Grossmont College Experiment Measurements & Significant Figures Lab Report

EXPERIMENT: MEASUREMENTS & SIGNIFICANT FIGURESQuestion
How does the accuracy of an instrument affect the accuracy of a measurement?
Objective
At the end of this lab, you should be able to: (1) identify the standard units of the metric system and make
conversions among units and (2) measure using metric system units.
Background
Physical quantities are always specified relative to a particular standard or unit, and the unit should
always be stated. One of the most important steps in applying the scientific method is experiment: testing
the prediction of a hypothesis. We will use the standard used by the international scientific community for
measuring these quantities: the SI metric system. A measurement without a unit is meaningless!
Measurements
All measurements need three pieces: magnitude, unit, and uncertainty.
The Metric System
The commonly accepted set of units used today is the Système International (SI). The SI system is based
on the metric system. The metric system is convenient because it is based on a decimal system (i.e.:
powers of ten). Therefore, it simplifies calculations by using a set of prefixes shown below.
Kilo
Hecto
Deca
Base unit
Deci
Centi
Milli
= 1000 base
units
= 100 base
units
= 10 base
units
—
= 0.1
(1/10)
base units
= 0.01
(1/100) base
units
= 0.001
(1/1000)
base units
SI units
The commonly accepted set of units used today is the Système International (SI). The seven common base
quantities are shown below.
Measurement
Unit
Unit abbreviation
Mass
Kilogram
kg
Length
Meter
m
Time
Seconds
s
Temperature
Kelvin
K
Current
Ampere
A
Amount of substance
mole
mol
Pressure
Pascal
Pa
Mass Balance
One of the most widely used instruments in the chemical laboratory is the mass balance or scale. A
balance measures the amount of matter you have, and the typical units are grams. For this part, you will
create a homemade mass balance using kitchen items. If you have a kitchen scale, you can check the
accuracy of your homemade mass balance using a store-bought kitchen scale.
To create our @Home Mass Balance measuring device, we will take advantage of the fact that
you have many ways to measure volumes using everyday items in your kitchen. For example, you have
measuring cups and teaspoons. You will use these, tap water, and a clothing hanger to
make your own mass balance. In order to know how much mass you have on your balance, you will be
taking advantage of the fact that we know the density of water. Density (d) is the amount of mass (m) per
unit volume (V). The equation for density can therefore be written as
Density =
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
Or can be abbreviated as:
d=
𝑚
𝑣
The density of water is very close to 1 g/mL. (For the purposes of this lab, we will assume that
the density is exactly 1 g/mL.) In other words, exactly one milliliter (mL) of water has a mass of
Exactly one gram. So, if you are able to tell how many mL of water you have, you can determine
how many grams of water you have. Below is a calculation that shows how you determine the
number of grams of water in one teaspoon of water and from a ¼ measuring cup. Note that the density
of water is used as a conversion factor in the dimensional analysis shown.
5𝑚𝐿
1 𝑡𝑒𝑎𝑠𝑝𝑜𝑜𝑛 * ( 1 𝑡𝑒𝑎𝑠𝑝𝑜𝑜𝑛 ) * (
1
4
𝑐𝑢𝑝 * (
8 𝑓𝑙𝑢𝑖𝑑 𝑜𝑧
1 𝑐𝑢𝑝
) *(
1 𝑔𝑟𝑎𝑚
1 𝑚𝐿
29.5735 𝑚𝐿
1 𝑓𝑙𝑢𝑖𝑑 𝑜𝑧.
) = 5 𝑔𝑟𝑎𝑚𝑠 (this number is exact)
) * (
1 𝑔𝑟𝑎𝑚
1 𝑚𝐿
) = 59. 147 = 60 𝑔𝑟𝑎𝑚𝑠 (𝑡ℎ𝑖𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑥𝑎𝑐𝑡)
For our mass balance, we can simplify these conversions to the following:
1 𝑡𝑒𝑎𝑠𝑝𝑜𝑜𝑛 = 5 𝑔𝑟𝑎𝑚𝑠
1
4
𝑐𝑢𝑝 = 60 𝑔𝑟𝑎𝑚𝑠 (𝑡ℎ𝑖𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑥𝑎𝑐𝑡, 𝑤𝑒 𝑟𝑜𝑢𝑛𝑑)
Sources of Error
No real physical measurement is exactly the same every time it is performed. The uncertainty tells us how
closely a second measurement is expected to agree with the first. Error can be classified as either random
or systematic:
● Systematic error: Reproducible deviation of an observation that biases the results, arising from
procedures, instruments, or ignorance.
● Random error: Uncontrollable differences from one trial to another due to environment,
equipment, or other issues that reduce the repeatability of an observation (e.g. dust, temperature
fluctuations, etc.).
Errors & Uncertainties
In general, the uncertainty of a measurement is determined by the precision of the measuring device (1).
The smaller the unit you use to measure with, the more precise the measurement is. When making a
measurement you must always estimate 1 place past the smallest division (1). For example a 100mL
graduated cylinder with 1mL graduation will have an uncertainty of +/- 0.1 mL.
● Accuracy: Accuracy is how closely a measurement comes to the ‘true’ value. It describes how
well we eliminate systematic error and mistakes (1).
● Precision: Precision is how exactly a result is determined without referring to the ‘true’ value. It
describes how well we suppress random errors and thus how well a sequence of measurements of
the same physical quantity agree with each other (1).
Summary
●
●
You should always use DECIMALS (not fractions!) to express metric measurements. For
example: write 2.25 cm, not 2 ¼ cm 2.
If a metric measurement is less than one, precede the decimal with a ZERO. For example, don’t
write .55 mm, write 0.55 mm
References
1. Chem Libre Text: Chapter 1. Retrieved on
https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/The_Basics_of_GOB_Chemistry_(Ball_
et_al.)/01%3A_Chemistry_Matter_and_Measurement
Equipment
●
●
●
●
●
●
Ruler (12 inch with centimeter and millimeters markings) or tape measure
Paper (please either print these data sheets or write your answers on a separate sheet of paper)
Binder Clips
Clothing Hanger
Ziplock bags (sandwich size, 4 total)
Store-bought kitchen scale (optional)
●
●
●
●
Small bowl
Tap water
Teaspoon (either measuring spoon or silverware)
Measuring cup to measure ¼ cup
Pre-Lab Questions
1. What does each unit represent?
a. mm = ________________________
b. m = ________________________
c. cm = ________________________
d. km = ________________________
2. How much does each one equal?
a. 1 m = _______ cm
b. 1 cm = _______ mm
c. 1 km = _______ m
3. Which measurement is the largest? Circle your answer for each pair.
a. 14 mm or 1 cm
b. 145 m or 145 km
c. 334 m or 1 km
d. 3.4 cm or 30 mm
e. 1 m or 990 cm
f.
10 km or 1000 cm
4. For our Mass Balance, we will have to use either 1tsp = 5 g and ¼ cup = 60 grams. Please
calculate the number of grams from the various volume measurements.
a. 2 tsp = ______ g
b. 1 cup = ______ g
c. 2 cups and 2 tsp = ______ g
Protocol & Data
Part 1: Length
1. Use a ruler or tape measure to find each measurement.
Height of the rectangle to the nearest centimeter? _______ nearest millimeter? _______
Width of the rectangle to the nearest centimeter? _______ nearest millimeter? _______
Please convert the height and width to inches (1 inch = 2.54 cm):
Diameter of the circle in millimeters? _______ centimeters? ________
Please convert the height and width to inches (1 inch = 2.54 cm):
Part 2: Mass & Volume
This will require you to make a mass balance tool that we can use for the remainder of the course.
1. Fill a shallow bowl or plastic container with tap water that feels neither warm nor cold. Set this water
out for several minutes to allow it to come to room temperature.
2. Grab a few hangers out of your closet. Play around with balancing them on the tip of your finger, on
The switch of a tall lamp, on a doorknob, or on the handle of a kitchen cabinet. Pick the hanger that seems
the most balanced (hangs the most straight). (Please review the mass balance video in Canvas for
additional ideas)
3. Grab two Ziploc bags that are the same size.
4. Experiment with hanging these bags on either side of your hanger using binder clips or clothespins.
You may even use masking tape if you use the same amount of tape on both sides. Note that the bags need
to be equally far apart from the center of the hanger to keep it balanced. (Take a look at the photos
provided on the next page.)
5. Now take one of the bags off the hanger, and open it.
6. Dunk a teaspoon or measuring cup into your water bowl, lightly scrape off the bottom of the measuring
cup/spoon against the rim of the bowl to remove any hanging droplets, and then pour the water into the
open bag. Repeat this process until you have 5 tsps in the bag. Seal the bag.
Note: that the contents of the bag now have a mass of about 5 grams. Seal the bag.
7. Clip the bag containing the water on one side of the hanger.
8. Find various objects in your house, and try putting them into the bag that is clipped to the other side of
the hanger. Pick an object that balances out the mass of the water. What is the mass of your object?
Record the approximate mass of your object in the data table below.
Note:
If the bag with your object is lower than the bag with the water, your object is heavier than 5 grams.
If the bag with your object is higher than the bag with the water, your object is lighter than 5 grams.
If the bag with your object is level with the bag with the water, your object has a mass of 5 grams.
9. Replace your object with what seems like a slightly heavier object. Add tsp water to the water bag until
both bags are level (balanced). What is the mass of your object? Record the approximate mass of your
object in the data table below.
Note:
If the bag with your object is lower than the bag with the water, you need to add more water.
If the bag with your object is higher than the bag with the water, you need to remove water.
If the bag with your object is level with the bag with the water, you are ready to record the mass!
10. Start with two fresh bags, clip them to opposite ends of the hanger, and make sure the hanger is
balanced.
11. Now remove one bag. Using a liquid measuring cup, measure out a quarter cup of water, put it into the
bag, and clip it back onto the hanger.
12. Find something in your house that will balance out the hanger when placed in the bag on the other
side. What is the approximate mass of the object? Record the approximate mass of your object in the data
table below.
13. Find another object that seems heavier. How many more teaspoons or quarter-cups of water do you
need to add to the water bag to get the two bags to balance? Record the approximate mass of your object
in the data table below.
14. Start with two fresh bags, clip them to opposite ends of the hanger, and make sure the hanger is
balanced. Find a different object and use the methods practiced above, determine the mass of the object
using both ¼ cup and teaspoon measurements. Record the approximate mass of your object.
15. To check the accuracy of your homemade mass balance, you will either need to have access to a
kitchen scale, or search and identify the known mass of an object you have access to.
If you have a kitchen scale:
Set your store-bought kitchen scale to measure masses in grams. Place a small plastic cup or tupperware
container on the store-bought kitchen scale, and then press the zero/tare button. Make sure the scale reads
zero at this point. While the scale is still on and reading zero grams, place a small object in the
cup/container. Record the mass of the water below. Use the same object and measure the mass using your
mass balance. Record the mass in the table below.
If you do not have a kitchen scale:
Please use google search or use another source to identify the known mass of an object you can measure
with your home balance. Record the mass in the table below.
16. Calculate the percent error.
Percent Error =
𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 − 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
* 100
Note:
The observed value will be the measurement from the mass balance.
The accepted value will be the measurement from your kitchen scale or google search.
Percent error _________ %
Mass measurements
Object
# of tsp
grams
# of ¼ cups
grams
Total mass (g)
5
5
—
—
5
—
—
1
60
—
—
—
—
60
Percent Error for object
Object
Actual Mass (g)
Observed Mass (g)
Percent Error (%)
Post-Lab Questions
1. How does the accuracy of your measuring tool affect your measurement value?
2. What is the base of the metric system?
3. For the mass balance, why are we able to use water as the liquid to compare the mass of an
unknown object to?
4. Did you make more random or systematic errors? How do you know?