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**First Order & Zero Order Reaction**

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**Rate The rate of a chemical reaction of process**

Is the velocity with which the reaction occurs. For drug A (decreasing) -dA/dt For Drug B (increasing) +dB/dt

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Rate Constant

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Zero order reactions Amount of drug A is decreasing at a constant rate for each time interval -dA/dt=-k0 k0= is the zero order rate constant and is expressed in units of mass/time Equation: At=A0-k0 t Ct=C0-k0 t

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At=A0-k0 t A A0 Slope=-k0 t

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**Drug Concentration (mg/ml) 100 2 95 4 90 6 85 8 80 10 75 12 70**

Time (hr) Drug Concentration (mg/ml) 100 2 95 4 90 6 85 8 80 10 75 12 70 5mg/ml 5mg/ml 5mg/ml 5mg/ml 5mg/ml 5mg/ml

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First order Half life The time required for the amount to decrease by one half life It is constant no matter what the initial concentation of a drug is

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C0 =100mg/ml at t=0 C =90mg/ml at t=4hr 90=-k0(4)+100 K0 =2.5mg/ml hr

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**The amount of drug A is decreasing at a rate that is proprotional to the amount of drug remaining.**

-dA/dt=K A At=A0e-kt Ct=C0e-kt

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Half life t1/2 The period of time required for the amount or concentration of a drug to decrease by one half.

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Not constant The zero order t1/2 is proportional to the initial amount or concentration of the drug and is inversely proportional to the zero order rate constant k0 t1/2= 0.5A0 k0

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Time (hr) Drug Concentration (mg/ml) 100 4 50 8 25 12 12.5 16 6.25 20 3.13 24 1.56

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First order The amount of drug eliminated over a certain time period increases as the amount of drug in the body increases. The amount of drug eliminated per unit of time decreases as the amount of drug in the body decreases But the fraction of a drug remain constant

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Zero order The amount of drug eliminated for each time interval is constant ,regardless of the amount in the body. In other words the amount of drug in the body does not change with the amount or concentration of the drug in the body. but the fraction removed varies

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**First Order Elimination**

Fraction of drug eliminated over preceding hour Amount of drug eliminated (mg) Amount of drug in the body (mg) time 0.15 - 1000 150 850 1 127 723 2 109 614 3 92 522 4 78 444 5 67 377 6

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**Fraction of drug eliminated over preceding hour**

Amount of drug eliminated (mg) Amount of drug in the body (mg) time - 1000 0.15 150 850 1 0.18 700 2 0.21 550 3 0.27 400 4 0.38 250 5 0. 60 100 6

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First order

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Toxicokinetic Calculations

Toxicokinetic Calculations

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