1. MENTAL MATH: Calculations Without a Calculator
Become confortable estimating calculations
Calculators NOT allowed on M/C questions
Able to calculations in your head or quickly on a sheet of paper
Video:

2. Five Basic Strategies
Rounding
Bounding
Scientific Notation
Fractions
Factor

3. Rounding Calculate the density of 32.2 g / 61.054 L.
good estimation ≈ 0.5
with a little practice, you see that:
32.2 is a bit larger than 30
BUT is not as much larger than 60,
as 32.2 is larger than 30.0:
So make it a bit higher, how about somewhere between
0.51 and 0.53?
(0.527)

4. Rounding - Practice Calculate the molarity of 88.4 mol / 10.7 L.
Adjust:
(8.26 M)

5. Five Basic Strategies
Rounding
Bounding
Scientific Notation
Fractions
Factor

6. Bounding 2.256 g of molar mass 4.00 g/mol. Calculate moles.
low boundary high boundary
(Try to make calculations easy, then estimate from there.)
For numerator.
2.25 is about ¼ between 2 and 3,
so how about ¼ of ? = 0.25
= 0.25 / ≈ / ≈ 0.06
or = 0.56 mol (You could have even guessed a little more than 0.5 and still be close)
(0.564 mol)

7. Bounding - Practice Number of grams of 3.47 mol at 12.0 g/mol.
low boundary high boundary
3.45 is about ½ between, so how about adding
½ ( =0.08) = 0.04
= 0.29
(0.289 mol)

8. Five Basic Strategies
Rounding
Bounding
Scientific Notation
Fractions
Factor

9. Scientific Notation - Rules
Adding or Subtracting
is one significantly larger than other?
if time, rewrite in standard notation
Multiplying
multiply coefficients; add exponents
Dividing
divide coefficients; subtract exponents
Raising to a Power
multiply coefficients; multiply exponents

10. Scientific Notation Number of mole: 0.0375 L of 0.0000000060 M
(3.75 x 10–2) * (6.0 x 10–9)
(1. coefficients  2. exponents  3. combine & simplify)
low boundary high boundary ¾th between
(20 is ½ way between)
exponen10(–2 +(–9) = 10–11
x = 2.2 x 10-10
(2.25 x mol)

11. Scientific Notation - Practice
keq = / ( )3
(1.1 x 1010)

12. Five Basic Strategies
Rounding
Bounding
Scientific Notation
Fractions
Factor

13. Fractions Mass of 0.667 mol with molar mass of 12.0 g/mol.
0.667 looks like = 2/ (a fraction)
Sig. Figs: 8.00 g.
(You may have been able to take 2/3rds of 12 in your head. {4,8,12})
(8.00 g)

14. Fractions
You should probably know:
Helpful:

15. Fractions You should probably know:
Also helpful are the 9th’s (They’re simple.)

16. Fractions And it helps to see the reverse:
So, if you see 0.777, or something similar, you can do math with the calculations (if it makes calculations simpler).

17. Fractions What do you do if you have a fraction in the denominator?
= 2
How did you get that? You flipped the fraction in the denominator.
In other words, the denominator of a denominator is a numerator.
What is 4 ÷ = ?

18. Practice
2.4 mol / 0.75 L. Calculate M.
rearrange:
b/c:
then:
(3.2 M)

19. Five Basic Strategies
Rounding
Bounding
Scientific Notation
Fractions
Factor

20. Factor Moles in 5.40 g of 12 g/mol sample. (0.45 mol) ends in zero
ends in two
both divisible by 2
both divisible by 3
(9/20 = 4.5/10 = 0.45)
(0.45 mol)

21. Calculate the number of moles in 8
Calculate the number of moles in 8.4 g of a sample with a molar mass of 28 g/mol.

22. Calculate the pH of a solution with a [H3O]+ = 0.0000125 M
** KNOW YOUR LOGS **
at least the very basics
Calculate the pH of a solution with a [H3O]+ = M
log 10x = x
 log(1 x 10x) = x

23. Calculate the pH of a solution with a [H3O]+ = 0.0000125 M
1. Express M as scientific notation: x 10–5 M
2. Bound: x 10– x 10–5
1 x 10– x 10–4
1.25 x 10–5 is slightly larger than 1 x 10–5,
and so it is closer to 10–4 than 10–5
so the exponent is probably 10–4 making pH between 4 & 5.
We’re working in logs. The coefficient of 1.25 makes the pH closer to 4.75 or a little larger. (pH = 4.9)

24. Calculate the pH of a solution with a [H3O]+ = 8.75 x 10–8 M)
1. Bound M between: 1 x 10–8 10 x 10–8
1 x 10– x 10–7
pH closer to 7 (8.75 x 10–8 is closer to 10–7 than 10–8; remember, we’re working in negative exponents).
How about 7.2?
answer is 7.05
Well, that may just be close enough for an M/C choice!

25. Significant Figures for pH:
How many significant figures are in: 8.75 x 10–8 M? 3
The pH = b/c the only the coefficient contains
the number of significant figures and
and not the exponent.
pH = has 3 sig figs. (not four!)

26. Balancing Redox Reactions by Half-Reactions in an Acidic Solution
Fin