(A) Unit Conversions and (B) Chemical Problem Solving Chemistry 142 B James B. Callis, Instructor Winter Quarter, 2006 Lecture #2

Friedrich von Hardenberg (Novalis),

All Measured Quantities Consist of a Number and a Unit

Example calculations using units Length : A car is 12 feet long, not “12 long”. A person is 6 feet tall, not “6 tall”. P 2-1 Area : A carpet measuring 3.0 feet(ft) by 4.0 ft has an area of: Area = P 2-2 Speed and Distance : A car traveling 350 miles(mi) in 7.0 hours(hr) has a speed of: Speed =

SI system of units

Derived SI Units Quantity Definition of Quantity SI unit Area Length squared m 2 Volume Length cubed m 3 Density Mass per unit volume kg/m 3 Speed Distance traveled per unit time m/s Acceleration Change in speed per unit time m/s 2 Force Mass times acceleration of object kg m/s 2 ( = newton, N) Pressure Force per unit area kg/(m s 2 ) ( = pascal, Pa) Energy Force times distance traveled kg m 2 /s 2 ( = joule, J)

Definitions - Mass & Weight Mass - The quantity of matter an object contains kilogram - ( kg ) - the SI base unit of mass, is a platinum - iridium cylinder kept in Paris as a standard! Weight - depends upon an object’s mass and the strength of the gravitational field pulling on it, i.e. w = f = ma.

Conversion Factors : I Equivalence statements can be turned into conversion factors by dividing one side into the other. 1 mile = 5280 ft 1 in = 2.54 cm In converting one set of units for another, the one desired is on top in the conversion factor, and the ‘old’ one is on the bottom so the old units are canceled out. P 2-3: Convert 29,141 ft into miles.

Conversion Factors - II 1.61 km = 1 mi P 2-4: Convert miles into kilometers: Conversions in the metric system are easy, as 1 km = 1000 m and 1 meter (m) = 100 centimeters (cm) and 1 cm = 10 millimeters (mm). P 2-5: Convert 8.89 km into cm

Conversion Factors - III Conversion factors can be combined. P 2-6: Convert 3.56 lbs/hr into units of milligrams/sec:

Liter = L = dm 3 = dm 3 cm 3 = mL m3m3m3m3

Conversion Factors - IV metric volume to liters P 2-7: The volume of the world’s oceans is 1.35 x 10 9 km 3. How many liters of water are in the oceans? conversion factors: 1 km = 1000 m 1 L = 1 dm 3 = m 3 or 1000 L = 1 m 3

How to Solve Chemistry Problems (1) Pose the Problem: Employ the Find, Given, Using Approach Find the unknown quantity, given known quantities and conversion factors, using known or derived formulas (equations). Very often, the problem is stated only in terms of the knowns and the unknown. It is up to you to discover the necessary conversion factors and formulae. (2) Solve the Problem Symbolically Rearrange and combine the formulae so that the unknown is on the left side of the equation.

How to Solve Chemistry Problems (cont.) (3) Perform a units analysis to determine what conversion factors are needed. (4) Place all numerical factors and their factor labels into the expression (formula) to be evaluated. (5) Perform the Calculations.

How to Solve Chemistry Problems (cont.) (6) Check the result: –Do the numbers make sense? –Do the units in the factor labels cancel properly to give the expected units for the answer?

Calculate the mass in grams of 1.00 ft 3 of Lead (density=11.3 g/ cm 3 )? Step 1: Pose the problem. Step 2: Solve the formula for mass symbolically. Problem 2-8: Calculation Involving Density (1)

Step 3: Perform units analysis to determine what conversion factors are needed. Step 4: Place all numerical factors and factor labels into the expression (formula) to be evaluated. Problem 2-8: Calculation Involving Density (2)

Step 5: Perform the Calculations. Step 6: Check the Result: Do the numbers make sense? Do the units in the factor labels cancel properly to give the expected units for the answer? Problem 2-8: Calculation Involving Density (3)

Buoyancy Method of Density Determination Based on Archimedes principle: A body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. If a solid weighs x g in air and y g in a fluid of density, z g/cm3, then the density of the solid is:

Find the density of a sample of brass in g/cm 3, given its mass in air (75.14 g) and water (66.21 g) and p water = g/cm 3 ), using the buoyancy method. Step 1: Pose the problem. Step 2: Solve the formula for density symbolically. Problem 2-9: Calculation Involving Density (1) Problem is correctly posed above.

Step 3: Perform units analysis to determine what conversion factors are needed. Step 4: Place all numerical factors and factor labels into the expression (formula) to be evaluated. Problem 2-9: Calculation Involving Density (2)

Step 5: Perform the Calculations. Step 6: Check the Result: Do the numbers make sense? Ans = Do the units in the factor labels cancel properly to give the expected units for the answer? Ans = Problem 2-9: Calculation Involving Density (3)

Answers to Problems in Lecture ft mi/hr mi km x 10 5 cm mg/s x L x 10 5 g = 3.20 x 10 2 kg g/cm 3