GATE2013-48

Question

A solution was prepared by dissolving $\text{100 mg}$ of protein $X$ in $\text{100 ml}$ of water. Molecular weight of protein $X$ is $\text{15,000 Da};$ Avogadro’s number = $6.022\times 10^{23}$.

Calculate the molarity$(\mu M)$ of the resulting solution.

• A. $66.6$
• B. $6.6$
• C. $0.67$
• D. $0.067$

Answer 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=66.6 μmol L−1