Concentration conversion:?

Question

I'm trying to wrap my mind around this question, but it seems its slightly eluding me. Anyways the total question is:

Glucose, a major energy-yielding nutrient, is present in bacterial cells at a concentration of about 1 mM. What is the concentration of glucose, expressed as mg/mL? How many glucose molecules are contained in a typical E. coli cell? (Recall that Avogadro's number = 6.023x1023.)

So, what I've thought out so far is that, 1 M = 1 mol/L, but then I get stuck at the idea, that I need to convert from 1 mol = 6.023x1023 atoms, but how is that suppose to help with the first part. The second part I can see, thats the number of glucose molecules are 1mM = 1x10-3 M x 6.023x1023 = 6.023x1020moles. I don't think thats correct.

Answer 1

How many glucose molecules are contained in a typical E. coli cell, varies with the volume of the E coli cell.

both the diameter & the length of the E coli rod varies.

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find volume of cell:

using "E. Coli cells are about 2μm long and 0.8μm in diameter" as an approximate average: the diameter of this cylinder 1.0053 um^3  (using the formula of V = πr2h)

1.0053 um^3 @ ...   1 cubic micrometer = 1.0e-15 liter = 1.005 e-15 litres

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find moles in cell, knowing that 1 mM = 1e-3 Molar:

1.005 e-15 litres @ 1e-3 Mol / litre = 1.0053-18 moles of glucose / cell

find molecules:

1.0053-18 mol glucose @ 6.022e23 molecules / mole = 6.054 e5 molecules

your answer @ 1 sig fig : 6e5 molecules of glucose / cell

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@ 1 mM,  What is the concentration of glucose, expressed as mg/mL?

1 mM equals 1e-3 moles / litre , ... equals 1e-6 moles / milliliter

1e-6 moles @ 180.16 g / mol = 1.8 e-4 grams / milliliter

@ 1000 mg / gram...your answer is: 1.8 e-1 mg / ml  (aka 0.18 mg/ml)

but "1mM" has only 1 sig fig. rounding off to 1 sig fig gives

your answer: 0.2 mg/ml