MeasurementMeasurementChapter 2Chapter 2

Units in LabUnits in Lab In lab we cannot always measure in SI In lab we cannot always measure in SI

units.units.

MassMass Grams (g)Grams (g)Volume Volume Milliliters (mL)Milliliters (mL)TemperatureTemperature Celsius (C)Celsius (C)LengthLength Centimeters Centimeters

(cm) or (cm) or millimeters millimeters (mm)(mm)

SI UnitsSI UnitsQuantityQuantity Base UnitBase UnitTimeTime Second (s)Second (s)LengthLength Meter (m)Meter (m)VolumeVolume Liter (L)Liter (L)MassMass Gram (g) Gram (g) TemperatureTemperature Kelvin (K)Kelvin (K)*Amount of *Amount of SubstanceSubstance

*Mole (mol)*Mole (mol)

* We will study the mole during the 2nd half of the course

Derived UnitsDerived Units A combination of base units forms a A combination of base units forms a

derived unitderived unit– Ex. Density = mass/volumeEx. Density = mass/volume– Mass = g and volume = L, then the unit Mass = g and volume = L, then the unit

for density is g/Lfor density is g/L

Accuracy vs PrecisionAccuracy vs Precision Accuracy is closeness to the true Accuracy is closeness to the true

measurement.measurement. Precision is getting same Precision is getting same

measurement repeatedly.measurement repeatedly. Think of playing darts...Think of playing darts...

– What would be accurate?What would be accurate?– What would be precise?What would be precise?– What would be both?What would be both?

Significant FiguresSignificant Figures Indicate how Indicate how accurateaccurate a a

measurement is.measurement is. The more significant figures the more The more significant figures the more

accurate.accurate. Significant figures come from Significant figures come from

measurements.measurements. We need rules if we don’t make the We need rules if we don’t make the

measurements.measurements.

Significant Figure RulesSignificant Figure Rules All non-zero digits are significant.All non-zero digits are significant. Zeroes are significant if:Zeroes are significant if:

– Between two significant figures Between two significant figures (middle zeroes)(middle zeroes)

– Follow a decimal point AND a significant Follow a decimal point AND a significant figure (trailing zeroes)figure (trailing zeroes)

Zeroes before significant figures are Zeroes before significant figures are NEVER significant NEVER significant (preceding zeros)(preceding zeros)

How many significant figures How many significant figures do the following have?do the following have?

1.1. 250.0 g250.0 g

2.2. 500 mL500 mL

3.3. 0.0057 kg0.0057 kg

4.4. 6008 cm6008 cm

4

1

2

4

Using Significant Figures in Using Significant Figures in Solving ProblemsSolving Problems

(Rounding)(Rounding) When adding or subtracting:When adding or subtracting:

– Round to least number of decimal placesRound to least number of decimal places When multiplying or dividing:When multiplying or dividing:

– Round to least number of significant Round to least number of significant figuresfigures

Example 1Example 1 What is the mass of a marble if the mass of What is the mass of a marble if the mass of

a marble and a beaker together is 77.89g a marble and a beaker together is 77.89g and the mass of the beaker alone is 70.7g?and the mass of the beaker alone is 70.7g?

77.89 g -70.7 g77.89 g -70.7 g 7.19 g, what’s the answer rounded to 7.19 g, what’s the answer rounded to

correct significant figures?correct significant figures? 7.2 g7.2 g

Example 2Example 2 Calculate the volume of an object Calculate the volume of an object

that has the following dimensions: that has the following dimensions: 3.4 cm by 30 cm by 0.220 cm.3.4 cm by 30 cm by 0.220 cm.

3.4 cm x 30 cm x 0.220 cm = 22.44 cm3.4 cm x 30 cm x 0.220 cm = 22.44 cm33

What’s the answer rounded to correct What’s the answer rounded to correct significant figures? significant figures?

20 cm20 cm33

Percent ErrorPercent Error Tells how far off from the accepted Tells how far off from the accepted

value your value is (experimental) as value your value is (experimental) as a percentage.a percentage.

Percent error has a positive value if Percent error has a positive value if the accepted value is greater than the accepted value is greater than the experimental value.the experimental value.

Percent error has a negative value if Percent error has a negative value if the accepted value is less than the the accepted value is less than the experimental value.experimental value.

Example Problem Example Problem A student measured the volume of a A student measured the volume of a

liquid to be 45.5mL, but the actual liquid to be 45.5mL, but the actual volume is known to be 48.00mL. volume is known to be 48.00mL. What is the student’s percent error?What is the student’s percent error?

48.00-45.548.00-45.5 x 100 = 5.21% x 100 = 5.21%48.0048.00

Numbered Heads TogetherNumbered Heads Together A student calculates the density of a A student calculates the density of a

substance at 1.40 g/mL. The correct, substance at 1.40 g/mL. The correct, or accepted, value of the density is or accepted, value of the density is 1.30 g/mL. What is the percent error 1.30 g/mL. What is the percent error of the student’s measurement?of the student’s measurement?

DensityDensity Density is mass per unit of volume.Density is mass per unit of volume. A sample of aluminum metal has a A sample of aluminum metal has a

mass of 8.4 g. The volume of the mass of 8.4 g. The volume of the sample is 3.1 mL. Calculate the sample is 3.1 mL. Calculate the density of aluminum.density of aluminum.

Density=2.7 g/mLDensity=2.7 g/mL Note: 1 mL = 1 cmNote: 1 mL = 1 cm33

Numbered Heads TogetherNumbered Heads Together Density is mass per Density is mass per

unit of volume.unit of volume. What is the mass of What is the mass of

5.6 mL of gold 5.6 mL of gold which has a density which has a density of 19.3g/mLof 19.3g/mL

D = D = massmass volume volume

19.3g/mL = 19.3g/mL = xx 5.6 5.6

mLmL Cross multiply to Cross multiply to

solve for x.solve for x. x = 110 gx = 110 g

Why not 108g?Why not 108g?

How would you find the How would you find the density?density?

A rectangular cube of metal.A rectangular cube of metal.– Volume:Volume:– Mass:Mass:

A liquid.A liquid.– Volume:Volume:– Mass:Mass:

A rock. A rock. – Volume:Volume:– Mass:Mass:

TemperatureTemperature We measure temperature in Celsius, We measure temperature in Celsius,

but the SI unit for temperature is but the SI unit for temperature is Kelvin…so there will be instances Kelvin…so there will be instances where we will need to convert.where we will need to convert.

Kelvin = C + 273Kelvin = C + 273 Celsius = K - 273Celsius = K - 273

Converting Units Converting Units (Metric System)(Metric System)

1g = 0.001 kg1g = 0.001 kg 1 g = 100 cg1 g = 100 cg 1 g = 1000 mg1 g = 1000 mg

Can switch any unit for gramsCan switch any unit for grams Conversion Factor: any 2 quantities Conversion Factor: any 2 quantities

that are equal can create a that are equal can create a conversion factor.conversion factor.

Example ProblemExample ProblemHow many milliliters are in 0.50 L?How many milliliters are in 0.50 L?

0.50L x 0.50L x = =

This is aconversion

factor

1000 mL1L 500mL500mL

Another exampleAnother exampleHow many kilograms are in 750g?How many kilograms are in 750g?

750g x 750g x ==0.001kg1g 0.75g

Try theseTry these1.1. How many L are in 1650mL?How many L are in 1650mL?2.2. How many seconds are in 30cs?How many seconds are in 30cs?3.3. How many km are in 5.76m?How many km are in 5.76m?4.4. How many mg are in 23g?How many mg are in 23g?

Let’s try another type of Let’s try another type of problem using factor label…problem using factor label…

How many seconds are in 5 days?How many seconds are in 5 days?

5 days x 5 days x x x x x = =

24 h1 day

60 min1h

60 s1 min

432000 s

You try this oneYou try this one How many days are in 7400 min?How many days are in 7400 min?

7400 min x _1h__ x 1 day = 5.1 days 60 min 24 h