Unit 1 Measurement & Lab Equipment Abstract This lab reviews the concept of scientific measurement, which you will employ weekly throughout this course. Specifically, we will review the metric system so that you will be able to measure length, mass, volume and temperature in metric units, and convert between the English and metric systems. You will also familiarize yourself with common laboratory equipment. You will review and practice scientific notation so that you will understand its use in scientific measurement. Finally, you will utilize basic statistical methods to evaluate data that you gather and graph. The sections entitled “Put what you have read into Practice” will be due as homework next week. Whatever you do not complete during the lab period should be completed at home. 1.1 Conversions within the Metric System Introduction Length, Mass, Volume To convert within the metric system, you must remember the following: k h da Base Units d c m µ n p kilo hecto deka meters, liters, grams deci centi milli micro nano pico 103 102 101 100 10-1 10-2 10-3 10-6 10-9 10-12 To convert between metric units, you will need to move the decimal to the right or to the left, relative to where you begin, as shown by this chart. This means that you will need to add a decimal to the end of any whole number! For instance “35” is the same as “35.” Example 1: Convert 5 mg to g. To get from mg to g requires you to move to the left on the chart 3 units, thereby moving the decimal to the left 3 units. Therefore the value will be 0.005 g. 3 Example 2: Convert 80 hectoliters to centiliters. To get from hecto to centi requires you to move to the right 4 units. Therefore the number will become 800000 hl. Example 3: Convert 400 ml to nl. To get from milli to nano requires you to move 6 units to the right. Notice that we are referring to the exponent associated with 10 when we count places to move the decimal- we are not counting actual words listed on the chart. Therefore 400ml becomes 400,000,000 nl. Tip Make sure you look at your answer to see if it makes sense! Does it make sense that 1 liter is the same as 0.001 ml?! No, because milliliters are smaller units than liters! Therefore you would know that you had moved the decimal the wrong way. One liter is equal to 1000 ml. Important conversions to know about water under standard conditions! 1 cc = 1ml 1dm3 = 1 liter 1 ml = 1 g 1 liter = 1 kg This means that 50 ml of water weighs 50 g. Also, 3 liters of water equals 3 kg. Check your understanding If you weigh 142 ml water, how many mg would it equal? ___________________ Temperature Temperature can be measured in Fahrenheit or in Celsius. Here in the US we are used to thinking of temperature in terms of °F. In science we evaluate temperature using the Celsius scale. It is called the centigrade thermometer because there are 100 (centi) degrees between the freezing (0°C) and boiling point (100°C) of water. To convert between the two, use the following conversions: Equations From Fahrenheit to Celsius: 1. Subtract 32 from degrees Fahrenheit 2. Multiply by 5 3. Divide by 9 From Celsius to Fahrenheit: 1. Multiply degrees Celsius by 9 2. Divide by 5 3. Add 32 4 From °F to °C 5 ℃ = (℉ − 32) 9 From °C to °F 9 ℉ = ℃ + 32 5 To get you thinking in terms of Celsius, know the following common knowledge points. This will help you evaluate your answer in terms of “does this make sense”? Freezing: 0°C = 32 °F Room Temperature: 21.1°C = 70 °F Body Temperature: 37°C = 98.6 °F Boiling: 100°C = 212 °F Example 1: What is the temperature in °C if the outside air temperature is 43°F? 1. 43-32 = 11 2. 11 x 5 = 55 3. 55 divided by 9 = 6.11 Therefore the answer is 6.11 °C. Practice Convert the following numbers to the units indicated. Indicate what each are measuring- are they units of mass, volume, or length? 1. 5.5 mg = _______ hg Unit of: ___________________ 2. 61 pl = _______ ml Unit of: ___________________ 3. 110 m = _______ km Unit of: ___________________ 4. 7.89 dg = _______ µg Unit of: ___________________ 5. 0.003 km = _______ mm Unit of: ___________________ Convert the following temperatures as indicted. You must show your work. Do not use a calculator! 6. 83 °F = _______ °C 9. 98 °C = _______ °F 7. 22 °C = _______ °F 10. 62 °F = _______ °C 8. _______ °F 4 °C = 5 1.2 Converting from English to Metric Units Converting from English to metric units: The basic metric unit of length is the meter. To compare English and metric values of length, it is handy to know that 1 inch = 2.54 cm. Mass is expressed in grams. To compare English and metric values of mass, it is handy to know that 1 kilogram = 2.21 pounds. Volume is measured in liters. To compare English and metric values of volume, it is handy to know that 1 ounce = 30 milliliters and 1 gallon = 3.8 liters. 1.3 Becoming familiar with Laboratory Equipment In this lab course, you will work with equipment and glassware that is common in the laboratory setting. Locate the following items. Graduated cylinder Beaker Erlenmeyer flask Triple Beam Balance Digital Balance Graduated Pipette Weigh boat Hot/Stir Plate Stir Bar ***Use the space below to make a sketch of each of them so that you will recognize it in the future. Measuring Volume: Fill your graduated cylinder with 45 ml of water. When measuring the volume of a liquid in a graduated cylinder, you will observe a “meniscus.” Locate the meniscus (and include it in your drawing.) Do you think that you should measure the volume from the top or bottom of the meniscus? Check with your instructor to make sure you are correct! 6 Now transfer the water to your beaker. Is this as accurate at measuring volume as the graduated cylinder? Using a Balance: For the digital and triple beam balance, practice using each by finding the mass of a coin. To do this, you will need to use a weigh boat since you typically do not want to place the material you are weighing directly on the balance. 1. Locate and place the weigh boat on the digital balance, on the triple beam balance, you may set the coin on the metal pan without the weigh boat. 2. “Tare” the digital balance in order to reset the balance to “0” grams. This will ensure that you do not add the weight of the weigh boat to what you are weighing. Make sure that your triple beam balance set to zero as well by using the adjustment knob underneath the pan. 3. Add the coin. Record the weight of the coin for each. Triple beam: ___________ grams Digital balance: ___________ grams 4. Which balance is more accurate, and why? Practice Now you will apply the knowledge you have gained. In this section of the lab, you will learn about the different pieces of laboratory equipment, as well as how to measure the different properties of matter with them. Using a Balance: During a practical, Sally Student and Sid Student were asked to find the weight of a penny on a digital balance. Sally found that the weight was 0.001 grams whereas Sid found that the weight was 4.3 grams. The correct answer was 2.5 grams. a. What do you think Sally might have done incorrectly? b. What might Sid have done incorrectly? 7 Understanding Meters: 1. Meters are the base unit of the metric system used to measure length. Please state what measuring device or devices you would use to measure an object in the following units: 3 mm: 20 cm: 1.5 m: 2. Find two items: one measured in centimeters (cm) and, if possible, one measured in millimeters (mm). Use the instruments that you listed in #1 to measure these objects. Write down the name of the item and how many centimeters or millimeters it measures. Please include the units (cm or mm) with your measurement. 3. Is a centimeter larger or smaller than a millimeter? 4. What property of these items do cm or mm measure: length, volume, mass or temperature? 5. The height of the average person is a little over 1.5 meters. Knowing this, is one centimeter larger or smaller than one meter? 6. Is one millimeter larger or smaller than one meter? 7. Runners often run a 5K, which is five kilometers (km). Is a kilometer larger or smaller than a meter? 8 Understanding grams: 8. Grams are the base unit of the metric system used to measure the amount of matter in an object. There are two instruments that you could use to measure something in grams. Please list those two instruments here (note: you will draw these instruments later). 9. Find one item that is measured in grams (g). Write down the name of the item and how many grams it weighs. Please include the units (g) with your measurement. 10. Find one item that is most likely measured in kilograms (kg). Are you able to measure this with the instruments that you listed in question 8? Why or why not? 11. Which item felt heavier, the item measured in grams or the item measured in kilograms? 12. Based off of your answer to number 8, is a gram larger or smaller than a kilogram? 13. What characteristic of these items do grams and kilograms measure: length, volume, mass, or temperature? 14. The other units that can be used to measure these items are either pounds or ounces. These are commonly used to measure the weight of objects. What property of the item(s) does weight measure? Is this property the same thing as your answer in number 13? 9 Understanding Liters: 15. Liters are the base unit of the metric system used to measure volume. Please list all of the pieces of glassware that could be used to measure volume. 16. If you were to pick two of these pieces of glassware to measure the volume of a liquid as accurately as possible, which two would you pick? Why? 17. Find one item that is used to measure liters (l). Find one item that is used to measure milliliters (ml). Write down the name of the item and how many liters or milliliters it measures. Please include the units (l or ml) with your measurement. 18. Which item was larger, the one used to measure liters or the one used to measure milliliters? 19. Based off of your answer in number 17, would you be able to place all of the contents of a 2 liter container into a 1000 ml container? 20. Would you be able to place the contents of a 1 liter container into a 600 mililiter container? 21. What characteristic of the contents of the container do liters measure: length, volume, grams or temperature? 10 1.4 Scientific Notation Introduction: Scientific Notation is a way of expression very large or very small numbers such that it is easy to write, easy to determine the value and easy to make comparisons to other numbers. For instance: • the number 342000033994 is a long number to write and difficult to say exactly what that number’s value is without some thought. Adding commas helps: 342,000,033,994, while easier to read is still large and long! • how does 342000033994 compare to 45645612825? How about 342,000,033,994 to 45,645,612,825- how much bigger or smaller is it? This is very hard to do at a glance! Putting the numbers in scientific notation makes it easy to quickly determine the value and to compare numbers. Try 3.42 x 1011 vs. 4.56 x 1010? It is much easier to compare these values! Scientific Notation is NOT difficult, but does require that you follow some simple steps, and that you use your common sense. Follow these steps each time: 1. Rewrite your number and put a decimal point after the *first* non zero digit. For instance, a. 1234567 becomes 1.234567 and b. 0.001234567 becomes 1.234567 2. Add “x 10” to the end of the digits a. 1234567 becomes 1.234567 x 10 and b. 0.001234567 becomes 1.234567 x 10 3. Count how many place values the decimal has moved from the original placement to the current placement. Write that number as your exponent. a. If the number became smaller when you moved the decimal, you will need the exponent to be positive: 1234567 becomes 1.234567 x 106 b. If the number became bigger when you moved the decimal, you will need the exponent to be negative: 0.001234567 becomes 1.234567 x 10-3 4. Always check your answers! Do they make sense? For instance: Does 1.234567 x 106 equal a larger number by 6 tens, 1234567? Yes! 11 What do the exponents mean, at a glance? Remember these values and you will be able to read the value of very large numbers very quickly. 103: thousands 10-3: thousandths 106: millions 10-6: millionths 109: billions 10-9: billionths Practice Convert the following numbers from full expression to scientific notation. 1,345,635,000 ____________________________________ 457.430 ____________________________________ 0.000554433 ____________________________________ 47777.0055 ____________________________________ 0.0044551111 ____________________________________ Convert the following numbers from scientific notation to full expression. 4.56 x 108 ____________________________________ 6.785544 x 10 -8 ____________________________________ 8.992233 x 106 ____________________________________ 9.11 x 10-2 ____________________________________ 6.789 x 105 ____________________________________ 1.5 Statistical Calculations Introduction To analyze data generated in the laboratory in order to determine its significance, you must first be equipped to evaluate your data from a statistical perspective. A review of basic statistical terms is included here for your review. 12 I. Mean: This is an average of a group of measurements. How to calculate mean? Add all values and divide by total number of values. Example: Values: 40, 38, 22, 20, 30 Mean = 40 + 38 + 22 + 40 + 30 divided by 5 Mean = 30 Equation 𝑥 = ! ! !!! ! ! II. Median: The value that is in the middle of a group of measurements. How to calculate median with an odd number of values? Using previous example: Example Values: 40, 38, 22, 20, 30 Rearrange from low to high: 20, 22, 30, 38, 40 Median = middle value = 30 How to calculate median with an even number of values? Using previous example: Example Values: 40, 38, 22, 20, 30, 24 Rearrange from low to high: 20, 22, 24, 30, 38, 40 Median = add two middle values and divide by 2 Median = 24 + 30 / 2 Median = 27 III. Range: The difference between the smallest and the largest measurements. How to calculate range? Using previous example: Equation Example Values: 40, 38, 22, 20, 30 Subtract smallest value from largest value Range = 40 – 20 = 20 13 𝑅 = 𝑀𝑎𝑥 − 𝑀𝑖𝑛 IV. Deviation: Measures how the measurements vary from the mean (+ or -). In other words, what is the difference between an actual measurement and the mean, or average, of the sample? How to calculate a deviation? Using previous example: Example: Values: 40, 38, 22, 20, 30 We determined the mean to be 30. We find the deviation for each number in the data set. The deviation for the value “38” would be +8. This value is 8 more than the mean. Equation 𝑑 = 𝑥! − 𝑥 V. Variance: This measures how much difference, or variation, there is between the values you have obtained. The smaller the variance, the closer the values will be to the mean. Likewise, the larger the variance, the farther the values will be from the mean. How do I calculate variance? Calculate the sum of the squared deviations divided by the number of values minus one. Using previous example: Equation Example: Values: 40, 38, 22, 20, 30 Variance= 100+64+64+100+0 = 82 5-‐1 (𝑥 − 𝑥)! 𝑠 = 𝑛−1 ! VI. Standard Deviation: Standard deviation gives you an idea of the widely spread your values are about the mean. The smaller the standard deviation, the closer your values will be to the average. If you were to graph data having a small standard deviation, you would expect a tall, thin bell shaped curve. On the other hand, if the standard deviation were large, your bell shaped curve would be wider. How to calculate Standard Deviation? Calculate the square root of the variance. Using previous example: Example: values- 40, 38, 22, 20, 30 The variance equaled 82. Take the square root of the variance. 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 82 = 𝟗. 𝟎𝟔 14 Equation 𝜎 = (𝑥 − 𝑥)! 𝑛−1 Tip Standard deviation can be used to evaluate the percentage of a population that is near “average”. One standard deviation to the left and right of the mean will cover 68% of the population; two standard deviations to the left and right of the mean will cover 95% of the population. Practice Purpose: In this exercise you will record the gender and height of everyone in the lab. You will determine the average height of males and females in your lab section. Materials and Methods Meter Stick Lab participants Have each individual list their gender and height on the whiteboard. Record this information in the data table provided. Where necessary, convert measurements recorded in English units to metric centimeters. Use the space provided to record deviations (required on next page). Results: Males (inches): Males (cm): Females (inches): 15 Females (cm): Males (inches): Males (cm): Females (inches): Females (cm): Figure 1. Height measurements of Biology 1406 Laboratory population. Use the data from your table to calculate the following, using the information and examples of each given previously (show your work!). Make sure that you use the data expressed in cm, not inches! ________________________________________________________________________ Size of sample: Males ___________ Females__________ Entire Class___________ ________________________________________________________________________ Mean height: Males ___________ Females__________ Entire Class___________ ________________________________________________________________________ Median Height: 16 Males ___________ Females__________ Entire Class___________ ________________________________________________________________________ Range of height: Males ___________ Females__________ 17 Entire Class___________