Question

A) new drug product that has a shelf life of 2.5 years (at room temperature, 25^OC). Assuming the drug undergoes 1st‐order degradation, estimate the degradation rate constant for drug at room temperature. (The units for your answer should be (1/yr).)

B) a new drug product that has a shelf life of 2.5 years (at room temperature, 25^OC). Assuming the drug undergoes 1st‐order degradation, calculate the half‐life for the drug for the degradation reaction at room temperature.

(The units for your answer should be years.)

Answer 1

1^st Answer

Given Shelf life t_0.9= 2.5 years

Order of reaction = 1^st order reaction

For first order reaction we had following equation

log C = log C_o- kt/2.303

log 0.9C_o = log C_o -kt_0.9/2.303

log0.9C_o – log C_o= - kt_0.9/2.303

log(C_o /0.9C_o )=kt_0.9/2.3033

0.0458=kt_0.9/2.303

0.0458=k (2.5 )/2.303

0.0458= K (1.08)

K = 0.0458/1.08 = 0.042 Years ^-1

2^nd Answer

Given Shelf life t_0.9= 2.5 years

Order of reaction = 1^st order reaction

For first order reaction we had following equation

log C = log C_o- kt/2.303

log 0.5C_o = log C_o -kt_0.5/2.303

log0.5C_o – log C_o= - kt_0.5/2.303

log(C_o /0.5C_o )=kt_0.5/2.3033

0.3010 = kt_0.5/2.3033

0.3010 = 0.042 t_0.5/2.3033

t_0.5 = 16.5 Years.