here is how to solve these using dimensional analysis (factor/label method).
3. order: administer 500 mg of theophylline in 250 ml of d5w.
available: the pump is set at 13 ml/h.
how many mg is the patient receiving per hour?
first, establish what labels
you want to end up with. that will be mg/hr, where mg is in the numerator and hr are in the denominator. next, you set up a serious of fractions, which are actually ratios which are designed to cancel out all the labels except for the ones you want to be left with (mg/hr). so, here is how you set up this problem:
500mg / 250ml (what you have on hand) x 13ml/1hr (rate of infusion) = 6500mg / 250ml (after doing the math and canceling out the ml labels) -->reduce to 26ml/hr
4. order: 1 liter of normal saline with 20,000 units of heparin to infuse at 42 ml/hr. how many units of heparin per hour will the nurse be infusing?
again, the labels
you want to end up with are units/hour. you are also going to need one conversion factor for 1 liter = 1,000 ml. here is how you set up this problem by dimensional analysis:
20,000units / 1liter (what you have on hand) x 42ml / 1hour (given infusion rate) x 1liter / 1,000ml (conversion factor) = 840,000units / 1,000hour (after doing the math and canceling out the liter and ml labels)reduce to 840 units/ hour
5. order: administer 7 units per hour of regular insulin iv.
available: regular insulin 50 units in 100 ml of 0.9 nacl.
the nurse would set the pump at how many ml per hour?
the labels you want to end up with are ml/hr. here is the set up:
100ml / 50units (what you have on hand) x 7unit / 1hour (given rate of administration) = 700ml / 50hr (after doing the math and canceling out the unit labels, reduce to) = 14ml / hr