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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:
<h3>Dimensional analysis:</h3>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:
Next, we calculate the rate at which the penicillin is delivered to this child:
After that, we calculate the total mass of penicillin that is delivered:
And get the new concentration once it is diluted to 100 mL:
And finally, we combine the mg/hr with the mg/mL to get the result in mL/hr as required:
Learn more about dimensional analysis: brainly.com/question/10874167