Laboratory 1 Fall 2019 - Bio 201 lab worksheet PDF

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Laboratory 1 BIO 201

Name and Section

Select Mathematical Skills used in Biology Scientific investigations in biology utilize a number of quantitative skills that we will assume that you are familiar with. The purpose of this lab is to review these skills, so that you will be comfortable with using them throughout the course and in your other science courses. Numbers and Nomenclature Familiarize yourself with Tables 1 and 2 in this lab and the inside back cover of the text. Scientists use the metric system, so it is essential that you become familiar with it. Table 1 gives the primary units of measurements that you will be using. Know the abbreviations for each unit of measurement. For temperature, you will be using Celsius or centigrade. We will use the symbol o for degrees. The C for Celsius will be assumed. Table 1. Metric System Units and Conversions

Table 2 gives the most common prefixes that are used in designating measurements. Know these prefixes and their corresponding values. For example a nanogram is 10-9 g and a milliliter is 10-3 l. You should also be able to determine the relationships between different measurements. For example 1 milliliter is 103 microliters. Be able to use these relationships to convert one measurement to another. The use of exponents will be important in doing this.

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Laboratory 1 BIO 201

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Table 2. Prefixes Used in the Metric System

Table 3. Common Abbreviations Unit mole molar meter liter gram

Abbreviation mol M m l or L g

Conversion factors A conversion factor is used to convert one unit such as milliliters to another unit such as microliters. The actual value of the measurement will not change, only the units of the measurement. In converting a measurement from one unit to the next, the original value is multiplied by the conversion factor. Since the value of the measurement is not changed, every conversion factor must equal 1. To create a conversion factor, you must know the relationship between the two units. For example the conversion factor for milliliters and microliters is “1 milliliter/1000 microliters.” This simply says that there are 1000 microliters in 1 milliliter. To create a conversion factor, you need to know the definitions of the different prefixes used in measurements (Table 2). Let’s take micro and milli as an example. Create a fraction with micro on the top and milli on the bottom micro/milli

or

10-6/10-3

See Table 2 to see where these exponents came from.

What do you have to do to the fraction to make it equal 1? The answer is to multiply it by 103. (10-6/10-3) x (103) = 10-3/10-3

or 103 micro/ milli = 1

therefore, 103 microliters = 1 milliliter. Example 1: Convert 3.25 milliliters to microliters. To do this you would multiply 3.25 milliliters times the conversion factor. (3.25 ml) (1000 μl / 1 ml) The ml cancel out and is replaced with μl (3.25 ml) (1000 μl / 1 ml) = 3250 ul or 3.25 x 103 μl Example 2: Convert 5.2 μl to ml. To do this you would use the same conversion factor, except that you would flip the orientation so that 1 ml is the numerator (top part of the fraction). (5.2 μl) (1 ml / 1000 μl)

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Laboratory 1 BIO 201

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The μl cancel out and is replaced with ml (5.2 μl) (1 ml / 1000 μl) = 0.0052 ml or 5.2 x 10-3 ml Working with exponents Writing numbers as exponents Numbers are often expressed with exponents, especially if they are very large or very small. All of the numbers that you will be using are to the base 10, so that exponents will be written as a factor of 10. For example 1,000 is 103 and 1/1,000,000 is 10-6. 100 is 1 and therefore is not written when expressing numbers with exponents. You should be comfortable in writing numbers with and without exponents. In practice when writing numbers with exponents, use scientific notation, in which a number is written as a number between 1 and 10 followed by and exponent of 10. For example, 57,600,000,000 is 5.76 x 1010 and 0.00000268 is 2.68 x 10-6. Adding and subtracting numbers with exponents To add or subtract two numbers with exponents, first be sure that each number is expressed with the same exponent. If the exponents differ, convert one of the numbers to a number with the other exponent. Next, if you are adding the numbers, just add the numbers not the exponents. The final value will have the same exponent as the original numbers. Similarly, if you are subtracting one number from another, subtract the number, and keep the exponents the same. Some examples are shown below: 1. (1.08 x 103) - (0.63 x 103) = 0.45 x 103 or 4.5 x 102 2. (5.52 x 10-5) - (0.71 x 10-5) = 4.81 x 10-5 3. (1.08 x 103) - (1.63 x 102) = (1.08 x 103) - (0.163 x 103) = 0.917 x 103 or 9.17 x 102 Multiplying and dividing numbers with exponents To multiply two numbers with exponents, first multiply the two numbers, and then add the two exponents. Some examples are shown below: 1. (1.08 x 103) x (0.63 x 103) = 0.6804 x 106 or 6.804 x 105 2. (5.52 x 10-5) x (0.71 x 10-5) = 3.92 x 10-10 3. (1.96 x 10-3) x (2.32 x 104) = 4.55 x 101 or 45.5 To divide two numbers with exponents, first divide one number into the other, and then subtract the two exponents. Some examples are shown below. Get in the habit of using scientific notation. 1. (6.52 x 103) ÷ (1.26 x 103) = 5.17 x 100 or 5.17 2. (5.52 x 10-5) ÷ (0.71 x 103) = 7.8 x 10-8 3. (6.22 x 106) ÷ (2.11 x 10-2) = 2.948 x 108 or 2.95 x 108

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Laboratory 1 BIO 201

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Calculating the reciprocal of numbers with exponents This type of calculation is a variation on the procedure of dividing numbers with exponents. Take the following example: Calculate the reciprocal of 2.7 x 10-15.  First write the reciprocal: 1/(2.7 x 10-15)  Rewrite the numerator 1 as a number that has an exponent. To do this remember that 1 = 100 and that any number multiplied by 1 does not change. Therefore 1 can be written: 1 x 100.  1/(2.7 x 10-15) can be rewritten as (1 x 100) / (2.7 x 10-15).  Use your calculator to calculate 1/2.7, and calculate 100/1015 by hand (Change -15 to +15).  The answer is 0.37 x 1015 or using scientific notations 3.7 x 1014.

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Laboratory 1 BIO 201

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In-class exercises to be done in class and reviewed with the TA. After checking your answers with the TA, make sure that you understand how to do the problems. Units of measurements 1. 3.25 mg =

μg

2. 5.2 ng =

μg

3. 2.3 l =

ml

Using exponents. 1. (3.58 x 103) - (1.44 x 103) =

2. (5.57 x 105) - (2.34 x 104) = 3. (2.00 x 105) x (4.00 x 104) = 4. (3.00 x 10-3) x (5.00 x 104) =

5. (8.36 x 103) ÷ (2.00 x 10-3) = 6. (6.9 x 10-3) ÷ (3.0 x 102) = 7. The reciprocal of (3.5 and 1017) =

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Laboratory 1 BIO 201

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Laboratory 1 BIO 201

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Figure 1. The Periodic Table. Modified from http://oxford-labs.com/wp-content/uploads/2009/04/periodic-table.jpg

Making solutions In this course, all of the solutions will be provided for you. While you will not need to make up solutions, you will need to know how solutions are made. Solutions are composed of solutes and solvents are usually expressed as molarity, with 1 Molar (1 M) defined as 1 mole of solute in 1 liter of solution. Likewise, a 1 millimolar (1 mM) solution contains 1 millimole of solute per 1 liter of solution. For most solutions, the solvent is distilled water. Benzene is a common organic solvent. A mole is not a unit of mass, so in making solutions the number of moles needed must be converted to a measurement of mass such as grams or micrograms. To do this you will need to know the molecular weight of your solute. This is usually given on the bottle of the chemical, but it can also be determined from the Periodic Table (Figure 1) by adding the atomic weight of each element in the chemical, taking into account the number of atoms of each element that is in the compound. For example the molecular weight of NaCl is 22.99 + 35.45 = 58.44. This means that a 1 M solution of NaCl will contain 58.44 g of NaCl in enough water to give 1 liter of solution. The molecular weight of CaCl2 is 40.08 + 2(35.45) = 110.98. What if you wanted to make a 50 mM solution of NaCl? How many g of NaCl would be needed to make 1 l of this solution? Use the equation x = (GMW)(Molarity)(Volume) to calculate the number of grams of solute in a solution of any molarity and volume. GMW = Gram-Molecular Weight = The mass, in grams, of 1 mole of a molecular compound is called the gram-molecular weight. It is numerically equal to the molecular weight. Express GMW as grams per mole, so the GMW of NaCl is 58.44 g/mol. Molarity is the final molarity of the solution. In this case it is 50 mM or 50 mmol/l. Express concentrations as moles/l for these calculations. Volume is the final volume of the solution. In this case it is 1 l. x = (GMW)(Molarity)(Volume) = (58.44 g/mol) (50 mmol/l) (1 l) Notice that mol and l cancel out. x = (58.44 g/mol) (50 mmol/l) (1 l) Be sure not to forget any abbreviations. In this case, m. Combine m with g. x = (58.44 g) (50 m) (1) x = 2922 mg = 2.922 g Often you will not need an entire liter of solution. Let’s assume that you only need to make up 50 ml of a 40 mM NaCl solution. How many g of NaCl would you need? Use the same equation, x = (GMW)(Molarity)(Volume) x = (GMW)(Molarity)(Volume) = (58.44 g/mol) (40 mmol/l) (50 ml) Notice that mol and l cancel out.

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Laboratory 1 BIO 201

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x = (58.44 g/mol) (40 mmol/l) (50 ml) Be sure not to forget any abbreviations. In this case, m and m. Combine m with g. x = (58.44 g) (40 m) (50 m) x = 116880 m m g Replace m m with 10-6 or μ (10-3 x 10-3 = 10-6). See Table 1. x = 116880 μg = 116.880 mg = 0.117 g Be very clear and correct when you write out your equations. In this way you can see what cancels out and what units and abbreviations are left. If you convert abbreviations to exponents (Table 1), then the final answer will involve multiplying with exponents. Diluting solutions Often times the solutions that are used in the lab are made from more concentrated stock solutions. To make the working solutions requires calculating the volume of the concentrated stock solution that needs to be diluted with water to give the appropriate volume of the working solution. This is like making a drink from a concentrated syrup. You take a small volume of the syrup and dilute it with water or carbonated water. An example will make this clearer. Assume that you have a 1 M stock solution of NaCl and you want to use it to make 75 ml of a 50 mM working solution. How many ml of the 1M solution will be needed to make 75 ml of a 50 mM solution? You can set up the following relationship: C1V1 = C2V2 The concentration of the first solution times the volume of the first solution equals the concentration of the second solution times the volume of the second solution. You know C1, C2, and V2, so you just need to solve for V1. V1 = (C2V2)/ C1 V1 = (50 mM) (75 ml) / (1 M) M cancels out V1 = (50 mM) (75 ml) / (1 M) Keep the remaining units and abbreviations V1 = (50 m) (75 ml) / (1) = 3750 m m l Replace m with 10-3 and do appropriate conversions. V1 = 3750 x 10-3 x 10-3 l = 3750 x 10-6 l = 3750 μl = 3.75 ml To make the solution, take 3.75 ml of the 1 M stock solution and dilute it with 71.25 ml of distilled water to give 75 ml of a 50 mM solution. Adjustable-volume pipettes Throughout the semester, you will be using adjustable-volume pipettes to measure volumes from 10 to 1000 μl, so it is important that you learn the correct technique in using them

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Laboratory 1 BIO 201

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from your TA. Become familiar with their use before you proceed with the lab. The volumes that you will be primarily using will be in microliters (μl). One microliter is 1/1000 of a milliliter which is 1/1000 of a liter. You will be using two different pipettes for different volume ranges, so be sure that you can identify each. The two pipettes are shown in Figure 2. They are labeled 20-200 μl and 200-1000 μl for the volume ranges. They can also be identified by the color of their top: yellow 20-200 μl, and blue 100-1000 μl, and the sizes of their barrels. However, be aware that different brands of pipettes use different colors. Each pipette uses disposable tips for measuring and dispensing liquids. Figure 3 shows the pipettes with tips. The 20-200 μl pipettes use yellow, opaque tips, while the 100-1000 μl pipette uses non-colored or blue, opaque tips (depending on the brand of the tips). These opaque tips allow you to see the fluid that has been drawn up into the tip. This allows you to check on your pipetting technique. What volumes are being registered in each pipette? Verify your answers with your TA. NEVER USE PIPETTES WITHOUT TIPS. THIS WILL CONTAMINATE AND CLOG THE PIPETTE AND MAKE IN UNUSABLE. ALWAYS LOOK AT THE SCALE ON THE SIDE OF THE PIPETTE WHILE YOU ARE DIALING THE PIPETTE. NEVER OVER-DIAL THE PIPETTE PAST THE HIGHEST VALUE. THIS CAN BREAK THE PIPETTE. NEVER UNDER-DIAL THE PIPETTE PASTE ZERO. THIS CAN ALSO BREAK THE PIPETTE.

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Laboratory 1 BIO 201

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Figure. 3. Adjustable pipettes with tips.

Figure 2. Adjustable pipettes.

Pipette tips Your TA will go over the correct method of pipetting. The pipette tips that you will be using have markings that can be used to verify the accuracy and correctness of your pipetting technique.

800μl

500μl

200μl

100μl

Figure 4. Pipette tips showing volume markings.

Try measuring the volumes shown in the figures, using the markings on the pipette tips to assess your technique. If you are off, then you are probably not pipetting correctly. Check with you TA to insure that you are pipetting correctly.

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Laboratory 1 BIO 201

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In Class work Making solutions 1. How many g of MgCl2 are needed to make 1 liter of a 0.5 M solution? Show your calculations. You will need to use the periodic table.

2. How many g of NaCl are needed to make 200 ml of a 300 mM solution? Show your calculations?

3. Starting with a 1M stock solution of KH2PO4, how many ml would be needed to make 100 ml of a 25 mM solution? Show your calculations.

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Laboratory 1 BIO 201

Name and Section

Homework due next lab meeting (16 pt.) Units of measurements 1. 4.3 g =

mg

2. 6.7 μg =

ng

3. 345 ml =

l

Using exponents 1. (6.6 x 104) - (3.0 x 103) =

2. (3.0 x 105) - (1.2 x 105) = 3. (4.50 x 104) x (3.00 x 103) = 4. (3.00 x 10-5) x (2.00 x 103) =

5. (5.0 x 105) ÷ (2.5 x 10-2) = 6. (9.6 x 10-4) ÷ (2.0 x 10-6) =

7. The reciprocal of (4.2 and 10-13) =

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Laboratory 1 BIO 201

Name and Section

Making solutions 1. How many g of CaBr2 are needed to make 300 ml of a 0.7 M solution? Show your calculations. You will need to use the periodic table.

2. Starting with a 1M stock solution of KH2PO4, how many ml would be needed to make 75 ml of a 200 mM solution? Show your calculations.

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