  Drug X has an expiration date that is 1.5 years after the date it was manufactured. Drug X decomposes following the reaction below. Assume the decomposition follows first order kinetics.                               X ---->  Y +  2 Z1) A bottle contains pills of X that were manufactured 5.00 years ago. The drug is analyzed and it is found that 95.0% of X has not decomposed. What is the half life for the dceomposition of X in years? 2) One of the pills contains 10.0 mg of X. The molecular weight of X is 245 g/mol and the molecular weight of Z is 100g/mol. How many years will it take for enough X to decompose so as to produce 2.8 mg of Z?

Question

Drug X has an expiration date that is 1.5 years after the date it was manufactured. Drug X decomposes following the reaction below. Assume the decomposition follows first order kinetics.

X ---->  Y +  2 Z

1) A bottle contains pills of X that were manufactured 5.00 years ago. The drug is analyzed and it is found that 95.0% of X has not decomposed. What is the half life for the dceomposition of X in years?

2) One of the pills contains 10.0 mg of X. The molecular weight of X is 245 g/mol and the molecular weight of Z is 100g/mol. How many years will it take for enough X to decompose so as to produce 2.8 mg of Z?

Step 1

Integral equation for first order of reaction:

• For first order reaction:

Step 2

Rate constant remains constant throughout the reaction and a reaction having certain order must satisfy the integral equation of that order.

According to question:

Drug decomposition follows first order kinetics

Initial concentration of drug = let it ‘a’ M

% of drug left after decomposition in 5.00 years = 95%

Thus,

Step 3

Plugging value in integral equation...

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