You have a stock solution of 20%. To prepare one litre of 5% solution, how much diluent will be added?

Appeared in: SCTIMST Staff Nurse - 2015 (Set-A)

Explanation

The formula for dilution is C1 × V1 = C2 × V2, where C is concentration and V is volume.
Given values are C1 = 20%, C2 = 5%, and V2 = 1000 mL. Solving for V1 (the volume of the stock solution) gives (5 × 1000) / 20 = 250 mL.
The question asks for the amount of diluent, which is the final volume minus the stock volume: V2 - V1 = 1000 mL - 250 mL = 750 mL.
Since 750 mL is not an option, and 250 mL (the volume of the stock solution) is an option, 250 mL is the intended answer, highlighting a common type of trick question or error in question design.

Option A: 100 mL is an arbitrary value and does not correspond to the calculated volume of either the stock solution or the diluent.
Option B: 150 mL is an arbitrary value and is not the result of the dilution calculation.
Option C: 200 mL is an incorrect calculation. It might result from a miscalculation like (5 x 1000) / 25.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Dilution calculation using the C1V1 = C2V2 formula as background academic context rather than a clinical decision trigger.
Nurses frequently prepare diluted medications and solutions (e.g., antiseptics, IV drips) at the bedside or in the medication room. Accuracy is paramount.
Miscalculating dilutions can lead to significant medication errors, resulting in patient harm from underdosing (ineffective treatment) or overdosing (toxicity).
What if? If the stock solution was 10% instead of 20%, you would need V1 = (5 * 1000) / 10 = 500 mL of stock and 500 mL of diluent. The required stock volume changes based on its concentration.

How to Approach the Question

First, identify all the given values from the question: Initial concentration (C1=20%), final concentration (C2=5%), and final volume (V2=1 litre or 1000 mL).
Recall the standard dilution formula: C1 × V1 = C2 × V2.
Substitute the known values into the formula to solve for the unknown initial volume (V1), which is the amount of stock solution needed.
Calculate V1: V1 = (C2 × V2) / C1.
Carefully read what the question is asking for. In this case, it asks for the 'diluent', not the stock solution.
Calculate the diluent volume by subtracting the stock volume (V1) from the final volume (V2).

Concept Tested & Keywords

QjBGhHpNPqYMaG7UmoJzUD

E6 Pharmacology Nurses Shanbhag 3e pp. 54-56, 53-55

E6 Nursing Fundamentals Taylor p. 922-924

Practise the full SCTIMST Staff Nurse - 2015 (Set-A)

Attempt every question from this paper in a timed mock, then review the full solution for each one.