Question

the patient receives 3G of ampicillin to be added to 100 mL D5W q8h the stock supply is 10000 mg vial of ampicillin directions say to reconstitute with 9.8 mL of NS to yield 500 mg/mL how many mL of ampicillin will you add to the iv bag for the correct dose

Please show work using dimensional analysis

Answer 1

Ampicillin Dosage calculation using Dimensional Analysis:

Step 1:

Dose ordered = 500mg/mL . This can be expressed as $\dpi{100} \fn_jvn \small \frac{500}{1}$

Dose on hand = 10000mg of ampicillin to be reconstituted with 9.8mL of NS.

After reconstitution, 10mL contains 10000mg. It is expressed as $\dpi{100} \fn_jvn \small \frac{10}{10000}$

Step 2:

Using dimensional analysis, it can be solved as

$\dpi{100} \fn_jvn \small \frac{500}{1} \times \frac{10}{10000}= \frac{10}{100} = 0.5mL$

Hence, 0.5mL contains 500mg of Ampicillin.

Step 3:

Here ordered dose is 3G of ampicillin

1 gram = 1000mg

3G = 3000mg

Dose on hand = 500mg

Quantity (v) = 0.5mL

Then,

$\dpi{100} \fn_jvn \small Amount in mL = \frac{Desired Dose}{Dose on hand}\times V$

By substituting the above value

$\dpi{100} \fn_jvn \small Amount in mL = \frac{3000}{500}\times 0.5$

Amount in mL = 3mL

Therefore, 3mL of ampicillin to be added in 100mL of IV bag to get the correct dose.

Note:

It can also be calculated using a simple method.

10000mg of ampicillin can be reconstituted with 9.8mL of NS.

Hence, 10mL = 10000mg

1 mL = 1000mg

Therefore to get 3000mg, 3mL to be mixed in IV bag.