Calculate the half-life of the antibiotic Ofloxacin in this patient

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Homework Statement
half life time
Relevant Equations
๐‘‡1/2 =(๐‘™๐‘›2) ๐‘ฅ ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘‘๐‘’ ๐‘‘๐‘–๐‘ ๐‘ก๐‘Ÿ๐‘–๐‘๐‘ข๐‘ก๐‘–๐‘œ๐‘›/ clarence.
A 70 kg patient is treated with ciprofloxacin (2 x 500 mg / d) for an infection
pulmonary. Ciprofloxacin is an antibiotic eliminated primarily by the kidneys, its
apparent volume of distribution is 3 [1 / kg) and its clearance is 0.5 (Wh x kg).
Calculate the half-life of ofloxacin in this patient. Later, his situation
degrades: it produces edema and the volume of distribution of ofloxacin increases to 125 liters.
After calculating the new half-life of ofloxacin in this patient,
Choose
the correct statement among the following 5:
Please choose an answer:
A. The half-life is extended by 60 min. NS.
B. The half-life is shortened by 30 min. NS.
C. The half-life is lengthened by 4h10 min. NS.
D. The half-life time remains unchanged.
E. The half-life is extended by 100 min. NS.to calculate the first half-life I did:

T1/2 =(ln(2) x volume distribution)/ clearance

v=70Kg x 3L/KG =210L
clearance 0.5L/H KG x70KG=35

T1/2= (ln(2) x 210)/ 35 = 4.158h

to calculate the second half-life:

k= ln(2) / T1/2
K= ln2/4.158 =0.166

clearance= K. V
clearance= 0.166 X 125= 20.83

T1/2= (ln (2) x125)/ 20.83 =4.158h

I get that the half-life time remains the same; I don't see where my error is. you can help me?
 
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I am layman in medicine and chemistry. As I have scarce knowledge on your system mechanism half time you say reminds me exponential decay as radioactive materials.
 
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havenly said:
Homework Statement:: half life time
Relevant Equations:: ๐‘‡1/2 =(๐‘™๐‘›2) ๐‘ฅ ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘‘๐‘’ ๐‘‘๐‘–๐‘ ๐‘ก๐‘Ÿ๐‘–๐‘๐‘ข๐‘ก๐‘–๐‘œ๐‘›/ clarence.

A 70 kg patient is treated with ciprofloxacin (2 x 500 mg / d) for an infection
pulmonary. Ciprofloxacin is an antibiotic eliminated primarily by the kidneys, its
apparent volume of distribution is 3 [1 / kg) and its clearance is 0.5 (Wh x kg).
Calculate the half-life of ofloxacin in this patient. Later, his situation
degrades: it produces edema and the volume of distribution of ofloxacin increases to 125 liters.
After calculating the new half-life of ofloxacin in this patient,
Choose
the correct statement among the following 5:
Please choose an answer:
A. The half-life is extended by 60 min. NS.
B. The half-life is shortened by 30 min. NS.
C. The half-life is lengthened by 4h10 min. NS.
D. The half-life time remains unchanged.
E. The half-life is extended by 100 min. NS.to calculate the first half-life I did:

T1/2 =(ln(2) x volume distribution)/ clearance

v=70Kg x 3L/KG =210L
clearance 0.5L/H KG x70KG=35

T1/2= (ln(2) x 210)/ 35 = 4.158h

to calculate the second half-life:

k= ln(2) / T1/2
K= ln2/4.158 =0.166

clearance= K. V
clearance= 0.166 X 125= 20.83

T1/2= (ln (2) x125)/ 20.83 =4.158h

I get that the half-life time remains the same; I don't see where my error is. you can help me?
Hi @havenly. Welcome to PF.

Iโ€™m sure someone here can help, but there are some problems with your question. Using my limited knowledge, here is a list of the problems I spotted. If you can fix them, you are more likely to get help.

1. Does (2 x 500 mg / d) mean a single dose of 1000mg? If not, what does it mean?

2. You have given the apparent volume of distribution as โ€œ3 [1 / kg) โ€œ. This makes no sense. Apparent volume of distribution should be in units of litres (l). I guess you mean โ€˜apparent volume of distribution per kg of body massโ€ (= 3 l/kg). Is that what you mean?

3. You said โ€œclearance is 0.5 (Wh x kg)โ€ but that makes no sense, Clearance is typically measured in units of l/h. Do you mean โ€œclearance per kg of body massโ€ which has units of l/(h.kg)?

4. You changed โ€œciprofloxacinโ€ to โ€œofloxacinโ€ halfway through the question. They are different antibiotics. Is that a mistake?

5. The question says new volume of distribution increases to 125 litres. Do you means 125 litres or 125 litres/kg?. I.e. is 125 in the same units as the initial value (3 l/kg)?

6. When the volume of distribution increases to 125 litres, does the clearance stay the same or change?

7. What do the letters โ€˜NSโ€™ stand for, in the list of alternative answers?

Iโ€™m guessing your question has been translated from another language (French?) which could be the reason for some of the problems.
 
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