Question

Dissolving 100 mg of protein x in 100 ml of water molecular wt of protein x is 15000 da

Answer 1

molar mass of 15,000 g mol−1.

First of all, I should mention that the problem is actually giving you the molecular mass of the protein, not its molecular weight.

The term molecular weight is currently used to denote relative molecular mass, which expresses the mass of a given molecule relativeto 112th of the mass of single carbon-12 atom. This implies that molecular weight is unitless.

On the other hand, molecular mass is expressed in unified atomic mass units, u, or daltons, Da.

More specifically, you have

1 u = 1 Da−−−−−−−−−−−−

Now, the thing to remember about the unified atomic mass unit is that it's equivalent to

1 u = 1 g mol−1−−−−−−−−−−−−−−−−−

In this case, a single protein X has a molecular mass of 15,000 Da, or 15,000 u, which means that it has a molar mass of

15,000u⋅1 g mol−11u=15,000 g mol−1

This means that one mole of protein X has a mass of 15,000 g

Now, use the molar mass of protein X to calculate how many moles you have in your sample

100mg⋅1g103mg⋅1 mole X15,000mg=6.667⋅10−6moles X

Since molarity is defined as the number of moles of solute present in one liter of solution, the molarity of your solution will be

c=6.667⋅10−6moles X100⋅10−3L=6.667⋅10−5mol L−1

I'm assuming that you need the molarity in micromoles per liter, μmol L−1

6.667⋅10−5molL−1⋅106μmol1mol=67.μmol L−1−−−−−−−−−−−−