Q. 2.66 - An Introduction to General, Organic, and Biological Chemistry

Question

Using conversion factors, solve each of the following clinical problems:

a. A nurse practitioner prepares an injection of promethazine, an antihistamine used to treat allergic rhinitis. If the stock bottle is labeled $25 \mathrm{mg}/\mathrm{mL}$ and the order is a dose of data-custom-editor="chemistry" $12.5 \mathrm{mg}$, how many milliliters will the nurse draw up in the syringe?

b. You are to give ampicillin data-custom-editor="chemistry" $25 \mathrm{mg}/\mathrm{kg}$ to a child with a mass of data-custom-editor="chemistry" $67 \mathrm{lb}$. If stock on hand is data-custom-editor="chemistry" $250 \mathrm{mg}/\mathrm{capsule}$, how many capsules should be given?

Step-by-Step Solution

Answer

(a) The $0.50 \mathrm{mL}$ will the nurse draw up in the syringe

(b) The no. of capsules should be given are $3.0$ capsules

Part (a) Step 1: Given information

We need to find the volume that nurse will draw up in the syringe 

Part (a) Step 2: Explanation

We know that

The $25 \mathrm{mg}/\mathrm{L}$ means $25 \mathrm{mg}=1 \mathrm{L}$

From the above it is clear that 

$25 \mathrm{mg}$ contains $1 \mathrm{L}$

Then $12.5 \mathrm{mg}$ contains $\frac{1 \mathrm{L}}{25 \cancel{\mathrm{mg}}}\times 12.5 \cancel{\mathrm{mg}}=0.50 \mathrm{L}$

As the no. of significant figures are two 

Therefore, required volume is,

$0.50 \mathrm{L}$

Part (b) Step 1: Given information

We need to find out no. of capsules that should be given 

Part (b) Step 2: Explanation

We know that 

The $1 \mathrm{kg}= 2.20 \mathrm{lb}$

And as given $1 \mathrm{kg}=25 \mathrm{mg}$

And $1 \mathrm{capsule}=250 \mathrm{mg}$

Therefore, no. of capsules are, 

$67 \cancel{\mathrm{lb}}\times \frac{1 \cancel{\mathrm{kg}}}{2.20 \cancel{\mathrm{lb}}}\times \frac{25 \cancel{\mathrm{mg}}}{1 \cancel{\mathrm{kg}}}\times \frac{1 \mathrm{capsule}}{250 \cancel{\mathrm{mg}}}=3.04545\approx 3.0$

As no. of significant figures are two