A solution was prepared by dissolving 100 mg of protein X in
100 ml of water.
Molecular weight of protein X is 15,000 Da;
Avogadro’s number = 6.022 × 1023.
Q.48 Calculate the molarity (μM) of the resulting solution.
- (A) 66.6
- (B) 6.6
- (C) 0.67
- (D) 0.067
Calculate Protein X Solution Molarity: 100 mg in 100 ml (15,000 Da)
Step-by-Step Calculation
1. Convert mass to grams: 100 mg = 0.1 g
2. Calculate moles: Moles = mass (g) / MW (g/mol) = 0.1 / 15,000 = 6.667 × 10⁻⁶ mol
3. Volume conversion: 100 ml = 0.1 L
4. Molarity (M): M = moles / L = 6.667 × 10⁻⁵ M
5. Convert to μM: 6.667 × 10⁻⁵ M × 10⁶ = 66.6 μM
Avogadro’s number (6.022 × 10²³) confirms molecules per liter but is unnecessary for direct molarity calculation.
Why Option (A) 66.6 is Correct
This matches the formula 0.1/(15000 × 0.1) × 10⁶ = 66.6 μM exactly, standard for protein solutions where 1 mg/ml = 0.0667 mM = 66.7 μM.
Explanation of Incorrect Options
- (B) 6.6: Results from using 1 L volume instead of 0.1 L (0.1/(15000 × 1) × 10⁶ = 6.67 μM)
- (C) 0.67: From mass in mg without gram conversion or volume error (100/(15000 × 0.1) × 10⁶ = 6667 μM, mismatched)
- (D) 0.067: Matches mM value (0.0667 mM), confusing units where 1 mM = 1000 μM
Quick Reference Table
| Option | Value (μM) | Common Mistake | Calculation Error |
|---|---|---|---|
| A | 66.6 | Correct | None |
| B | 6.6 | Volume as 1 L | Divide by 10 extra |
| C | 0.67 | Mass units wrong | mg instead of g |
| D | 0.067 | Unit confusion | Reported as mM |
