Problem-Solving in Chemistry

Problems in Chemistry• Tend to fall into two categories, Tend to fall into two categories,

algebraic or conversion.algebraic or conversion.

– In algebraic problems you are In algebraic problems you are solving for an unknown.solving for an unknown.

– In conversion problems you are In conversion problems you are changing units.changing units.

Conversions within the Metric System

Remember, it’s a decimal-based system.

Conversions should be easy.

Use the factors in Table C to figure out the conversion fact.

Convert 129 milligrams to grams.

Look for milligrams in Table C

Find the row: Factor is 10-3

What does that mean?It means 1 X 10-3 g = 1 mgThis is the conversion fact!

Conversion Fact or Definition

• Once you have your conversion fact, you can choose the ratio method or the factor label method to do the work.

1 X 10-3 g = 1 mg or .001 g = 1 mg

Equivalently, 1 g = 1000 mg

Ratio Method129 mg as 1 mg X g .001g

(129 mg) • .001 g = 1 mg • X g

X = .129 g

1 X 10-3 g = 1 mg or .001 g = 1mg

as means =

Ratio Method129 mg as 1000 mg X g 1g

(129 mg) • 1 g = 1000 mg • X g

X = .129 g

.001 g = 1mg or 1 g = 1000 mg

Factor-Label Method• In the factor label method, you

always take the given and multiply it by the conversion factor.

• The conversion factor is a ratio like 12 inches or 1 meter 1 foot 100 cm

Factor-Label Method129 mg .001 g = .129 g 1 mg

1 X 10-3 g = 1 mg or .001 g = 1mg

Given Conversion factor

Factor-Label Method129 mg 1 g = .129 g 1000 mg

Use 1 g = 1000 mg

Given Conversion factor

129 milligrams = 0.129 grams

Think about your answer for Think about your answer for a moment. Does it make a moment. Does it make

sense? sense? Yes, you switched to a larger unit, so the number should be smaller!

Convert 2.765 km to meters.

Kilometers to meters

From Table C: the factor is 103

Or 1 X 103 meters = 1 km, 1000 m = 1km

2.765 km 1 X 103 meters = 2765 m 1 km

Convert 2.765 km to meters.

2.765 km = 2765 meters

Does this answer make sense?Does this answer make sense?

Try a few more problems!• How many liters are in 345

milliliters?

• This problem is worded a little differently. Think about how you are doing the conversion.

• From ________ to _________?

345 milliliters to liters345 milliliters to liters

345 milliliters = 0.345 litersDoes this answer make sense?Does this answer make sense?

What’s the conversion fact?

1 X 10-3 liters = 1 milliliter

10-3

345 ml 1 X 10-3 l = 0.345 l 1 ml

How many meters are in 893 cm?Convert 45 kilograms to grams.How many deciliters are in 0.59 liters?Convert 78 millimeters to meters.How many milligrams are in 240 grams?

8.93 meters8.93 meters

45000 grams45000 grams

5.9 deciliters5.9 deciliters

0.078 meter0.078 meter

240000 240000 milligramsmilligrams

The Factor-Label Method or

Dimensional Analysis• A more general A more general conversionconversion

technique.technique.• More powerful in multistep More powerful in multistep

problems.problems.• Much loved by chemists!Much loved by chemists!

Problem: Convert 3.5 years to seconds.Problem: Convert 3.5 years to seconds.

What information do you What information do you need to solve this need to solve this problem?problem?

You need to know a bunch of relationships or equalities. We use these equalities to make conversions factors.

For days to seconds, the For days to seconds, the relationships are?relationships are?

• 1 year = 365 days• 1 day = 24 hours• 1 hour = 60 minutes• 1 min = 60 seconds

Use the equalities to set up conversion factorsconversion factors. Conversion factors are ratios.

Convert 3.5 years to seconds

• In the factor-label method, you In the factor-label method, you alwaysalways multiply! multiply!

• Let the Let the unitsunits do the work in setting do the work in setting up your conversion factors.up your conversion factors.

3.5 years X 365 days X 24 hours X 60 min X 60 sec 1 year 1 day 1 hour 1 min

And the answer is …110,376,000 seconds110,376,000 seconds

Problem: How many quarters Problem: How many quarters in $23.00in $23.00

• Recall: What relationship do you Recall: What relationship do you need to solve this problem?need to solve this problem?

• Set-up: How would you set the Set-up: How would you set the problem up?problem up?

$23.00 X 4 quarters = the # of quarters1 dollar

$23.00 $23.00 92 quarters 92 quarters

You just have to be a little You just have to be a little careful when you are working careful when you are working with less familiar units. Take with less familiar units. Take your time!your time!

Try converting 192 cm to meters.

1 m = 100 cm

192 cm X 1 meter = 100 cm

1.92 meter

RecallRecall:

Set-upSet-up:

How many quarts are in 3.5 gallons?How many milliliters are in 3.7 liters?Convert 27 decimeters to meters.Convert 5.65 centigrams to grams.How many kilometers are in 23468 meters?

Use the factor-label method for these!

14 quarts14 quarts

3700 milliliters3700 milliliters

2.7 meters2.7 meters

0.0565 grams0.0565 grams

23.468 kilometers23.468 kilometers

K H D d c m• “Kids have dropped over dead converting metrics.” = gram, meter, sec, liter, etc.• Upper-case: kilo or 1000X, hecto or 100X, deka or

10X• Lower-case: deci or 1/10, centi or 1/100, milli or

1/1000.• As the unit gets smaller, the number has to get

bigger.• Convert 25 mg to grams. Move decimal 3 places to

the left, or .025 grams.