Question

Question #b1065

Answer 1

`"135 mL"`

Explanation:

Notice that the dosage of Deltazone is expressed in micrograms per kilogram per minute, `mu"g kg"^(-1)"min"^(-1)`, but that the problem wants you to determine how many milligrams must be administered in an hour to a patient whose weight is given in kilograms.

This tells you that you must convert the dosage from the units given to you to milligrams per pound per hour, `"mg lb"^(-1)"h"^(-1)`. To do that, use the conversion factors

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 mg" = 10^3mu"g")color(white)(a/a)|)))`

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 kg " ~~ " 2.205 lb")color(white)(a/a)|)))`

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 h " = " 60 min")color(white)(a/a)|)))`

So, use these conversion factors to get

`6 color(red)(cancel(color(black)(mu"g")))/(color(blue)(cancel(color(black)("kg"))) * color(green)(cancel(color(black)("min")))) * "1 mg"/(10^3color(red)(cancel(color(black)(mu"g")))) * (1color(blue)(cancel(color(black)("kg"))))/("2.205 lb") * (60color(green)(cancel(color(black)("min"))))/"1 h" = "0.1633 mg lb"^(-1)"h"^(-1)`

Now, use the weight of the patient to determine how much Deltazone would be needed per hour

`165 color(red)(cancel(color(black)("lb"))) * 0.1633 "mg"/(color(red)(cancel(color(black)("lb"))) * "h") = "26.945 mg h"^(-1)`

Now all you have to do is figure out what volume of D5W solution would contain this many milligrams of Deltazone

`26.945color(red)(cancel(color(black)("mg Deltaz."))) * "250 mL"/(50color(red)(cancel(color(black)("mg Deltaz.")))) = "134.7 mL"`

You should round this off to one sig fig, since that is how many sig figs you have for the dosage, but I'll leave it rounded to three sig figs, just for good measure

`"volume of D5W" = color(green)(|bar(ul(color(white)(a/a)"135 mL"color(white)(a/a)|)))`