Dopamine is available as 400 mg in 250 mL of D5W. A 2 year old weighing 12 kg is receiving 10 mcg/kg/min. How many hours will the infusion last?

55.5556 hours.

Step-by-step explanation:

Let's solve the problem.

The amount of dopamine rate applied to a person is based on the formula: 10mcg/kg/min. Such relation can be express as follows:

(10mcg/kg/min) =

(10mcg/kg) * (1/min)

Now by multiplying by the weight (12 kg) of the 2 years old person, we have:

(10mcg/kg) * (1/min) * (12kg) =

(10mcg*12kg/kg) * (1/min) =

(120mcg) * (1/min) =

120mcg/min, which is the rate of dopamine infusion, which can be express as:

(120mcg/min) * (60min/1hour) =

(120mcg*60min) / (1hour*1min) =

7200mcg/hour=

1hour/7200mcg, which means that for each hour, 7200mcg dopamine are infused.

Because the D5W product has 400 mg of dopamine, then we need to convert 400 mg to X mcg of dopamine in order to use the previous obtained rate. This means:

Because 1mcg=0.001mg then:

(400mg) * (1mcg/0.001mg) =

(400mg*1mcg) / (0.001mg) =

400000mcg, which is the amount of dopamine in D5W.

Now, using the amount of dopamine in D5W and the applied rate we have:

(rate) * (total amount of dopamine) = hours of infusion

(1hour/7200mcg) * (400000mcg) = hours of infusion

(1hour*400000mcg) / (7200mcg) = hours of infusion

(55.5556 hours) = hours of infusion

In conclusion, the infusion will last 55.5556 hours.