Question

A client with hypertension who weighs 72.4 kg is receiving an infusion of nitroprusside (Nipride) 50 mg in D5W 250 ml at 75 ml/hour. How many mcg/kg/minute is the client receiving? (Enter numeric value only. If rounding is required, round to the nearest tenth.)

Answer 1

To solve this problem it is necessary to simply apply the concepts related to cross-multiply and proportion between units.

Let's start first by relating the amount of dose needed to be supplied per hour, in other words,

The infusion of 250ml should be supplied at a rate of 75ml / hour, so what amount x of mg hour should be supplied with 50Mg.

$\frac{x}{75ml/hour} \rightarrow \frac{50mg}{250ml}$

$x \rightarrow \frac{50mg*75ml/hour}{250ml}$

$x \rightarrow \frac{3750mg}{250hour}$

$x \rightarrow 15\frac{mg}{hour}$

Converting to mcg units we know that 1mg is equal to 1000mcg and that 1 hour contains 60 min, therefore

$x \rightarrow 15\frac{mg}{hour}$

$x \rightarrow 15\frac{mg}{hour}(\frac{1000mcg}{1mg})(\frac{1hour}{60min})$

$x \rightarrow 250mcg/min$

The dose should be distributed per kilogram of the patient so if the patient weighs 72.4kg,

$Dose = \frac{250mcg/min}{72.4kg}$

$Dose = 3.5 \frac{mcg/min}{kg}$

Therefore the client will receive 3.5mcg/kg/min.