# Question #b1065

##### 1 Answer

#### Explanation:

Notice that the dosage of Deltazone is expressed in *micrograms per kilogram per minute*, *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*,

#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)|)))#