Pharmacy calculation question

A patient requires an intravenous infusion of 0.9%w/v sodium chloride. In your hospital pharmacy department you have Water for Injections, BP and 4.5%w/v sodium chloride solution, BP. Assuming no volume displacements effects, which of the following volumes of 4.5%w/v sodium chloride solution, BP need to be added aseptically to an expandable PVC infusion bag containing 100ml Water for Injections,BP to produce the requisite sodium chloride concentration?

A. 25mL
B. 50mL
C. 100mL
D. 125mL
E. 150mL


To start out this looks pretty tricky! But actually quiet simple. You have a 4.5% solution ie there are 4.5g of Sodium Chloride in 100ml of the solution. 


C1V1=C2V2
4.5xV1=0.9x100 (you do not know the resulting volume of solution ie V2 but assume 100ml for the moment).
So, 4.5xV1=90
V1=90/4.5 = 20ml (you know this ACTUAL answer would be a little larger than this as there is an increase in volume)


So then check this answer with the options available. The closest here is 25ml. 25ml of a 4.5ml solution contains 1.125g of sodium chloride. So 1.125 in a 125ml solution is a 1.125/125x100 which is 0.9. So option A, would be the correct answer.