Question

The recommended maintenance dose of penicillin for children is 1.0 mg/kg/hr by injection. Of 10 mL of a 25 mg/mL solution of penicillin is added to a 100 mL bottle of saline, what is the delivery rate for a 40 pound child

Answer 1

This problem is providing us with the recommended maintenance dose of penicillin for children as 1.0 mg/kg/hr by injection. Thus, the delivery rate for a 40-pound child is required, if 10 mL of a 25 mg/mL solution of penicillin is added to a 100-mL bottle of saline. At the end, the result is 8.0 mL/hr:

Dimensional analysis:

In chemistry, dimensional analysis allows us to obtain a specific result given relevant information about it. Although a formula is not always provided, one can use the units as a reference for the calculations.

For example, this problem asks for the rate, in mL/hr, at which a child gets this dose, so the first step will be to get the mass of the child in kilograms:

$40 lb*\frac{0.4536kg}{1lb}= 18.144kg$

Next, we calculate the rate at which the penicillin is delivered to this child:

$1.0\frac{mg}{kg*hr} *18.144kg=18.144\frac{mg}{hr}$

After that, we calculate the total mass of penicillin that is delivered:

$10mL*25\frac{mg}{mL} =250 mg$

And get the new concentration once it is diluted to 100 mL:

$\frac{250mg}{10mL+100mL}=2.27\frac{mg}{mL}$

And finally, we combine the mg/hr with the mg/mL to get the result in mL/hr as required:

$18.144\frac{mg}{hr} *\frac{1mL}{2.27mg}\\ \\=8.0\frac{mL}{hr}$

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