Laboratory Measurements

Learning Objectives

• Learn how to identify metric units used in measurement of mass (kilogram, gram and milligram), length (meter, centimeter and millimeter) and volume (cubic meter, liter and milliliter) as well as relate these units of measurement to the world in which you live.
• Be able to correctly use and read common laboratory instruments such as a meter stick, thermometer, balance and graduated cylinder.
• Understand the concept of density and calculate the density of solutions.
• Understand and use significant figures.
• Learn and understand the safety criteria.

Introduction

The purpose of this lab is to introduce students to the laboratory setting (including safety) and learn the process of observation, instrument usage and data recording. In the laboratory environment, you will encounter many different types of instruments and equipment. In this lab you will learn how balances are used to measure the mass of an object (weight is the effect of gravity on the mass of an object). You will use a thermometer to measure temperature. A metric ruler (commonly referred to as a meter stick) will be used to measure distances that may be the length, height or width of some object. Finally, graduated cylinders will be used to measure volumes of liquids.

Metric System

Scientists, nurses and employees in the health care industry must have the skills to carry out laboratory procedures, take measurements, and report results accurately and clearly. How well they do these things can determine the success of an experiment and even life or death of a patient. The system of measurement used in science, hospitals, and clinics around the world is the metric system. The metric system is a decimal system in which measurements of each type are related by factors of 10. For example, you use a decimal system when you change U.S. money 1 dime is the same as 10 cents or one cent is 1/10 of a dime. A dime and a cent are related by a factor of 10 as is the relationship between a dime and a dollar.

Most of the rest of the world uses the metric system only. The most common metric units are listed in Table LM.1.

A unit must always be included when reporting a measurement. For example, 5.0 m indicates a quantity of 5.0 meters. Without the unit, we would not know the system of measurement used to obtain the number 5.0. It could have been 5.0 feet, 5.0 kilometers, or 5.0 inches. Thus, a unit is required to complete the measurement reported. For larger and/or smaller measurements, prefixes are attached in front of the standard unit. Some prefixes such as kilo are used for larger quantities; other prefixes such as milli are used for smaller quantities. The most common prefixes are listed in Table LM.2.

Using Table LM.2, if you have measured 5.0 g, then the number of kilograms measured is: $$\begin{array}{}\text{(1)}& 5.0\text{g}\times \frac{1\text{kg}}{1000\text{g}}=0.0050\text{kg}\end{array}$$ And the number of micrograms is: $$\begin{array}{}\text{(2)}& 5.0\text{g}\times \frac{1\mu \text{g}}{0.000001\text{g}}=5.0\times {10}^6\mu \text{g}\end{array}$$

Measured and Exact Numbers

When we measure the length, volume, or mass of an object, the numbers we report are called measured numbers. Suppose you stepped on a scale this morning and noted you weighed 145 lb. Your scale is a measuring tool and your weight is a measured number. Each time we use a measuring tool to determine a quantity; the result is a measured number.

Exact numbers are obtained when we count objects. Suppose you counted 5 beakers in your laboratory drawer. The number 5 is an exact number. You did not use a measuring tool to obtain the number. Exact numbers are also found in the numbers that define a relationship between two metric units or between two U.S. units. For example, the numbers in the following definitions are exact: 1 meter is equal to 100 cm; 1 foot has 12 inches. See Table LM.3.

Significant Figures in Measurements

In measured numbers, all the reported figures are called significant figures. The first significant figure is the first nonzero digit. The last significant figure is always the estimated digit. Zeros between other digits or at the end of a decimal number are counted as significant figures. However, leading zeros are not significant; they are placeholders. Zeros are not significant in large numbers with no decimal points; they are placeholders needed to express the magnitude of the number. When a number is written in scientific notation, all the figures in the coefficient are significant.

Calculations involving measurements must reflect the certainty of the measurements themselves. This means the calculated result must follow specific significant figure rules:

Multiplication or Division:

The calculated result must have the same number of significant figures as the measurement with the least number of significant figures.

Example: When multiplying a length of 15 m by a width of 200 m to obtain an area.

We cannot leave the resulting area as 4,625 m${}^2$ because neither of the two measurements have 4 significant figures. 18.5 m has 3 significant figures, and 250 m has only 2 significant figures. This means the final result should be limited to only 2 significant figures and the answer must be recorded as 4,600 m${}^2$.

Addition or Subtraction:

The calculated result must have the same number of decimal places as the measurement with the least number of decimal places.

Example: When adding two masses (25.0 g and 38.2 g) together to calculate a total mass.

$$\begin{array}{}\text{(3)}& 75.0g+38.2g=113.2g\end{array}$$

This is the correct answer because both 75.0 g and 38.2 g have one decimal place. So the final answer will also have one decimal place.

Exact numbers are considered to have an infinite number of significant figures because they are not measurements. This means when you perform a calculation like Equation LM.1 to convert 5.0 g to kilograms, the 1 kg/1000 g does not impact the final result because the conversion factor contains exact numbers. The measurement, 5.0 g, has two significant figures and therefore the final answer should also have 2 significant figures: 0.0050 kg.

Accuracy and Precision

Accuracy is a measure of how close a value is to an expected or intended value. Precision is a measure of how close values are to one another. These concepts can be illustrated using the Bullseye target shown in Figure LM.1. The goal is to have as many attempts (shown as arrows) hit the center of the target. The closer the attempts are to the target, the better the accuracy. The closer the attempts are to one another, the greater the precision.

The first image shows the best accuracy and precision because the attempts are all clustered close to one another at the center. The second image shows good precision because they are all close to one another, but the accuracy is poor because the cluster is far from the center. The third image is accuracy because the attempts, on average, are around the Bullseye but the precision is poor because they are not clustered close together. The last image is neither accuracy nor precision because the attempts are far from the center and are not close together.

Using a Calibrated Instrument

Some instruments are digital, which means the measurement is provided as a readout that you record. The balances you will be using in the lab is an example of a digital instrument, and all digits in the readout must be recorded (including any zeros at the end). A calibrated instrument has markings for determining measurements. When using a calibrated instrument, pay attention to the calibration marks or lines on the device. Each line or division is a unit of measure, and these divisions may have subdivisions to more accurately determine the measured value. It is a good rule of thumb to note that the finer the subdivisions, the more precise the instrument and typically the more expensive the instrument. When taking a reading of a graduated instrument, the user should be able to estimate one digit or decimal place past the smallest calibration mark.

The relationship between the number of subdivisions and the different precisions associated with calibration marks is made clearer by looking at examples of a ruler, shown in Figure LM.2. Using the first (top) ruler, which is calibrated from 0 to 10 cm, the length of the box above the ruler is not 0 cm nor is it 10 cm; it falls somewhere in-between. The length of the box is less than half the distance to 10 cm, so the length should be recorded less than 5 cm. A reasonable recording would be 2 or 3 cm. The second (middle) ruler is calibrated to the nearest 1 cm, and now it can be clearly seen that the length of the box falls between 2 and 3 cm. It can also be seen that the length is a little more than half-way between 2 and 3 cm, and therefore a reasonable recording could be 2.6 or 2.7 cm. The last ruler (bottom), with a magnified view on the far-right is calibrated to the nearest tenth (1/10) of a cm (or 1 mm). The length of the box now appears to be somewhere between 2.6 and 2.7 cm and appears to be a little closer to 2.6 cm. A reasonable recording of the length of the box using the third ruler could be 2.61 or 2.62 cm.

All of these ruler examples require that the last recorded digit of the measurement be estimated. The certainty of the measurement increases as the device offers more subdivisions in the calibration marks.

Temperature

In the laboratory we measure in degrees Celsius (° C), which is based on the freezing point and boiling point of pure water, $0.0$ $\text{℃}$ (2 significant digits) and $100.0$ $\text{℃}$ (four significant digits), respectively. The Celsius scale has 100.0 degrees of separation between ice and steam. The Kelvin scale is similar to the Celsius scale. The freezing point of water is 273.15 K and the boiling point of water is 373.15 K. Note that there is no degree sign. Since most thermometers used in the laboratory are only precise to the one-tenth of a degree, the freezing point may be recorded as 273.2 K.

Density and Volume

Volume of a rectangular container (i.e., box) is the length x width x height of the given space. If each distance is measured in meters (m), then the resultant volume is in cubic meters or m${}^3$. Similarly, if each distance is measured in centimeters (cm), then the resultant volume calculated is cubic centimeters (cm${}^3$) or ‘cc’ which is equivalent to one milliliter (1 mL). Density is a ratio of the mass compared to the occupied volume (Equation LM.4), where $D$ = density, $m$ = mass and $v$ = volume. Density is an intensive property, which means it does not depend on the amount or size of a substance; it only depends on the identity of the substance. The density of a specific substance is constant at a certain temperature, no matter how small, larger, light, or heavy it is. This is because the ratio of mass to volume stays constant.

$$\begin{array}{}\text{(4)}& D=\frac{m}{V}\end{array}$$

Using a Balance

• If the balance has sliding doors, measurements should be recorded with the doors closed.
• Never add a substance directly to a container (i.e., weigh boat) on the balance. Once you have the mass of the container, which should be clean and dry, remove it from the balance, set it on the counter and add the required amount of substance.
• Return the container to the balance for the measurement. If you have not added enough of the substance, again remove the container from the balance and add more of the substance.
• If you have added too much to the container, do NOT return the substance to the original container, because you do not want to run the risk of contaminating the stock supply for students who use the balance after you. Excess must be discarded in the appropriate waste container.
• If you spill a chemical on the balance or the countertop, clean it up and dispose of it in the appropriate waste container. Brushes are available next to the balance. You may ask the TA or instructor for assistance, if needed.

Procedure

A. Safety

• Find the fire extinguisher, the shower and the eye wash fountains. Report this in the hand-in sheet.
• Also describe the proper clothing attire necessary to perform lab work.

B. Density of a Block:

1. Obtain a bag of solid blocks and record the unknown code found on bag. All blocks in the same bag are made of the same substance. Measure and record the masses of each sample. The blocks can be placed directly on the balance.
2. Using a metric ruler, measure the length ($l$), width ($w$), and height ($h$) of each sample in units of centimeters (cm). Be sure to record these measurements to the correct number of decimal places. Refer to the introduction for guidance.
3. Calculate the volume ($V$) of each block using the formula given in the introduction. Record the calculated volume for each block to the appropriate number of significant figures.
4. Calculate and record the density of each block.

C. Measuring Water: A study in Uncertainty and Significant Figures

1. Measure and record the mass of a dry Styrofoam cup.
2. Obtain a 150 mL beaker and measure a volume of 73 mL of deionized water using the markings on the beaker. Deionized (DI) water can be found in the large white containers (carboys) and in the blue-topped squirt bottles next to the sinks.
3. Pour the measured volume of DI water into the pre-massed Styrofoam cup and record the mass of water and cup. Pour the water sample down the sink. Dry the Styrofoam cup using a paper towel.
4. Repeat steps 2-3 two more times for a total of three trials using the same beaker. You must use a new sample of DI water every time by pouring the water samples from each trial down the sink after you have obtained the mass of water and cup. Dry the cup between trials.
5. Calculate and record the mass of water for each trial by subtracting the mass of the cup.
6. Calculate and record the range of water masses by subtracting the lowest value from the highest value.
7. Calculate the average mass of water from the 3 trials.
8. Using the average mass of water and the 73 mL volume measured by the beaker, determine (calculate) the density of the water. Be sure to report the density to the appropriate number of significant figures.

9. You will now repeat steps 2 - 4 using a 100 mL graduated cylinder to measure 73.0 mL of DI water instead of a beaker. Do not throw away your last trial (keep the water in the Styrofoam cup).

10. Perform the same calculations as steps 5-8 for the graduated cylinder results.
11. Using a thermometer, measure the temperature of the water in the Styrofoam cup for the last trial and record to the correct number of decimal places. Table LM.5 shows the density of pure water at different temperatures (the first column and first row are temperature readings). Using your recorded temperature, record the expected water density. For example, if you found your water sample to have a temperature of $25.2$ $\text{℃}$, the density of water at that temperature is 0.9969965 g/mL.

D. Density of an Unknown:

1. Obtain an unknown metal or metal shot from the fume hood and record its code.

2. Accurately measure and record the mass of a weigh-boat.

3. Add between 20 and 25 g of unknown metal to the weigh-boat and record the mass. Calculate the EXACT mass of metal used.

4. Add approximately 50 mL of water to a 100 mL graduated cylinder. Record the volume to the appropriate number of decimal places.

5. CAREFULLY, so as not to break the bottom of the graduated cylinder, add the metal from step 3 to the liquid in the graduated cylinder.

Note:

You may hold the graduated cylinder at a 45 degree to aid in adding the metal to the liquid.

1. Tap the graduated cylinder lightly so as to remove any air bubbles that may be trapped between pieces.

2. Record the new volume on the graduated cylinder.

3. Using the volume displaced (Volume from Step 7 minus Volume from Step 4) as the volume of the metal added, calculate the density of the unknown metal.