The Mathematics of Chemistry

Mr. Kinton’s Honors Chemistry The Mathematics of Chemistry

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

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

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

There are 7 SI Base Units: SI 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 Units

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! Converting using Dimensional Analysis

Here is an easy way to remember conversions: Unit 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 Conversion

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

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 Final Note On Conversions

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

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

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

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 Scientific Notation

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

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. Sample Problems

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) You Try!

The Mathematics of Chemistry