A plasmid of 3,200 bp is present in a solution at a concentration of $1.5\mu \text{g}/\mu \text{l}$. How many plasmid molecules are there in $10\mu \text{l}$ of this solution? (Use Avogadro’s number $6.022\times 10^{23}{\text{mol}}^{-1}$ and the average molecular weight of a base pair $660\text{Da}$.)

Step-by-step solution

1. Calculate the molecular weight of one plasmid: $3,200\text{bp}\times 660\text{Da/bp}=2.112\times 10^6{\text{g mol}}^{-1}$.
2. Find the total mass of plasmid in $10\mu \text{l}$: $1.5\mu \text{g/}\mu \text{l}\times 10\mu \text{l}=15\mu \text{g}=1.5\times 10^{-5}\text{g}$.
3. Convert mass to moles: $\text{moles}=\frac{1.5\times 10^{-5}\text{g}}{2.112\times 10^6{\text{g mol}}^{-1}}=7.1\times 10^{-12}\text{mol}$.
4. Multiply by Avogadro’s number to get number of molecules: $7.1\times 10^{-12}\text{mol}\times 6.022\times 10^{23}=4.28\times 10^{12}$.
5. Round to two significant figures: $4.3\times 10^{12}$ plasmid molecules.

Concept tested: Calculating plasmid copy number

Published 25 September 2026 · How this solution was prepared and checked