What must the inital does of the drug be in order for the drug concentration 3.00 hours afterward to be 5.0 mg/kg body weight?

The rate constant is: 4.26x10^-3min^-1

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The rate constant is given as per minute, this means this is a first order reaction.

The rate equation for this can be written as,

(dc)/(dt) = -0.00426 xx c

Separating varaibles,

1/c dc = -0.00426 dt

Integrating wrt t,

ln(c) = -0.00426t+k

at t=0, c = c_0

ln(c_0) = 0+k

Therefore,

ln(c) = -0.00426t+ln(c_0)

But we know at t= 180 min , c = 5 mg/kg body

ln(5) = -0.00426 xx 180 + ln(c_0)

1.60944 = -0.7688 + ln(c_0)

ln(c_0) = 2.37824

c_0 = exp(2.37824)

c_0 = 10.786 mg/ kg body

**Therefore the initial dose should be 10.786 mg/kg body**

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