Chapter 3

Problem Solving in Chemistry

3 Methods of Solving Problems

G M K h da b d c m m p Factor Labeling Formula

Metric Conversions

pnmcdbdahkMG Move the decimal to the right

Move the decimal to the left

o Every metric unit is different from its neighbor by a factor of ten from kilo- to milli-, above or below that range, the units increase or decrease by a factor of 103

o When converting between two units the decimal point is moved the number of places equal to the distance between the two unit in the chart above and in the same direction of movement

Factor Label Method of Conversion

Use conversion factors to systematically move from one unit to the next, cancelling out units on the diagonal in each step.

Convert 18 m = _______ cm

100 cm = 1 m 1 m = 100 cm 11

100

m

cm1

100

1

cm

m

18m100 cm

1 m= 1800 cm

Multistep Factor Label Problems

Convert

350 tsp = ______ L

Using the following conversion factors

1 tsp = 5 mL

1 L = 1000 mL

350 tsp 5 mL

1 tsp

1 L1000 mL

= 1.75 L

Multi-step Factor Label Practice

Convert 3 min= ______ms

Use 1 min=60 s and 1000 ms = 1 s

Convert 32oz = _____ g

Use 16 oz=1 lb, 2.2 lb = 1kg, 1kg=1000 g

Multi-dimensional Factor Label Problems

Convert 25 g/mL = ______ kg/dL

• Convert one unit at a time• Recognize that one unit is in the denominator

25 g

1 mL

1 Kg

1000 g

100mL

1 dL=2.5kg/dL

Multidimensional Factor Label Practice

Convert 85 km/hr = _________m/s

Convert 0.6 L/min = ________ qt/hrUse 1qt = 1.1L

Factor Label Problems with Squared or Cubed Units

Convert 25 in2 = ______ cm2

• Recognize that although 1in = 2.54 cm,

1in2 does not equal 2.54 cm2

• Both the unit and its value must be squared

2

25 in2 25 in2 2.45 cm

1in= 6.4516 cm2

1 in2

x = 160 cm2

Problem Solving Strategy Before you break out your calculator, read the problem all the way

through. Make sure you understand what the question is asking.

Write down all of the information you have been given. Keep in mind, you may be given more facts than you need to use in order to perform the calculation.

Write down what it is that you are solving for (desired value).

Write down some useful information like the equation or equations you will use in order to solve the problem along with any conversion factors that might be needed

**Rearrange to create a working equation**

Problem Solving Continued

Before you plug the numbers into the equations, check the units required for the equations. You may need to perform

unit conversions before you can apply the equations.

Once you are certain your units are in agreement, plug the numbers into the equation and get your answer.

Round your answer to the correct number of digits and make sure your answers have units. Use the given values to determine the number of sig figs in your answer.

***Remember that conversion factors and counting numbers have an unlimited number of significant figures***

Ask yourself whether the answer seems reasonable..

Sample Word Problem It is known that four hundred pounds of iron metal

occupy a volume of 0.02234 cubic meters. Calculate the cubic feet of iron in a statue that has been determined to contain 54.5 kilograms of iron.

Given Desired Value Useful Items

400 lbs. Fe/0.02234 m3

54.5 kg Feft3 Fe D=M/V V=M/D

1kg = 2.2 lbs1 cubic foot = 2.83 x 104 cm3

1 m3 = 1 x 106 cm3

Sample Word Problem The price of gasoline this morning is $3.99/gal. You

are planning a trip out east to visit a friend and estimate the total distance roundtrip to be 2480 miles. What will the gasoline cost for the trip? The owner’s manual stated that our car gets 15 km per liter.

Given Desired Value Useful Items

$3.99/gal2480 mi/round trip15 km/L

Cost for trip Millage/”millage rate” = volumeVolume x “cost rate” = total cost1mi = 1.6 km1L = 1.1qt4qt = 1 gal