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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