1. The Mathematics of Chemistry
Mr. Kinton’s Honors Chemistry
The Mathematics of Chemistry

2. Measurement definitive values Can be counted Conversion factors
Exact Numbers
Inexact Numbers
definitive values
Can be counted
Conversion factors
Measured quantities
Have error
Limitations in equipment
Measurement

3. Measurement We are concerned about two things:
Precision: how individual measurements agree with one another
Accuracy: how individual measurements agree with the “true” value

4. Scientific Units In everyday life we use Standard or Customary units
In other places in the world, the metric system is used.
Science uses SI units

5. SI Units
There are 7 SI Base Units:

6. Converting Units
Scientists prefer the metric and SI units because unit conversion is easier
This is because every unit is some multiple of 10
Convert to have meaningful measurements

7. Converting using Dimensional Analysis
Chemists use this as a way of canceling out units and solving problems involving math.
This method requires us to know certain conversion factors.
What are some examples of conversion factors that you have used before?
Let’s look at some examples!

8. Unit Conversion
Here is an easy way to remember conversions:

9. Conversion Here is how it works: Larger to smaller Convert 50 kg to g
Start with the unit given -50 kg
Determine how many grams are in a kilogram
Use dimensional analysis or the factor label method
50 kg 1,000g ,000 g
1 kg

10. Conversion Here is how it works: Smaller to larger
Convert 5000 mL to L
Start with the units given mL
Determine how many L are in a mL
Use dimensional analysis
5000 mL 1L L
1000 mL

11. You Try Make the following conversions
252 dam (decameter) to dcm (decimeter)?
51 cL (centiliter) to hL (hectoliter)?

12. Final Note On Conversions
Mega (M)- 106, 1Mm= 100,000 m
Micro (u)- 10-6, 1um= m
Nano (n)- 10-9, 1nm = m
We will use these measurements later in the course

13. Significant Figures
Digits of a measured quantity including the uncertain one
For Example, let’s examine these 2 balances

14. How to Count Significant Figures
Zeros within a number are always significant
4308 and each have 4 significant figures
Zeros at the beginning of a number are not significant
has only 2 significant digits
Zeros at the end of a number and after the decimal are significant
and 3.00 have 3 significant digits

15. Counting Significant Figures
Numbers ending in zero depend on a decimal point
130 is only 2 significant figures
130. is 3 significant figures
How many significant figures are present?
105
0.005
40.0
220
2220.

16. Sig Figs in Calculations
Multiplication/Division
Addition/Subtraction
Answer must contain a number with the fewest significant figures
Ex) Area = (6.221 cm)(5.2 cm) = cm2 = 32 cm2
Answer must align with the fewest number of decimal places
Ex) = = 105
Sig Figs in Calculations

17. Practice with Sig Figs 230 x 12 =? 0.4058/0.003 =? 5482.3/25 =?
Multiplication/Division
Addition/Subtraction
230 x 12 =?
0.4058/0.003 =?
5482.3/25 =?
x x =? =?
– =? =?
74, , ,003.7 =?
Practice with Sig Figs

18. Scientific Notation
Used to remove ambiguity of zeros at the end of a number
Example: 10,300 g has how many significant figures?
Using Scientific Notation, up to 5 sig figs can be given
1.03 x 104
1.030 x 104
x 104

19. Density Amount of mass in a unit volume Density = mass/volume
Units g/cm3 or g/mL
Temperature dependent

20. Sample Problems
Calculate the density of mercury if 1.00 x 102 g occupies a volume of 7.36 cm3
Calculate the volume of 65.0 g of liquid methanol (wood alcohol) if its density is g/mL
What is the mass in grams of a cube of gold (density = g/cm3) if the length of the cube is 2.00 cm.

21. You Try!
Calculate the density of a g sample of copper with a volume of 41.8 cm3
A student needs 15.0 g of ethanol. If the density of ethanol is g/mL, how many milliliters are needed.
What is the mass, in grams of 25.0 mL of mercury (density = 13.6 g/mL)