Question

Question:The average distance between base pairs measured parallel to the axis of a double-helical DNA molecule is 3.4 angstroms. The average molecular weight of a pair of nucleotides is about 650 g mol-1. What is the approximate length in millimeters of a single DNA molecule of molecular weight 2.8 × 109 g mol-1 (a value typical for the DNA of some bacteria)? About how many base pairs does this DNA contain?

Short answer

The number of base pairs present in the deoxyribonucleic acid (DNA) molecule is $4.6\times {\text{10}}^{\text{6}}$, and the length of the single DNA is 1.5mm.

Step-by-step solution

Calculate the number of base pairs.

The distance between base pairs measured parallel to the axis of a double-helical deoxyribonucleic acid (DNA) molecule is$3.4\stackrel{\circ }{A}$.

The average molecular weight or molar mass of a pair of nucleotides is${\text{650 gmol}}^{\text{- 1}}$.

The molecular weight of a single deoxyribonucleic acid (DNA) molecule is$2.8\times {\text{10}}^{\text{9}}{\text{gmol}}^{\text{- 1}}$ respectively

Calculate the number of base pairs in the deoxyribonucleic acid (DNA)

Number of base pairs = $\frac{2.8\times {\text{10}}^{\text{9}}{\text{gmol}}^{\text{1}}}{{\mathbf{\text{650 gmol}}}^{\mathbf{\text{- 1}}}}$

The number of base pairs present in deoxyribonucleic acid (DNA) is $4.3\times {\text{10}}^{\text{6}}$.

Calculate the length of a single deoxyribonucleic acid (DNA).

Now determine the length of the single DNA molecule using the conversion factor.

$=\left(4.3\times {10}^6\right)\times 3.4\stackrel{\circ }{A}$ $\left(\text{1}\stackrel{\circ }{A}{\text{= 10}}^{\text{- 7}}\text{mm}\right)$

role="math" localid="1663571838907" $=\left(4.3\times {10}^6\right)\times 3.4\stackrel{\circ }{A}\times \frac{{10}^{\text{- 7}}\text{mm}}{1\stackrel{\circ }{A}}$

data-custom-editor="chemistry" $$\begin{gathered} \text{= 14.62}\times {\text{10}}^{\text{- 7}}\text{mm} \\ \text{= 1.5 mm} \end{gathered}$$

The approximate length of a single deoxyribonucleic acid (DNA) molecule is 1.5mm.