Ordered is cephalothin 500 mg IM. The medication label states: the addition or 4 ml of sterile water yields 0.5 g in 2.2 ml of suspension

What is the Rx? And S? Show all work

1 answer

Rx: Cephalothin 500 mg IM
S: Add 4 ml of sterile water to yield 0.5 g in 2.2 ml of suspension

To find the concentration of cephalothin in the suspension, we can use the equation:
Concentration (C) = amount of drug (A) / volume of solution (V)

Given information:
1 g of cephalothin is equivalent to 1000 mg

Amount of drug (A) = 500 mg
Volume of solution (V) = 2.2 ml

Concentration (C) = A / V = 500 mg / 2.2 ml = 227.27 mg/ml

We are given that adding 4 ml of sterile water yields 0.5 g (500 mg) of cephalothin in 2.2 ml of suspension. Therefore, we need to find the amount of water required to dissolve 500 mg of cephalothin.

Let x be the amount of water in ml.

Since we are adding 4 ml of sterile water in total, the volume of the suspension will be 2.2 ml + x ml.

Now we can set up a proportion to solve for x:
500 mg / 2.2 ml = 500 mg / (2.2 ml + x ml)

Cross multiplying, we get:
500 mg * (2.2 ml + x ml) = 500 mg * 2.2 ml

Simplifying, we have:
1100 ml * mg + 500 mg * x ml = 1100 mg * ml

Dividing both sides by 500 mg, we have:
2.2 ml + x ml = 2.2 ml

Subtracting 2.2 ml from both sides, we get:
x ml = 0 ml

This tells us that no additional water is needed to dissolve 500 mg of cephalothin in 2.2 ml of suspension. Therefore, the Rx is to add 4 ml of sterile water to yield 0.5 g in 2.2 ml of suspension.