Question

An E. coli cell contains about 2.6 x 10⁸ions, which constitute about 1% of the mass of the cell, and each ion has an average molecular mass of40g.

(a) What is the approximate mass of the cell?

(b) The same cell contains about 2 x 10⁸ carbohydrate molecules, which have an average molecular mass of 150g. mol^-1. Approximately what percentage of the cell's mass is carbohydrate?

(c) The molecular mass of E. coli DNA is about 5.6 x 10⁹g . mol^-1, and it accounts for about 6%of the cell's mass. How many DNA molecules does the cell contain?

Short answer

Answer

1. The approximate mass of the cell is $1.7\times {10}^{-12}$g.
2. The approximate percentage of the cell's mass is carbohydrate are 2.8% .
3. Only one DNA molecule exists in E. coli cells.

Step-by-step solution

Definition of Concept

Compound molecules contain atoms from two or more different elements.Water (H2O), for example, has three atoms: two hydrogen (H) atoms and one oxygen (O) atom.

Find the approximate mass of the cell

$$\begin{gathered} \left(a\right)Considerthegiveninformation: \\ {N}_{ions}=2.6\times {10}^8 \\ {N}_{ions}=\frac{N}{N_A} \\ =4.32\times {10}^{-16} \\ Where{N}_{A}isAvogadro\text{'}scons\tan t,6.022\times {10}^{24}mo.l \\ Theionmasspercentis1\%. \\ DividethemassofionsbythemasspercenttofindthemassofE.coli. \\ {m}_{cell}=\frac{m_{ions}}{w_{ions}} \\ =\frac{1.7\times {10}^{-14}g}{1\%} \\ =1.7\times {10}^{-12} \\ Therefore,therequiredapproximatemassofthecellis=1.7\times {10}^{-12}. \end{gathered}$$

Find the approximate percentage of the cell's mass is carbohydrate

$$\begin{gathered} \left(b\right)Considerthegiveninformation: \\ {N}_{carbohydrates}=2\times {10}^8 \\ {n}_{carbohydrates}=\frac{N}{N_A} \\ =3.32\times {10}^{-16} \\ M=150g^{-1}mol \\ {m}_{carbohydrates}=n\times M \\ =4.98\times {10}^{-14}g \\ Puttingthevaluesinthegivenformula, \\ {W}_{carbohydrates}=\frac{m_{carbohydrates}}{m_{cell}} \\ =0.028 \\ =2.8\% \\ Therefore,therequiredapproximate \\ percentageofthecell\text{'}smassiscarbohydrateare2.8\%. \end{gathered}$$

Find the number of DNA molecules does the cell contain

$$\begin{gathered} \left(c\right)Considerthegiveninformation: \\ {M}_{DNA}=5.6\times {10}^{9}gmo{l}^{-1} \\ w=0.6\% \\ Puttingthevaluesinthegivenformula, \\ {m}_{DNA=}W\times m_{cell} \\ =0.6\%\times 1.7\times {10}^{-12}g \\ =1\times {10}^{14}g \\ {N}_{DNA}=\frac{m_{DNA}}{m_{DNA}}\times N_A \\ =1 \\ Therefore,onlyonemoleculeofDNAinE.colicell. \end{gathered}$$