Question

If one synthesized every possible DNA molecule, each with 20 subunits, how much would your collection of molecules weigh? the average molecular mass of a DNA subunit is 165 g mol⁻¹.

Answer 1

Answer 2

Count All Possible DNA Combinations:

• Each of the 20 subunits can be A, T, C, or G (4 choices).

• Total combinations = $4^{20}$ ≈ 1.1 trillion unique sequences.

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1. Weigh One DNA Molecule:

• Each subunit weighs 165 g/mol.

• A 20-subunit DNA molecule weighs:

  $$20\times 165=3,300\text{g/mol}\mathrm{.}$$

2. Convert to Grams per Molecule:

• Avogadro’s number tells us $6.022\times 10^{23}$ molecules = 1 mole.

• So, one molecule weighs:

  $$\frac{3,300\text{g/mol}}{6.022\times 10^{23}}=5.48\times 10^{-21}\text{g}\text{(a vanishingly small number!)}\mathrm{.}$$

3. Multiply by Total Sequences:

• Total weight = (1.1 trillion sequences) × (5.48 × 10⁻²¹ g/molecule).

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• Final weight = 6.02 × 10⁻⁹ g (6.02 nanograms).

4.