I 100 mL o a pharmaceutical preparation contains 20 mL o a 50% w/v solution o benzalkonium chloride, what is the percent strength o that agent in the solution

The percentage strength of the agent is 10 %

Since 100 mL of a pharmaceutical preparation contains 20 mL of a 50% w/v solution of benzalkonium chloride, we desire to find the percentage strength of that agent in the 100 mL solution.

Let C₁ = percentage strength of 20 mL solution = 50 %, V₁ = initial volume = 20 mL, C₂ = percentage strength of agent in 100 mL solution and V₂ = final volume = 100 mL.

Since the initial quantity of agent in 20 mL solution equals the final quantity of agent in 100 mL solution, we have that

C₁V₁ = C₂V₂

So, making C₂ = percentage strength of agent in 100 mL solution the subject of the formula, we have

C₂ = C₁V₁/V₂

Substituting the values of the variables into the equation, we have

C₂ = C₁V₁/V₂

C₂ = 50 % × 20 mL/100 mL

C₂ = 50 % × 0.2

C₂ = 10 %

So, the percentage strength of the agent is 10 %.

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