First Order & Zero Order Reaction 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 Rate Constant 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 At=A0-k0 t zero order Drug concentration(mg/ml) A 120 A0 100 Slope=-k0 80 60 zero order 40 20 0 t 0 2 4 6 Time (hr) 8 10 12 Drug Concentration (mg/ml) 100 95 90 85 80 75 70 5mg/ml 5mg/ml 5mg/ml 5mg/ml 5mg/ml 5mg/ml Time (hr) 0 2 4 6 8 10 12 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 Drug concentration(mg/ml) zero order 120 100 80 60 zero order 40 20 0 0 2 4 6 Time (hr) 8 10 12 C0 =100mg/ml at t=0 C =90mg/ml at t=4hr 90=-k0(4)+100 K0 =2.5mg/ml hr 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 Half life t1/2 The period of time required for the amount or concentration of a drug to decrease by one half. 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 Drug Concentration (mg/ml) Time (hr) 100 0 50 4 25 8 12.5 12 6.25 16 3.13 20 1.56 24 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 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 First Order Elimination time Amount of drug Amount of drug in the body (mg) eliminated (mg) Fraction of drug eliminated over preceding hour 0 1000 - 0.15 1 850 150 0.15 2 723 127 0.15 3 614 109 0.15 4 522 92 0.15 5 444 78 0.15 6 377 67 0.15 zero order zero order on semilog paper 1200 1000 800 600 Series1 400 concentration concentration 1000 100 Series1 10 200 0 1 0 1 2 3 time 4 5 6 0 1 2 3 time 4 5 6 time Amount of drug Amount of drug in the body (mg) eliminated (mg) Fraction of drug eliminated over preceding hour 0 1000 - - 1 850 150 0.15 2 700 150 0.18 3 550 150 0.21 4 400 150 0.27 5 250 150 0.38 6 100 150 0. 60 First order first order on semilog paper first order 1000 1200 conc 800 Series1 600 conc 400 concentration 1000 100 Series1 conc 10 200 1 0 0 1 2 3 time 4 5 6 0 1 2 3 time 4 5 6