molecular biology tough question.?

Question

To the nearest power of ten, how many protein molecules with a molecular weight of 25,000 are found in a crystal that is 3 mm on each side? Assume that a crystal is 50% water and that the density of a protein is the same as that of water.

Answer 1

Water has a density - pretty much by definition - of 1 kg per liter. And a liter is equal to a cubic decimeter or a million cubic mm.

Assuming that your crystal is a cube, being 3 mm on a side gives it a volume of 27 cubic mm or 2.7 x 10 -5 L. If it were just water, that amount would weigh 2.7 x 10^-5 kg or 0.027 g.

The problem with the question is that it doesn't specify whether the crystal is 50% by molecule count or 50% by mass. I suspect it meant mass, so we'll go with that. Half the mass would be 0.0135 g.

A mole of something would have a mass in grams equal to its molecular weight. So one mole of protein molecules would weigh 25000 g. Dividing that into 0.0135 g tells us that we have 5.4 x 10^-7 moles of protein.

One mole is 6.022 x 10^23 molecules. We have 5.4 x 10-7 moles. Multiplication tells us that we have 3.25 x 10^17 molecules. Rounding to the nearest power of ten suggest that we have about 10^17 protein molecules in that crystal (about a hundred thousand million million).

Lots!