Answers for Laboratory Calculation Problem Set #1

1. You need to make a 1:5 dilution of a solution. You need 10 ml of the diluted solution. How much initial sample and diluent should you use?

**Answer**: 1:5 dilution = 1/5 dilution = 1 part sample and 4 parts
diluent in a total of 5 parts. If you need 10 ml, final volume, then you need
1/5 of 10 ml = 2 ml sample. To bring this 2 ml sample up to a total volume of
10 ml, you must add 10 ml - 2 ml = 8 ml diluent.

2. How would you prepare 500 ml of a 10% NaCl solution?

**Answer**: In this problem, the % solution is the number of grams
solute in 100 ml solvent, so a 10% solution of NaCl is 10 grams NaCl in 100 ml
water. But you need 500 ml, final volume, so 10 g x 5 = 50 g NaCl.

3. If you have DNA with a concentration of 2 µg/µl, how much DNA (in µl) must be added to make a 20 µl solution with a DNA concentration of 1 µg/µl?

**Answer**: Since you know the initial concentration (2 µg/µl),
the final concentration (1 µg/µl), and the final volume (20 µl),
the following formula can be used to calculate the amount of DNA needed
(initial volume)

**(initial concentration)(initial volume) = (final concentration)(final volume)**- (2 µg/µl)(X µl) = (1 µg/µl)(20 µl)
- X µl = (1 µg/µl)(20 µl) / 2 µg/µl
- X µl = 10 µl DNA

4. You have a 10x TBE buffer. To run a gel, you need 500 ml of a 2x solution of TBE. How do you make a 500 ml solution of 2x TBE buffer from the 10x buffer?

**Answer**: Since you know the initial concentration (10x), the final
concentration (2x), and the final volume (500 ml), you can use the formula:

**(initial concentration)(initial volume) = (final concentration)(final volume)**- (10x)(X ml) = (2x)(500 ml)
- X ml = (2x)(500 ml) / 10x
- X ml = 100 ml of 10x TBE

Then, to calculate the amount of water needed, use the following formula:

**final volume - initial volume = volume of diluent**- 500 ml total - 100 ml of 10x TBE = 400 ml water

5. You want to make a 0.5% agarose gel. How much agarose (in grams) do you need to make up a 50 ml gel solution?

**Answer**: There are at least two methods for solving this question
(as with many dilution problems): logically and mathmatically.

**Logically**:- 0.5% means 0.5 grams in 100 ml, so if you only need 50 ml, you need 0.5 g / 2 = 0.25 g agarose for a 50 ml gel solution.
**Mathematically**:- 0.5 g/100 ml = X g/50 ml
- (0.5 g) (50 ml)/100 ml = X g
- 0.25 g = X g

6. What is the DNA concentration of a 50 µl solution which contains 10 µl of DNA at a concentration of 4 µg/µl?

**Answer**: There are two ways to solve this problem:

- Calculate the total amount of DNA in the solution, then divide by the
total volume:
- 10 µl x 4 µg/µl = 40 µg of DNA
- 40 µg DNA/ 50 µl = 0.8 µg/µl

- Just plug the values into the formula:
- (initial concentration)(initial volume) = (final concentration)(final volume)
- (4 µg/µl)(10 µl) = (X µg/µl)(50 µl)
- X µg/µl = (4 µg/µl)(10 µl) / 50 µl
- X µg/µl = 0.8 µg/µl

7. How would you make a 3x TBE buffer from a 12x TBE buffer for a total volume of 200 ml?

**Answer**: Since you know the initial concentration (12x), the final
concentration (3x), and the final volume (200 ml), you can use the formula:

- (initial concentration)(initial volume) = (final concentration)(final
volume)
- (12x)(X ml) = (3x)(200 ml)
- X ml = (3x)(200 ml) / 12x
- X ml = 50 ml of 12x TBE

Then, to calculate the amount of water needed;

- 200 ml final volume - 50 ml initial volume of 12x TBE = 150 ml water (diluent)

Thanks are given to Tim Allen and the MMG graduate students for providing these problems.

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