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Using Units of Measurement

Jeff Lawrence (Z31)

Concentrated solutions can be expressed in terms of fold-concentrated. If a standard, final concentration is termed 1X (1 fold concentrated), a solution concentrated ten-fold is termed 10X. A 1X solution can be made from a 10X solution be diluting the 10X solution ten-fold. Examples:
Amount
Final (1X) stock
__Conc. Stock Fold for 1L How? __
50 mg/ml 50 mg/ml 1000 X 1 mL (50,000 mg/ml)/(50 mg/ml) = 1000
10 mg/ml 50 mg/ml 5000 X 200 mL (50,000 mg/ml)/(10 mg/ml = 5000
20 mg/ml 10 mg/ml 500 X 2 mL
0.2% 40% 200 X 5 mL (5 mL)*(200X) = (1000 mL)*(1X)
0.4% 40% 100 X 10 mL (10 mL)*(100X) = (1000 mL)*(1X)
1% 40% 40 X 25 mL
50 mM 1 M 20 X 50 mL
20 mM 1 M 50 X 20 mL
20 mM 0.4 M 20 X 50 mL 0.4 M=400 mM; (400 mM)/(20 mM)=20X

1. Make 20 mL of 5 M NaOH, molecular weight 40 g/mol:
1 M = 40 g/L
1 M = 4g/(100 mL)
1 M = 0.4g/(10 mL)
1 M = 0.8g/(20 mL)
5 M = 4.0 g/(20 mL)
∴ Add 4 g NaOH to 20 mL water

2. Make 100 mL of a 200X stock for ampicillin, used at a final concentration of 50 mg/ml:
1X = 50 mg/ml
200X = 200*50 mg/ml = 10,000 mg/ml = 10 mg/ml
(10 mg/ml)*(100 mL) = 1000 mg = 1 g
∴ Add 1 g ampicillin to 100 mL water

3. How much of this stock do I use to make plates with a concentration of 20 mg/ml ampicillin?
(10,000 mg/ml stock)/(20 mg/ml final) = 500X
∴ Use 1 mL of this stock for every 500 mL plates; or 2 mL per liter.

4. If 200X methionine is 0.9%, what is the final concentration in plates?
(0.9%)/200 = .0045%
OR:
0.9% = 0.9g/(100 mL) = 0.009g/ml = 9 mg/ml = 9000 mg/ml
&there4 conc. is (9000 mg/ml)/200 = 45 mg/ml

5. How much 40% galactose is added to make 500 mL of MacConkey-Galactose?
MacConkey plates use 1% final concentration of galactose
(40%)/(1%) = 40X
∴ Use 1 mL per 40 mL plates
(500 mL)/(40 mL) = 12.5
∴ Use 12.5 mL of 40% galactose to make 500 mL of 1% galactose

Last Update: Thursday June 19 2014
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Eric Kofoid
eckofoid at ucdavis.edu