Q.No. 21 The number of molecules of a nucleotide of molecular weight 300 g/mol present in 10 picomoles is __________ x 1012 (round off to 2 decimal places).
Number of Nucleotide Molecules in 10 Picomoles
The number of molecules of a nucleotide (molecular weight 300 g/mol) in 10 picomoles is 6.02 × 1012. This numerical answer requires converting picomoles to moles and multiplying by Avogadro’s number, rounded to two decimal places.
Step-by-Step Solution
- Number of moles = amount in picomoles × 10-12, since 1 picomole = 10-12 mol. For 10 picomoles, moles = 10 × 10-12 = 1 × 10-11 mol.
- Number of molecules = moles × Avogadro’s number (6.022 × 1023 molecules/mol). Thus, 1 × 10-11 × 6.022 × 1023 = 6.022 × 1012.
- Divide by 1012 and round: 6.022 × 1012 / 1012 = 6.022, so x = 6.02 (rounded to 2 decimal places).
Precise Calculation
- Moles = 10 × 10-12 = 10-11 mol
- Molecules = 10-11 × 6.02214076 × 1023 = 6.02214076 × 1012
- Thus, x = 6.02 (rounded to 2 decimal places)
Note on Options
This fill-in-the-blank has no MCQ options; it’s numerical. Common errors include forgetting pico-to-mole conversion (10-12) or using wrong Avogadro value, leading to off-by-1012 or factor errors.
In competitive exams like GATE Biotechnology or IIT JAM, such questions test mole concept application to biomolecules. The molecular weight (300 g/mol) is given but unused here, as molecule count depends only on moles, not mass for count (mass would be moles × MW = 10-11 × 300 = 3 × 10-9 g, but irrelevant).
Practice tip: Memorize 1 pmol = 10-12 mol × NA ≈ 6.02 × 1011 molecules per pmol, so 10 pmol = 6.02 × 1012.
For variations, if mass-based, divide mass by MW for moles first.
Exam Relevance
- GATE BT 2020 Q21: Exact question; answer 6.02
- IIT JAM Prep: Builds on stoichiometry; similar in CY/BL papers
- Common Pitfalls: Confusing pico (10-12) with nano (10-9); always convert units explicitly
