Question

The molecular mass of albumin is 60 kDa. What is the concentration of a 1.2 % m/m solution of albumin in milligrams per millilitre? What is the molar concentration?

Answer 1

The concentration of albumin is a) `"12 mg/mL"` and b) `2.0 × 10^"-4" color(white)(l)"mol/dm"^3`.

Explanation:

A dalton (Da) is simply another name for a unified atomic mass unit (u).

`"1 kDa = 1000 Da"`

Thus, an atomic mass of 60 Da is the same as a mass of 60 u.

A molecular mass of 60 kDa is the same as a mass of 60 000 u.

The question is really saying that the molar mass of albumin is 60 000 g/mol.

a) Concentration in milligrams per millilitre

A 1.2 % (m/m) solution contains 1.2 g of albumin in 100 g of solution.

Since the solution is so dilute, we can assume that its density is 1.00 g/mL.

`"Concentration" = (1.2 color(red)(cancel(color(black)("g albumin"))))/(100 color(red)(cancel(color(black)("g solution")))) × ("1000 mg albumin")/(1 color(red)(cancel(color(black)("g albumin")))) × (1 color(red)(cancel(color(black)("g solution"))))/("1 mL solution") = "12 mg albumin"/"1 mL solution"`

The concentration of albumin is 12 mg/mL.

b) Concentration in terms of molarity

`"Concentration" = (1.2 color(red)(cancel(color(black)("g albumin"))))/(100 color(red)(cancel(color(black)("cm"^3color(white)(l) "solution")))) × ("1 mol albumin")/("60 000" color(red)(cancel(color(black)("g albumin")))) × (1000 color(red)(cancel(color(black)("cm"^3color(white)(l) "solution"))))/("1 dm"^3 color(white)(l)"solution") = (2.0 × 10^"-4"color(white)(l) "mol albumin")/("1 dm"^3color(white)(l) "solution")`

The concentration of albumin is `2.0 × 10^"-4" color(white)(l)"mol/dm"^3`.