Calculate the amount needed for a certain concentraintion- please explain detailed so I understand

Question

Calculate the amount of β-mercaptoethanol needed in a 15 ml extraction buffer to obtain a concentration of 10 mM. β-mercaptoethanol is available as a 98% (W/W) solution. Assume a molecular weight of 78.13 g/mol, ρ=1.114 g/ml.

thank you so much

Answer 1

Moles=Molarity×Volume

Molarity (concentration) = 10 mM = 10×10^-3 M = 0.01 M

Volume = 15 ml = 0.015 L

Moles of β-ME=0.01M×0.015L=0.00015moles

Convert moles to grams:

Mass of β-ME=0.00015 moles×78.13 g/mol=0.01172 g

Convert grams to volume (using density, ρ = 1.114 g/ml for the 98% solution):

Volume of β-ME solution=1.114(g/ml)/ 0.01172g​ = 0.0105ml = 10.5µl

Result: Add 10.5 µl of the 98% β-mercaptoethanol solution to your 15 ml buffer for a 10 mM concentration.