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

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

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

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

SI Units There are 7 SI Base Units:

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

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!

Unit Conversion Here is an easy way to remember conversions:

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 50,000 g 1 kg

Conversion Here is how it works: Smaller to larger Convert 5000 mL to L Start with the units given- 5000 mL Determine how many L are in a mL Use dimensional analysis 5000 mL 1L 5L 1000 mL

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

Final Note On Conversions Mega (M)- 106, 1Mm= 100,000 m Micro (u)- 10-6, 1um= 0.000001 m Nano (n)- 10-9, 1nm = 0.000000001 m We will use these measurements later in the course

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

How to Count Significant Figures Zeros within a number are always significant 4308 and 40.05 each have 4 significant figures Zeros at the beginning of a number are not significant 0.0026 has only 2 significant digits Zeros at the end of a number and after the decimal are significant 0.0200 and 3.00 have 3 significant digits

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.

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) = 32.3492 cm2 = 32 cm2 Answer must align with the fewest number of decimal places Ex) 20.4 + 1.322 + 83 = 104.722 = 105 Sig Figs in Calculations

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 =? 74.077 x 2.100 x 16.0037 =? 230 + 12 =? 0.4058 – 0.003 =? 5482.3 + 25 =? 74,077 + 2,100 + 16,003.7 =? Practice with Sig Figs

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 1.0300 x 104

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

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 0.791 g/mL What is the mass in grams of a cube of gold (density = 19.32 g/cm3) if the length of the cube is 2.00 cm.

You Try! Calculate the density of a 374.5 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 0.789 g/mL, how many milliliters are needed. What is the mass, in grams of 25.0 mL of mercury (density = 13.6 g/mL)