# The concentration of a drug in the body is often expressed in units of milligrams per kilogram of body weight. What must the initial dose of the drug be in order for the drug concentration to be 5.0 mg/kg body weight after 3.00 hours? Its rate constant is 0.00426min^-1 and its initial concentration was 25.0 mg/kg body weight

If we assume a first order rate law, then we can use the integrated rate law equation

ln ([A]t/[A]o) = - kt

where [A] are the concentrations at time t and time zero, k is the rate constant, and t is the time. While we show A as the concentrations, we can use the amounts of A in any units as long as the units are the same. In this case, we can use the dosages (mg/kg) as the concentrations.

ln (25/5) = - (0.00426 min^-1)t

t = 378 minutes

The units need to be in minutes since the value of the rate constant was in inverse minutes. If we need it in a different unit of time, we can then do conversions to other units.

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