POGIL - Measurement (Short)

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Chemistry 430 POGIL : Measurement & Units

Measurements, and subsequently calculations, allow the determination of some of the properties of a substance. E.g. Mass and density.

Part 1: SI Base Units and Prefixes

Units tell us what scale is being used for measurement. Some common units and prefixes that you will encounter frequently in this course are given below.

Units Common Prefixes

Dimensional Analysis

One unit can be converted to another by using a conversion factor. Some helpful examples are shown below, with conversion factors in parenthesis:

Convert 155g/cm3 to kg/L (1 kg = 1000g and 1000 cm3 = 1 L)

Note that in each case, the correct choice is the one that allows the cancellation of the unwanted units. This method of converting between units is called the factor-‐labeling method or dimensional analysis.

Base Quantity Name of Unit Symbol

Mass Kilogram kg

Length Meter m

Time Second s

Amount of Substance Mole mol

Temperature Kelvin K

Prefix Symbol Meaning

Mega M 106

Kilo k 103

Centi c 10-2

Milli m 10-3

Micro µ 10-6

Nano n 10-9


Conceptual Task 1a:

Use dimensional analysis to convert between each unit. Unit conversions are shown in parenthesis.

1. How many Joules are in 125 Calories? (1 Calorie = 4184 Joules)

2. Gold has a density of 18.0 g/cm3. What is the density of Gold in kg/cm3?

For each conversion below, first predict whether the answer will be larger or smaller, including a brief justification. Then, solve the conversion problem.

a. Molybdenite is a breakthrough material that can be manufactured as thin as 0.65 nm. Represent this thickness in centimeters.

My answer will be [larger] [smaller] than 0.65 because:

Solution:

b. Chemists will often use the Average Atomic Mass, found on the Periodic Table of the Elements, to determine the number of atoms of a particular element present in a given mass of that element. For example, Carbon has an AAM of 12.011 grams. This tells a chemist that it takes 12.011 grams of Carbon to equal 6.02 x 1023 atoms of that element. Chemists use a distinct unit to represent this large number of atoms, the mole. 1 mole of any element is equal to 6.02 x 1023 atoms of that element. Imagine that a chemist has a beaker containing 24 grams of Carbon. How many moles of Carbon are in the beaker?

My answer will be [larger] [smaller] than 12.011 because:

Solution:


3. Use the fictitious conversion factors below to perform the requested unit conversions using dimensional analysis: 1 sack = 7 bips; 4 tolls = 3 smacks; 12 tolls = 1 lardo; 5 smacks = 1 bip; 8 lardos = 7 fleas

a. Calculate the number of smacks in 1.00 lardo.

b. Calculate the number of lardos in 1.00 bip.

c. How many sacks are in 1.00 smack?

4. Mr. Cook is going on a trip to the Amazon with 38 lucky students. Upon arrival, they find that their guides have abandoned them, leaving them for dead. To survive, Mr. Cook knows that he and each of his students need at least 1200 calories a day. Having a vast knowledge of bugs (he did watch the Lion King before), he knows that on average, each 5g bug that he consumes will provide 7 calories of energy. How many kilograms of bugs must Mr. Cook and his students catch daily in order to survive?

Part 2: How we deal with Quantitative Measurement Scientific Notation Measurements and calculations in chemistry often require the use of very large or very small numbers. In order to make handling them easier such numbers can be expressed using scientific notation. All numbers expressed in this manner are represented by a number between 1 and 10 multiplied by a power of 10.

The number of places the decimal point has moved determines the power of 10. If the decimal point has moved to the left then the power is positive, to the right, negative. Conceptual Task 1b:

5. Write each number given below in scientific notation.

a. 0.0025 meters

b. 10000.00 cm3

c. 0.00000000407 mL


6. Write each number below in regular notation.

a. 1.6 x 10-‐5

b. 6.02 x 1023 atoms

c. 6.5 x 10-‐8m

Significant Figures

When reading the scale on a piece of laboratory equipment such as a measuring cylinder or a burette, there is always a degree of uncertainty in the recorded measurement. The reading will often fall between two divisions on the scale and an estimate must be made in order to record the final digit. This estimated final digit is said to be uncertain and is reflected in the recording of the numbers by using +/-‐. All those digits that can be recorded with certainty are said to be certain. The certain and the uncertain numbers taken together are called significant figures.

Determining the number of significant figures present in a number

A. Any non-‐zero integers are always counted as significant figures. B. Leading zeros are those that precede all of the non-‐zero digits and are never counted as significant figures. C. Captive zeros are those that fall between non-‐zero digits and are always counted as significant figures. D. Trailing zeros are those at the end of a number and are only significant if the number is written with a decimal point. E. Exact numbers have an unlimited number of significant figures. (Exact numbers are those which are as a result of counting

e.g. 3 apples, or by definition e.g. 1kg = 2.205lb). F. In scientific notation the 10x part of the number is never counted as significant.

Determining the correct number of significant figures to be shown as the result of a calculation

G. When multiplying or dividing. Limit the answer to the same number of significant figures that appear in the original data

with the fewest number of significant figures. H. When adding or subtracting. Limit the answer to the same number of decimal places that appear in the original data with

the fewest number of decimal places.

i.e. don’t record a greater degree of significant figures or decimal places in the calculated answer than the weakest data will allow.

Conceptual Task 1c:

7. Determine the number of significant figures in each number shown below, and cite the rules above that support your

answer. The first problem has been done for you as an example. Answer Justification

a. 500.0 4 sig figs Rules A, D b. 100 c. 0.00200 d. 1.002 e. 0.00043308 f. 6.02 x 1023


8. In the lab, there are three digital balances setup next to one another. Choose a small object (a pen or pencil will suffice) and record the mass given by each of the three digital balances in the data table below.

a. How did the measurements of the same object differ?

b. Why did the measurements of the same object differ?

c. Are the three measurements above the same measurement? Justify your response.

d. Re-‐read the introductory paragraph for the section on Significant Figures. What role does uncertainty play in making measurements in the laboratory?

Balance A Balance B Balance C

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POGIL - Measurement (Short)