Q.75 You have a 50 mg/mL stock solution of arginine. To prepare 1 liter of growth medium for
an arginine auxotroph that requires 70 μg/mL of arginine, the volume of this stock solution
that should be added is _____________ mL (up to 1 decimal point) .

Preparing a growth medium for an arginine auxotroph using a 50 mg/mL arginine stock
solution to achieve a final concentration of 70 μg/mL in 1 liter is a standard
calculation in microbiology and biotechnology. This type of problem is frequently asked in
CSIR NET Life Sciences exams and emphasizes correct unit conversion and dilution principles.

Calculation Steps

The stock solution concentration is 50 mg/mL. Since
1 mg = 1,000 μg, this is equivalent to:

50 mg/mL = 50,000 μg/mL

The required final concentration is 70 μg/mL in a total volume of
1 liter (1,000 mL).

Total arginine needed:

70 μg/mL × 1,000 mL = 70,000 μg

Let V be the volume (in mL) of stock solution required. Then:

50,000 × V = 70,000

Solving for V:

V = 70,000 / 50,000 = 1.4 mL

Therefore, 1.4 mL of the 50 mg/mL arginine stock solution is required.

Unit Conversion and Dilution Formula

The dilution can also be calculated using the standard dilution equation:

C₁V₁ = C₂V₂

• C₁ = 50,000 μg/mL (stock concentration)
• C₂ = 70 μg/mL (final concentration)
• V₂ = 1,000 mL (final volume)

Substituting values:

50,000 × V₁ = 70 × 1,000

V₁ = 1.4 mL

Step-by-Step Dilution Summary

• Convert stock concentration: 50 mg/mL = 50,000 μg/mL
• Calculate total arginine required: 70 μg/mL × 1,000 mL = 70,000 μg
• Calculate stock volume needed: 70,000 / 50,000 = 1.4 mL
• Add 1.4 mL of stock to 1 liter of base medium

Context for Auxotroph Studies

Arginine auxotrophs are mutant strains that cannot synthesize arginine and must obtain it from
their growth medium. Supplementing the medium with an exact concentration of arginine
(70 μg/mL in this case) ensures proper growth without excess supplementation, which is
critical in experiments involving bacterial or yeast genetics.

Common Errors and Explanations

• Forgetting to convert mg/mL to μg/mL, leading to incorrect volumes
• Ignoring the total final volume of 1,000 mL
• Misapplying the dilution formula

Using the correct approach, the dilution formula C₁V₁ = C₂V₂
clearly confirms the correct answer as 1.4 mL.

CSIR NET Exam Tips

Such questions test your ability to handle unit conversions and dilution calculations accurately.
They are common in Life Sciences exams, especially in microbiology and biotechnology sections.
Always convert units first, write down the dilution formula, and solve step by step to avoid mistakes.