Question

The required amount of adjusting substance required to make a hypotonic solution, isotonic is given by the (where, W = adjusting substance, a = freezing point depression of unadjusted solution and b= freezing point depression of water)

• A. \(W=\frac{a-0.52}{b}\)
• B. \(W=\frac{0.52-a}{b}\)
• C. \(W=\frac{0.52-b}{a}\)
• D. \(W=\frac{b-0.52}{a}\)

Answer 1

The Correct Option is B

To solve this question, we need to understand the relationship between freezing point depression and isotonic solutions.

An isotonic solution has the same osmotic pressure, and consequently, the same freezing point depression as physiological fluids like blood. To adjust a hypotonic solution to be isotonic, it is necessary to add a certain amount of an adjusting substance to reach the desired depression of the freezing point.

Given:

• \(a\) = freezing point depression of the unadjusted solution
• \(b\) = freezing point depression of water due to the added adjusting substance
• \(0.52\) = typical freezing point depression (in degrees Celsius) needed for a solution to be isotonic with human blood plasma.

The requirement is to achieve this isotonic point by compensating the existing condition (\(a\)) with an appropriate adjustment (\(b\)).

We use the formula:

\(W = \frac{0.52 - a}{b}\)

This formula translates to: The required amount \(W\) of the adjusting substance equals the difference between the desired isotonic freezing point depression (\(0.52\)) and the current depression (\(a\)), divided by the depression caused by the adjusting substance (\(b\)).

Let's verify this with the options:

• \(W=\frac{a-0.52}{b}\): This would be inappropriate as it suggests subtracting \(0.52\) from \(a\), a hypotonic condition.
• \(W=\frac{0.52-a}{b}\): This is the correct formula and matches our derivation above.
• \(W=\frac{0.52-b}{a}\), \(W=\frac{b-0.52}{a}\): Both do not match the required calculation logic.

Therefore, the correct answer is \(W=\frac{0.52-a}{b}\), as it correctly adjusts the solution to become isotonic by compensating the existing freezing point depression.