- used to express very large or very small

numbers, and/or to indicate precision(i.e., to maintain the correct number

of significant figures)

Form: (# from 1 to 9.999) x 10exponent

800 = 8 x 10 x 10

= 8 x 102

2531 = 2.531 x 10 x 10 x 10

= 2.531 x 103

0.0014 = 1.4 10 10 10

= 1.4 x 10–3

Put in standard form.

1.87 x 10–5 = 0.0000187

3.7 x 108 = 370,000,000

7.88 x 101 = 78.8

2.164 x 10–2 = 0.02164

Change to scientific notation.

12,340 = 1.234 x 104

0.369 = 3.69 x 10–1

0.008 = 8 x 10–3

1,000,000,000 = 1 x 109

6.02 x 1023 = 602,000,000,000,000,000,000,000

Using the Exponent Key

EXP

EE

The EE or EXP or E key means “times 10 to the…”

How to type out 6.02 x 1023:

6 EE. 0 32 2

6 y x. 0 32 2

x 16 . 0 2 EE 320

y x 32x 16 . 0 2 0

not…

or…

and not…

How to type out 6.02 x 1023:

6 EE. 0 32 2

WRONG!

WRONG!

TOO MUCH WORK.

Also, know when to hit your (–) sign.

(before the number,

after the number,

or either one)

4.3 x 10–9 4.3 E –9or

1.2 x 105 2.8 x 1019

But instead is written…

=

1 . 2 EE 5

92 . 8 EE 1

Type this calculation in like this:

This is NOT written… 4.3–15

4.2857143 –15Calculator gives…

4.2857143 E–15or…

–6.5 x 10–19

5.35 x 103 or 5350

2.9 x 1023

7.5 x 10–6 (–8.7 x 10–14) =

4.35 x 106 (1.23 x 10–3) =

5.76 x 10–16 9.86 x 10–4 =

8.8 x 1011 x 3.3 x 1011 =

5.84 x 10–13

Essential Mathof Chemistry

Units must be carried into the

answer, unless they cancel.

0.64 kg-ms2

5.2 kg (2.9 m)

(18 s)(1.3 s)=

4.8 kg (23 s)

(18 s)(37 s)= 0.57 kg

s

Solve for x. x + y = z

x + y = z – y – y

x = z – y

x and y are connected by addition. Separate them using subtraction. In general, use opposing functions to separate things.

The +y and –y cancel on the left,

leaving us with…

Solve for x. x – 24 = 13

x – 24 = 13 +24 +24

x = 37

x and 24 are connected by subtraction. Separate them using the opposite function: addition.

The –24 and +24 cancel on the left,

leaving us with…

Numerical Example

Solve for x. F = k x

F = k xk k

x = Fk __

x and k are connected by multiplication. Separate them using the opposite function: division.

( )__1k

F = k x( )__1k

(or)

The two k’s cancel on the right,

leaving us with…

Numerical Example

Solve for x. 8 = 7 x

8 = 7 x7 7

x and 7 are connected by multiplication. Separate them using the opposite function: division.

( )__17

8 = 7 x( )__17

(or)

The two 7’s cancel on the right,

leaving us with…x =

87 __

Solve for x. ___ x

BA = TRH

___

BAH = xTR

One way to solve this is to cross-multiply. BAH = xTR

Then, divide both sides by TR.

The answer is… ___BAHTR

x =

1TR( )___1

TR( )___

Solve for T2, where…

P1 = 1.08 atm

P2 = 0.86 atm

V1 = 3.22 L

V2 = 1.43 L

T1 = 373 K

P1V1T2 = P2V2T1

____ T1

P1V1 = P2V2

T2

____

1P1V1

( )____ 1P1V1

( )____

T2 = P1V1

______P2V2T1

132T2 = (1.08 atm)(3.22 L)_____________________(0.86 atm)(1.43 L)(373 K)

= K