Question

Show your complete solution to earn points. Glucose, a major energy-yielding nutri￾ent, is present in bacterial cells at a concentration of about 1.6mM (mM=millimolar). 

What is the concentration of glucose, expressed as mg/mL? How many glucose mol￾ecules contained in a typical E. coli cell? (Recall Avogadro’s number= 6.023x1023)

Given: Glucose concentration= 1mM= 1x10-3 mol/L, Molecular weight=180g/mol, Vol￾ume= 1x10-15 L

Answer 1

To convert the concentration of glucose to mg/mL we use the molar mass of glucose (M= 180 g/mol) and the equivalency to mililiters to find:

$c = \frac{n}{V} = 1.6\, mM=\frac{1.6\, mmol\,glucose}{1\,L} * \frac{180\,mg\,glucose}{1\,mmol\,glucose}*\frac{1\,L}{10^3\,mL}$

$c = \frac{1.6\, \cancel{mmol\,glucose}}{1\,\cancel{L}} * \frac{180.156\,mg\,glucose}{1\,\cancel{mmol\,glucose}}*\frac{1\,\cancel{L}}{10^3\,mL}=0.288\frac{mg}{mL}$

Then, the number of glucose molecules N on a single E. coli cell can be found if we remember that N/N_A = n = c * V, where N_A is the Avogadro number. After rearranging we find that:

$N =c*V*N_A$

$N=(6.023\times10^{23}\frac{molecules}{\cancel{mol}})(\frac{1.6\times10^{-3}\cancel{mol}}{1\,\cancel{L}})(10^{-15}\cancel{L})$

$N=9.6368\times10^5\, molecules$

In conclusion, the concentration of glucose is 0.288 mg/mL and a typical E. coli cell has approximately 963680 molecules of glucose.

References:

• Chang, R. (2010). Chemistry. McGraw-Hill, New York.