Sample problem and solutions

Sample problem and solutions.

There are three sets of ten problems each. Each set of ten problems is followed by the solution to the problems.

It may be helpful to first read the information on serial dilutions from the BIO440 website: serial dilutions

1. How would you prepare 800 mls of a 10% sodium chloride (NaCl, a powder) solution in water?

2. How would you prepare 500 mls of a 10% ethanol (C₂H₆O) solution in water?

3. How would you prepare 1.2 L of a 0.7 M sodium chloride (NaCl, a powder) solution in water?

4. How would you prepare 10 mls of a 0.5 M ethanol (C₂H₆O) solution in water?

5. If you have a stock solution containing 500,000 units of Rubisco / ml, how would you make up 200 ml of a solution containing 0.025 units of Rubisco / ml?

6. If you have a stock solution of 3 M potassium chloride (KCl, a powder), how would you make up 200 ml of a 5 µM (micromolar) solution of KCl?

7. Describe three separate ways in which you could dilute something 1:100.

8. For a particular analysis, you need to dilute a commercial tequila 1 x 10^-12. What is a reasonable way of doing this?

9. If you were to add 1 gallon of blood to three gallons of water, and then take 1 ounce of that dilution and add it to 9 ounces of water, and then take 7 mls of that dilution and add it 563 mls of water, what would the final dilution be?

10. If you were to dilute shark liver oil 1 x 10^-5, and then found that the concentration of a particular fatty acid was 2.5 pg / L in that dilution, what was the concentration of that fatty acid in undiluted shark liver oil? (pg = picogram)

1. How would you prepare 800 mls of a 10% sodium chloride (NaCl, a powder) solution in water? 800 * 0.1 = 80; measure 80 g NaCl, add H2O to 800 ml

2. How would you prepare 500 mls of a 10% ethanol (C₂H₆O) solution in water?

500 * 0.1 = 50; measure 50 ml ethanol, add 450 ml H2O

3. How would you prepare 1.2 L of a 0.7 M sodium chloride (NaCl, a powder) solution in water? 1.2 L * 0.7 M NaCl / L * 58.5 g NaCl /mole = 49.14 g NaCl; measure 49.14 g NaCl and add water to 1.2 L

4. How would you prepare 0.2 L of a 0.2 m sodium chloride (NaCl, a powder) solution in water? 0.2 L x 0.2 m NaCl / L H20 * 58.5 g NaCl /mol = 2.34 g NaCl

measure 2.34 g NaCl, add 200 mls H2O

4. How would you prepare 10 mls of a 0.5 M ethanol (C₂H₆O) solution in water?

10 ml * 0.5 M ethanol / 1000ml * 46 g ethanol / M ethanol = .23 g ethanol; measure 0.23 g ethanol and add water to 10 ml

5. If you have a stock solution containing 500,000 units of Rubisco / ml, how would you make up 200 ml of a solution containing 0.025 units of Rubisco / ml?

Ci * D = Cf --> D = Cf/Ci; (0.025 U / ml) / (5 x 10^5 U / ml) = 5 x 10 ^-8;

therefore want to carry out a serial dilution such that you have a total dilution of 5 x 10^-8, and so that your last diln = 200 ml. You need to use a serial dilution because you can't measure out volumes smaller than 1 µl.

These dilutions are more complex than simple 1:10 dilutions. For example, a 5 x 10^-8 dilution is not the same as a 1/ (5 x 10^8). This is the equivalent of a 5/10^8 dilution.

Therefore the easiest way to solve these problems is to break them into 2 parts. Another way of writing 5/10^8 is (5/10) * (1/10^7). So to perform this dilution, first take 5 parts of the stock and add it to 5 parts diluent = 5/10 dilution. Then dilute this stock 1 x 10^-7 ( ie, 1/1000, then 1/1000, then 1/10). Your last 1/10 can be done so that the final volume = 200 ml, i.e 20 ml solute and 180 ml diluent.

6. If you have a stock solution of 3 M potassium chloride (KCl, a powder), how would you make up 200 ml of a 5 µM (micromolar) solution of KCl?

Ci * D = Cf --> D = Cf/Ci; (5 x 10^-6) / 3 = 1.7 x 10 ^-6

therefore want to carry out a serial dilution such that you have a total dilution of 1.7 x 10^-6, and so that your last diln = 200 ml. You need to use a serial dilution because you can't measure out volumes smaller than 1 µl. This problem is similar to #5. Various answers, ie 1.7 ml stock + 10 ml H2O (=1.7/10 dilution), then 1ml that dilution + 999 mls H2O (=1.7 *10^-4), then 2 ml first diln + 198 mls H2O (=1.7 * 10^-6)

7. Describe three separate ways in which you could dilute something 1:100.

various answers, i.e, a)1 ml solute + 99 mls diluent

b) 1 ml stock + 9 mls H2O, then 1 ml first diln + 9 mls H2O (=10^-2)

c) 1 gallon stock + 99 gallons diluent; or a 1/5 diln followed by a 1/20 diln

8. For a particular analysis, you need to dilute a commercial tequila 1 x 10^-12. What is a

reasonable way of doing this? need to carry out a serial dilution such that you have a total dilution of 1 x 10^-12. You need to use a serial dilution because you can't measure out volumes smaller than 1 µl. Various answers, ie 1 ml tequila + 999 mls H2O (=10^-3), then another 10^-3, another 10^-3, another 10^-3 = 10^-12

1/4 * 1/10 * 7/570 = 3.1 x 10 ^-4

Set #2

1. How would you prepare 500 mls of a 15% sodium chloride (NaCl, a powder) solution in water?

2. How would you prepare 700 mls of a 15% ethanol (C₂H₆O) solution in water?

3. How would you prepare 1.5 L of a 0.3 M sodium chloride (NaCl, a powder) solution in water?

4. How would you prepare 0.7 L of a 0.5 m sodium chloride (NaCl, a powder) solution in water?

7. Describe three separate ways in which you could dilute something 1:10.

8. For a particular analysis, you need to dilute a commercial tequila 1 x 10^-15. What is a

reasonable way of doing this?

9. If you were to add 1 gallon of blood to 6 gallons of water, and then take 2 ounces of that dilution and add it to 9 ounces of water, and then take 7 mls of that dilution and add it 533 mls of water, what would the final dilution be?

10. If you were to dilute shark liver oil 1 x 10^-4, and then found that the concentration of a particular fatty acid was 3 pg / L in that dilution, what was the concentration of that fatty acid in undiluted shark liver oil? (pg = picogram)

1. How would you prepare 500 mls of a 15% sodium chloride (NaCl, a powder) solution in water? 500 ml * 0.15 g NaCl / ml = 75 g NaCl; measure 75 g NaCl, add H2O to 500 ml

2. How would you prepare 700 mls of a 15% ethanol (C₂H₆O) solution in water?

700 ml soln * 0.15 ml ethanol / ml soln= 105 ml ethanol; measure 105 ml ethanol, add 450 ml H2O

3. How would you prepare 1.5 L of a 0.3 M sodium chloride (NaCl, a powder) solution in water?1.5 L * 0.3 M NaCl / L * 58.5 g NaCl /mole = 26.32 g NaCl; measure 26.32 g NaCl and add water to 1.5 L

4. How would you prepare 0.7 L of a 0.5 m sodium chloride (NaCl, a powder) solution in water? 0.7 L x 0.5 m NaCl / L H20 * 58.5 g NaCl /mol = 2.97 g NaCl

measure 2.97 g NaCl, add 700 mls H2O

7. Describe three separate ways in which you could dilute something 1:10.

various answers, i.e, a)1 ml solute + 9 mls diluent

b) 1 ml stock + 4 mls H2O, then 1 ml first diln + 1 mls H2O (=10^-1)

c) 1 gallon stock + 9 gallons diluent; or a 1/2.5 diln followed by a 1/4 diln

8. For a particular analysis, you need to dilute a commercial tequila 1 x 10^-15. What is a

reasonable way of doing this? need to carry out a serial dilution such that you have a total dilution of 1 x 10^-15. You need to use a serial dilution because you can't measure out volumes smaller than 1 µl. Various answers, ie 1 ml tequila + 999 mls H2O (=10^-3), another 10^-3, another 10^-3, another 10^-3, another 10^-3 = 10^-15

9. 9. If you were to add 1 gallon of blood to 6 gallons of water, and then take 2 ounces of that dilution and add it to 9 ounces of water, and then take 7 mls of that dilution and add it 533 mls of water, what would the final dilution be? D = parts solute / (parts solute + parts diluent) 1/7 * 2/11 * 7/540 = 3.4 x 10 ^-4

3 x 10^4 pg / L, or 30 ng/L

Set #3

1. How would you prepare 200 mls of a 5% sodium chloride (NaCl, a powder) solution in water?

2. How would you prepare 600 mls of a 12% ethanol (C₂H₆O) solution in water?

3. How would you prepare 1.3 L of a 0.9 M sodium chloride (NaCl, a powder) solution in water?

4. How would you prepare 0.5 L of a 0.1 m sodium chloride (NaCl, a powder) solution in water?

7. Describe three separate ways in which you could dilute something 1:1000.

8. For a particular analysis, you need to dilute a commercial tequila 1 x 10^-14. What is a

reasonable way of doing this?

9. If you were to add 6 gallon of blood to one gallons of water, and then take 2 ounces of that dilution and add it to 11 ounces of water, and then take 7 mls of that dilution and add it 33 mls of water, what would the final dilution be?

10. If you were to dilute shark liver oil 1 x 10^-4, and then found that the concentration of a particular fatty acid was 6.5 pg / L in that dilution, what was the concentration of that fatty acid in undiluted shark liver oil? (pg = picogram)

1. How would you prepare 200 mls of a 5% sodium chloride (NaCl, a powder) solution in water? 200 ml * 0.05g NaCl /ml =10 g NaCl; measure 10 g NaCl, add H2O to 200 ml

2. How would you prepare 600 mls of a 12% ethanol (C₂H₆O) solution in water?

600 ml soln * 0.12 ml ethanol / ml soln= 72 ml ethanol; measure 72 ml ethanol, add 527 ml H2O

3. How would you prepare 1.3 L of a 0.9 M sodium chloride (NaCl, a powder) solution in water?1.3 L * 0.9 M NaCl / L * 58.5 g NaCl /mole = 68.4 g NaCl; measure 68.4 g NaCl and add water to 1.3 L

4. How would you prepare 0.5 L of a 0.1 m sodium chloride (NaCl, a powder) solution in water? 0.5 L x 0.1 m NaCl / L H20 * 58.5 g NaCl /mol = 2.95 g NaCl

measure 2.95 g NaCl, add 500 mls H2O

7. Describe three separate ways in which you could dilute something 1:1000.

various answers, i.e, a)1 ml solute + 999 mls diluent

b) 1 ml stock + 4 mls H2O, then 1 ml first diln + 199 mls H2O (=10^-3)

c) 1 oz stock + 999 oz diluent; or a 1/2.5 diln followed by a 1/400 diln

8. For a particular analysis, you need to dilute a commercial tequila 1 x 10^-14. What is a

reasonable way of doing this? need to carry out a serial dilution such that you have a total dilution of 1 x 10^-14. You need to use a serial dilution because you can't measure out volumes smaller than 1 µl. Various answers, ie 1 ml tequila + 999 mls H2O (=10^-3), another 10^-3, another 10^-3, another 10^-3, another 10^-2 = 10^-14

6/7 * 2/13 * 7/40 = 2.3 x 10 ^-2

6.5 x 10^4 pg / L, or 65 ng/L