24 ARRHENIUS PROBLEM. 10 points. A multi-national Pharma has developed a new mir

Question

24 ARRHENIUS PROBLEM. 10 points. A multi-national Pharma has developed a new miracle drug, however the half-life tin at Temp-25 °C is T1/2-32 days. At Templ The Vice President of Sales and Marketing is not pleased and he has decided to veto the release of the drug to the marketplace. He demands that the formulation team re-develop the drug such that the new half - life is Tj/2 100 days. At Temp> The team decides to explore increasing the stability by lowering the storage temperature. APPROACH: Solve for k1 and k2 using the equation for half- life, T1/2 0.693/k (for both half-lives, 32 days and 100 days) and solve for Temp> using the Arrhenius Equation for ln(k1/k2), with slope = E/R = 650 T1-298"K, To determine T

Explanation / Answer

Rate constant at first half life of 32 days at 25 C (298K)

K1 = 0.6932/32 = 0.0216625 s-1

Rate constant at half life of 100 days

K2 = 0.6932/100 = 0.006932 s-1

From the Arrhenius equation

ln (k2/k1) = (E/R) (1/T1 - 1/T2)

ln (0.006932/0.0216625) = (650) (1/298 - 1/T2)

-1.13943 = (650) (1/298 - 1/T2)

(1/298 - 1/T2) = - 0.00175297

- 1/T2 = ( - 0.00175297) - (1/298)

1/T2 = 0.00510868

T2 = 195.75 K

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