**Learning Objectives**

- Define the International System of Units (measurement system).
- Define a unit of measurement and demonstrate the ability to convert measurements.
- Define length, temperature, time, volume, mass, density, and concentration.
- Define significant figures and describe measurement techniques.

**Introduction**

Just like you and your friend communicate using the same language, scientists all over the world need to use the same language when reporting the measurements they make. This language is called the metric system. In this lesson we will cover the metric units for length, mass, density, volume and temperature, and also discuss how to convert among them.

## Metric Measurement

What do all of these words have in common: thermometer, barometer, diameter, odometer and parameter? All of these words end in **-meter**. You have probably heard this word before, but what does it mean? Meter at the end of a word means *measure*. You use all kinds of measurements each day. How much sugar is needed in the cookies you are baking? Will it be warm enough to leave your jacket at home? How fast are you driving? How much will a bag of apples cost? How much time will it take you to get home from work?

**The units of measure in the English and metric systems**

Most Americans are taught the English or standard system of measurement, but never get a good dose of the metric system. Lucky for you, it is a much easier system to learn than the English system because all the measurements are *base 10* – meaning that when you are converting from one to another, you will always be multiplying or dividing by a multiple of *10*. This is much easier than trying to do calculations between ounces and pounds, and feet and miles.

Because you may not be used to thinking metrically, it may take a little practice using and working with the metric system before you gain a better understanding of it and become more fluent in the measurement language of scientists (and most non-Americans). I challenge you to sprinkle a little more metric in your life. Maybe read the milliliter measurement on your soda can or glance at the kilometer reading on your speedometer. Being able to picture metric quantities will really help with the rest of this course.

## Length

We are going to start with the units of length so we can get back to this word meter that we started out with. The meter is the basic unit of length in the metric system. A meter is a tiny bit longer than a yard. For distances much longer than a meter, you would add the prefix kilo- to make the measurement kilometer. A kilometer is the metric version of our mile, even though it is a bit shorter than our mile. A kilometer is equivalent to exactly 1,000 meters. Any unit that has the word kilo- in front of it is equivalent to 1,000 units. You can attach the prefix kilo- to just about anything. If something takes 1,000 seconds, it takes a kilosecond. If a forest has 1,000 trees, it has a kilotree. You get the idea.

The balance measures mass in grams.

For distances much shorter than a meter, we would use either a centimeter or a millimeter. A centimeter is about the width of your pinky. There are exactly 100 centimeters in a meter. In fact, anything that has the prefix centi- is one-hundredth the size of that base unit. This should be very easy to remember, because there are 100 cents in a dollar. One cent is one-hundredth of a dollar!

The last prefix you should be familiar with is milli-. There are exactly 1,000 millimeters in a meter. Anything that has the prefix milli- is 1,000th the size of its base unit. This one is a bit more difficult to remember, but it is definitely the prefix you would use the most in a chemistry class.

## Mass

Next on our list of important metric quantities is mass. This is one of the most important measurements a chemist makes. Mass is how much of something you have, or the amount of matter in an object. Do not confuse this with volume; volume is a derived unit It is derived by multiplying the length times the width times the height of an object. Mass is measured using a balance, and the basic unit for mass is the gram. To give you an idea of the relative size of a gram, the mass of a penny is about 2.50 grams.

Sometimes people get confused with the difference between mass and weight. They end up being quite similar because everything you and I do takes place on Earth. But, mass and weight differ because mass is how much of something you have and weight is the force of gravity on an object. Take a look at this example. Both of these blocks have the same mass (one kilogram, or 1,000 grams), but one is on Earth and the other is on the moon. Because the Earth has more mass than the moon, it is going to pull the block with more force. This is why things on Earth have more weight than things on the moon, even though both have the same mass. This may be difficult to imagine because it is not like you are going to the moon on a daily basis to check this out.

**Pre-Lab Questions**

1. The SI system unit for the amount of a substance is_____________.

**2. The International System of Units (SI) is ___________________________________________. (provide a definition)**

**3. Convert 15.00oF to oC.**

**4. Convert 5.00 miles to kilometers**

**5. A_______________ is the curve that forms between the liquid and the surface of the container as the result of the following properties of liquids: _______________________, _________________, and _________________. **

**6. ____________________ is defined as mass per unit of measure.**

**7. The definition of % ***m/V*** is ________________________. (provide the formula)**

**8. Explain why significant figures include only the certain digits of a measurement.**

**9. When reading a graduated cylinder made of glass, one must read the volume at eye level from the _________________________ of the meniscus.**

**10. A volumetric flask contains 25.0 mL of a 14% ***m/V*** sugar solution. If 2.5 mL of this solution is added to 22.5 mL of distilled water, what is the %*** m/V ***of the new solution. (use the formula from question 7 to calculate this answer).**

**11. Calculate experimental error (aka percent error) using the following data: the measured value equals 1.4 cm; the accepted value equals 1.2 cm.**

**12. What is the volume of an irregularly shaped object that has a mass 3.0 grams and a density of 6.0 g/mL**

**Procedure:**

**I.** **Length Measurements**

**Materials you will need:**

**·** **Metric ruler**

**·** **CD or DVD**

**·** **Key**

**·** **Spoon**

· **Fork**

1. Gather the metric ruler, CD or DVD, key, spoon, and fork.

2. Look at the calibration marks on your ruler to determine the degree of uncertainty and number of significant figures that can be made when measuring objects with the ruler.

**Note: Record every measurement you make with this ruler to the same decimal place. Remember to do this any time you use this ruler throughout the experiment.**

1. Measure the length of each of the following objects (CD or DVD, Key, Spoon, Fork) with the ruler in centimeters (cm) to the correct level of precision and record in **Data Table 1.**

2. Convert the measurements for each of the objects from centimeters to millimeters and record in **Data Table 1**.

3. Convert the measurements for each of the objects from millimeters to meters and record in **Data Table 1**.

**II.** **Temperature Measurements**

**Materials you will need:**

· **Pyrex one-cup measuring cup**

· **Thermometer (Fahrenheit OK, Celsius would be best)**

· **Safety glasses**

· **Potholder**

· **Plastic cup**

· **Ice cubes**

· **Tap water (hot and cold)**

1. Gather the 1 cup Pyrex measuring cup, cup (plastic or drinking), and thermometer.

**Note: Your thermometer is probably going to be in Fahrenheit scale, and you will have to convert to Celsius and Kelvin.**

1. Look at the calibration marks on the thermometer to determine the degree of uncertainty and number of significant figures that can be made when measuring temperature.

**Note: Record every measurement you make with this thermometer to the same decimal place. Remember to do this any time you use this measuring device throughout the experiment.**

1. Turn on the tap water to hot. Let the water run as hot as possible for approximately 15 seconds.

2. Fill the 1-cup measuring cup to the 1/3 cup mark with hot tap water.

3. Measure the temperature of the hot tap water with the thermometer and convert to degrees Celsius (°C) to the correct precision of the thermometer. Record the measurement in **Data Table 2**.

**Note: When measuring the temperatures place the thermometer into the water so that the silver bulb is fully submerged, but not touching the sides or bottom of the glass beaker. The measurement is complete when the thermometer remains the same temperature without changing.**

1. Put on safety glasses.

2. Place Pyrex measuring cup in the microwave and heat until you see bubbles breaking the surface of the water. The time it takes differs for different microwaves.

3. Allow the water to heat unit it comes to a **full boil**. As soon as the water is boiling fully, measure the temperature with the thermometer and record the measurement to the correct level of precision. Record the measurement in **Data Table 2**.

4. Allow the water to continue boiling for approximately 5 minutes. After 5 minutes, measure the temperature with the thermometer and record the measurement to the correct level of precision. Record the measurement in **Data Table 2**.

5. Once you are done with this experiment, carefully remove the measuring cup from the microwave using a potholder and set aside to cool.

6. Turn on the tap water to cold. Let the water run as cold as possible for approximately 15 seconds.

7. Fill the cup (plastic or drinking) approximately half-full with cold tap water.

8. Measure the temperature of the cold tap water with the thermometer and record the measurement to the correct level of precision. Record the measurement in **Data Table 2**.

9. Add a handful of ice cubes to the cup of cold tap water and allow them to sit in the cold water for approximately 1 minute.

10. After 1 minute stir the ice water with the thermometer.

11. the temperature of the ice water after 1 minute with the thermometer and record the measurement to the correct level of precision. Record the measurement in **Data Table 2**.

12. Allow the ice to remain in the water for an additional 4 minutes.

13. After the additional 4 minutes stir the ice water with the thermometer.

14. the temperature of the ice water after 4 minutes with the thermometer and record the measurement to the correct level of precision. Record the measurement in** Data Table 2**.

15. Convert the temperature measurements for each of the 6 water samples from °F to °C and K. Record the converted temperatures in **Data Table 2**.

**III.** **Mass Measurements (Conversions)**

1. Review the different object(s) listed in **Data Table 3**.

1. Use the masses provided for each of the object(s) in grams and record in **Data Table 3**.

2. Decide which pennies (before or after 1982) you are using for your calculations and stick with the choice throughout the conversions and indicate your choice.

3. Decide if you are using a pen or a pencil and stay with that choice throughout the entire conversion exercise and indicate your choice.

***Since we cannot accurately measure mass at home, I have provided you with the mass of the objects:**

**Penny after 1982**

**Penny before 1982**

**Dime**

**Quarter**

**Pen**

**Pencil **

**2.50 g**

**3.10 g**

**2.268 g**

**5.670 g**

**16.00 g**

**4.40 g**

**Experimental Results**

**Data Table 1: Length Measurements**

**Object**

**Length in cm**

**Length in mm**

**Length in m**

**CD/DVD**

**Spoon**

**Fork**

**Key**

**Data Table 2: Temperature Measurements**

**Temperature in oF**

**Temperature in oC**

**Temperature in K**

**Hot from Tap**

**Boiling**

**Boiling for 5 min**

**Cold from Tap**

**Ice Water – 1** **min**

**Ice Water – 5 min**

**Data Table 3: Mass Measurements (Conversions)**

**Mass**

**Mass in Grams (g)**

**Mass in Milligrams (mg)**

**Mass in Kilograms (Kg)**

**Pen or Pencil**

**3 pennies**

**1 quarter**

**2 quarters + 3 dimes**

**4 dimes + 5 pennies**

**3 quarters + 1 dime + 5 pennies**

**key**

**Key + 1 quarter + 4 pennies**

**Post-Lab Questions**

**1. Water boils at 100°C at sea level. If the water in this experiment did not boil at 100°C, what could be the reason?**

**2. While heating two different samples of water at sea level, one boils at 102°C and one boils at 99.2°C. Calculate the percent error for each sample from the theoretical 100.0°C.**

3. In the movie, “*Raiders of the Lost Ark*“, Indiana Jones takes a gold idol from a cave. The statue is resting on a table which is rigged with a weight sensor. The weight sensor can detect when the weight is removed and will set off a series of unfortunate accidents. To prevent this from happening, Indiana replaces the gold idol with a bag of sand. The volume of the gold idol is approximately 1.0 L. The density of gold is 19.3 g/mL and the density of sand is 2.3 g/mL.

a. Assuming the idol is pure gold, what volume would the bag of sand have to be in order to weigh exactly the same as the idol and not set off the booby-traps?

b. Let us assume that Indiana is successful in removing the idol and returning with it to his laboratory. He decides to determine if it is pure gold. He weighs the idol and measures the volume by a water displacement method. The results are mass = 16.5 kg and volume of water displaced = 954 mL. Is the idol made of pure gold? Explain your answer based on the experimental results

4. **An unknown, rectangular substance measures 3.60 cm high, 4.21 cm long, and 1.17 cm wide. If the mass is 21.3 g, what is this substance’s density (in grams per milliliter)?**

5.**A sample of gold (Au) has a mass of 26.15 g. Given that the theoretical density is 19.30 g/mL, what is the volume of the gold sample?**

**6. A student was given an unknown metal. The student determined that the mass of the metal was 30.2 g. The student placed the metal in a graduated cylinder filled with 20.0 mL of water. The metal increased the volume of water to 22.9 mL. Calculate the density of the metal and determine the identity of the metal using the table below.**

**Densities of Metals in g/mL**

Lead

11.3

Silver

10.5

Nickel

9.90

Zinc

7.14