1. Quantitative Chemistry Chemistry 10 Handy Math Skills

2. Scientific Notation 1. Write each of the following in scientific notation: a) 1003.09___________________ b) 0.00405___________________ c) 23.01___________________ d) 0.00002___________________ 2. Write each of the following in ordinary notation: a) 2.01 x 10 5 ___________________ b) 6.60 x 10 -3 ___________________ c) 4.33 x 10 10 ___________________ d) 9.21 x 10 -4 ___________________

3. Multiple Factor Expressions 1. solve: 5 x 35 ----------- = 7 2. solve: (386)(29) ------------- = (14)(4) 3. solve: (2.36 x 10 6 )(4.71 x 10 -3 ) ------------------------------- = 4.11 x 10 -4

4. Ratios RATIO:The relationship in number or degree (e.g., units / dimensions) between two quantities, sometimes written as a fraction. Examples: a) A cake recipe calls for 1 cup of sugar and 2 cups of flour. The ratio of sugar to flour in the recipe is: “1 cup sugar to 2 cups flour” or “1 : 2” or “1 / 2” b) In one molecule of methane, CH 4, the ratio of hydrogen atoms to carbon atoms is: “4 hydrogen atoms to 1 carbon atom” or “4 : 1” or “4 / 1” c) In the chemical equation, 2H 2 + O 2  2H 2 O, the ratio of O 2 molecules to H 2 O molecules is: “1 O 2 molecule to 2 H 2 O molecules” or “1 : 2” or “1 / 2”

5. More on Ratios Since ratios can be expressed as fraction (which they always are in chemistry), then they follow all the mathematical properties of fractions – they have a numerator and a denominator; they represent the division operation of numerator divided by denominator; they permit canceling of identical values (labels / units and arithmetic factors) in the numerator and denominator. Examples: a) The ratio of “6 apples to 2 oranges” or “6 apples / 2 oranges” an be written: 6 apples 3 apples note that the labels “apples” and ------------- = ------------- = 3 apples/orange oranges remain, because they are 2 oranges 1 orange (“3 apples per orange”) different and do not cancel. b) The ratio of “10 miles : 20 miles” can be written: 10 miles 1 Since this ratio has exactly the same units in ------------ = ----- = 0.5 the numerator and denominator, the identical 20 miles 2 units cancel and the ratio is dimensionless.

6. Proportions Proportion: A statement of equality between two ratios. If a value in one of the ratios is unknown, then the proportion can be “solved” for the unknown. A common method of solution is “cross-multiplication.” Example Using a proportion to solve a problem: There are 5280 feet in one mile. The ratio of feet to miles is 5280 ft / 1 mi. How many feet in 0.5 miles? Step 1: Write the proportion X ft 5280 ftX is unknown ---------- = ---------- 0.5 mi 1 mi Step 2: Solve for X by cross-multiplying both sides by 0.5 mi: X ft 5280 ft (0.5 mi)(X ft) (0.5 mi)(5280 ft) 0.5 mi x --------- = 0.5 mi x ----------or --------------------- = --------------------- 0.5 mi 1 mi (0.5 mi) (1 mi) (0.5 mi)(5280 ft) X ft = ---------------------- = 2640 ft (1 mi)

7. The Factor-Label Method Conversion factor: a ratio of two quantities each with units (dimensions) that is used to solve proportions. Swapping the numerator and denominator of a conversion factor does not alter its value (the value of a conversion factor always = 1) (but does invert the units). Example – Convert 283 feet to miles –Use the conversion factor = 5280 ft / 1 mile –Multiply: (283 ft)(1 mi / 5280 ft) – you want the same units in numerator and denominator to cancel out! 283 ft 1 mi (283)(1 mi) x --------- = --------------- = 0.0536 mi 5280 ft 5280 Note that applying a conversion factor is short-cut to the same arithmetic you use when cross-multiplying to solve proportions! (See previous slide)

8. Conversions Practice Easy The density of mercury is 13.6 g/mL. What is the mass of 3.55 mL mercury? The density of lead is 11.3 g/mL. What is the mass of 45 mL of lead? Harder 3.A mole of copper contains 6.02 x 10 23 atoms. How many copper atoms are there in 0.525 moles of copper? Challenging 4.A solution of barium nitrate ( Ba(NO 3 ) 2 ) contains 61.2 g per liter of solution. One mole of barium nitrate has a mass in grams equal to the M r (molar mass) of barium nitrate. How many moles of barium nitrate are contained in one liter of the solution?