Question #200355

Show your complete solution to earn points. Glucose, a major energy-yielding nutrient, 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 molecules 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, Volume= 1x10-15 L

Expert's answer

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.

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