The first order rate constant is 1.87 x 10^-3 min^-1 at 37°C for reaction of cisplatin. Suppose the concentration of cisplatin in the bloodstream of a patient is 4.73 x 10^-4 mol/L. Calculate the concentration exactly 24 hours later.
ln(No/N) = kt
No = 4.73E-4
N = ?
k = in the problem
t = 24 hours changed to min since k in in min.
To calculate the concentration after 24 hours, we can use the first order rate equation:
ln(C_t / C_0) = -k * t
where:
- C_t is the concentration at time t
- C_0 is the initial concentration
- k is the rate constant
- t is the time
First, let's convert the given time of 24 hours to minutes:
24 hours = 24 * 60 minutes
t = 1440 minutes
Now, we can substitute the values into the equation to solve for C_t:
ln(C_t / C_0) = -k * t
ln(C_t / 4.73 x 10^-4) = -(1.87 x 10^-3 min^-1) * (1440 min)
Now, let's solve for C_t:
ln(C_t / 4.73 x 10^-4) = -2.6928
To find C_t, we can exponentiate both sides of the equation:
e^(ln(C_t / 4.73 x 10^-4)) = e^(-2.6928)
C_t / 4.73 x 10^-4 = 0.067534
Now, isolate C_t:
C_t = 0.067534 * 4.73 x 10^-4
C_t = 3.194 x 10^-5 mol/L
Therefore, the concentration of cisplatin in the bloodstream after exactly 24 hours is 3.194 x 10^-5 mol/L.