Question

You are given a stock soltuion of (-)-epicatechin (EC, MW=290.26 g/mol) in water (0.94 mg/mL). You prepare a series of solutions by serial dilution as follows: (1) diluting 0.5 mL of the stock solution to 10 mL with water (solution A), (2) diluting 1.5mL of solution A with 4 mL of water (solution B), and (3) diluting 3 mL solution B with 9 mL water (Solution C). What is the concentration of solution C (mg/mL and microM)? What is the overall DF? How many "fold" has the stock solution been diluted to solution C?

Answer 1

Let the stock solution volume is 1000 mL

Now, the amount of epicatechin = 0.94 mg per mL of water

1000 mL solution contains = 1000 x 0.94 = 940 mg of epicatechin = 0.94 g

No of moles of epicatechin = Mass / Molar mass

= 0.94 g / 290.26 g/mol

= 0.0032 mol

Concentration of stock solution = 0.0032 mol/1000 mL = 0.0032 mol/L

Solution A -

Stock solution volume = V1 = 0.5 mL = 0.5/1000 L

Stock solution concentration = C1 = 0.0032 mol/L

Solution volume of A (V2) = (0.5+10) = 10.5 mL = 10.5/1000 L

Concentration of Solution A = C2 =?

Since V1 X C1 = V2 X C2

or , (0.5/ 1000 ) x 0.0032 = (10.5 /1000) x C2

or, C2 = 1.52 X 10^-4 mol/L

Solution B -

Solution A volume = V1 = 1.5 mL = 1.5/1000 L

Solution A concentration = C1 = 1.52 X 10^-4 mol/L

Solution volume of A (V2) = (1.5+4) = 5.5 mL = 5.5/1000 L

Concentration of Solution B = C2 =?

Since V1 X C1 = V2 X C2

or , (1.5/ 1000 ) x 1.52 X 10^-4 = (5.5/1000) x C2

or, C2 = 4.14 X 10^-5 mol/L

Solution C -

Solution B volume = V1 = 3 mL = 3/1000 L

Solution B concentration = C1 = 4.14 X 10^-5 mol/L

Solution volume of A (V2) = (3+9) = 12 mL = 12/1000 L

Concentration of Solution C = C2 =?

Since V1 X C1 = V2 X C2

or , (3 / 1000 ) x 4.14 X 10^-5 ​ = (12/1000) x C2

or, C2 = 1.035 X 10^-5 mol/L = 1.035 X 10^-5 M

Conentration in mg/mL

= (Concentration in mole x molar mass in mg/mol) / 1000 mL/L

= (1.035 X 10^-5 mol/L x 290.26 x 1000 mg/mol) / 1000 mL/L

= 0.003 mg/mol

Concentration in microM = 10^-6 M

1.035 X 10^-5 M = 1.035 x 10^-5 / 10^-6 microM = 10.35 microM

Dilution fold = 0.94 / 0.003 = 313.33 times