A patient with a possible acetaminophen drug overdose goes to the emergency room

Question

A patient with a possible acetaminophen drug overdose goes to the emergency room. The attending physician notes the symptoms of acetaminophen overdose and decides to pump the patient's stomach. The physician must also decide whether to administer the specific antidote, N-acetylcysteine in order to limit liver damage. Administration of the antidote is recommended if serum acetaminophen levels are greater than 200.0 ug/mL four hours after ingestion. The patient reports having taken acetaminophen at 6 a.m. At 2pm, their serum acetaminophen level is 86.2 ug/mL and at 6 pm their serum levels are 27.8 ug/mL. For all calculations use given times as exact figures.

a.) Assuming metabolism of acetaminophen is first order, determine the rate constant.

b.) What was the serum acetominophen level 4 hours after ingestion? Should the patient be given the antidote? How did you decide?

c.) How much acetaminophen did the patient ingest, in milligrams? The patient reports the tablets taken contained 500.0 mg acetaminophen each. If this is true, how many tablets did the patient take? assume the patient has a typical blood volume of 2.00 L.

a.) k=________________

b.) acetaminophen level @ 4hrs=__________________ give antidote?________________________________________________________

c.) mg taken=_____________________   # of tablets taken:__________________________

Explanation / Answer

a)

if first order:

ln(A) = ln(A0) - kt

assume, to get (A)

initially --> 2 pm --> 86.2 ug/mL

after --> 6 pm (4 hr) --> 27.8 ug/mL

so

substitute

ln(A) = ln(A0) - kt

ln(27.8 ) = ln(86.2 ) - k*4

k = (ln(27.8 )- ln(86.2 ) ) /(-4) = 0.28290 1/h

b)

find initial concnetration:

t from 6 am o 2 pm = 8 h

ln(86.2) = ln(A0) - 0.28290*8

A0 = exp( ln(86.2)+0.28290*8 ) = 828.709 ug/mL

after 4 hrs:

ln(A) = ln(828.709 ) - 0.28290*4

A = exp(ln(828.709 ) - 0.28290*4)

A = 267.2725 ug/mL

YES, admin him an antidote since

C > C toxic

c)

if he has V = 2 l

then

ug/mL = 828.709 mg/mL * 2000 mL = 828.709 *2000 = 1657418 ug = 1657418*10^-6 g = 1.657 g = 1657 mg

if 1 pill contains = 500 mg

then, he took little more than 3 pills!

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