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A drug becomes ineffective after 30% decomposition. The original concentration of a sample was 5mg/mL which becomes 4.2 mg/mL during 20 months. Assuming the decomposition of first order, calculate the expiry time (in months) of the drug in months.
Correct answer is between '40.7,50.3'. Can you explain this answer?
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A drug becomes ineffective after 30% decomposition. The original conce...
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A drug becomes ineffective after 30% decomposition. The original conce...
Given:
- Original concentration of the drug sample = 5 mg/mL
- Concentration after 20 months = 4.2 mg/mL
- Drug becomes ineffective after 30% decomposition
Approach:
To solve this problem, we can use the concept of first-order kinetics. The rate of decomposition of the drug follows a first-order reaction, which means that the rate of decomposition is directly proportional to the concentration of the drug remaining.
Step 1: Calculate the rate constant (k)
We can use the formula for first-order kinetics: ln(Ct/C0) = -kt
Where:
- Ct is the concentration at time t
- C0 is the initial concentration
- k is the rate constant
Rearranging the equation, we get: k = -ln(Ct/C0) / t
Using the given values:
- Ct = 4.2 mg/mL
- C0 = 5 mg/mL
- t = 20 months
Substituting the values into the formula, we can calculate the rate constant (k).
Step 2: Calculate the half-life (T1/2)
The half-life of a first-order reaction is given by the equation: T1/2 = ln(2) / k
Using the calculated value of k, we can find the half-life of the drug.
Step 3: Calculate the expiry time
The drug becomes ineffective after 30% decomposition. This means that the concentration remaining should be 70% of the original concentration (100% - 30% = 70%).
Using the formula for first-order kinetics: Ct = C0 * e^(-kt)
We can rearrange the equation to solve for time (t): t = -ln(Ct/C0) / k
Using the given values:
- Ct = 0.7 * C0
- C0 = 5 mg/mL
- k (calculated from step 1)
- Solve for t to find the expiry time in months.
Step 4: Check the solution
The calculated expiry time should be between 40.7 and 50.3 months.
This approach considers the first-order kinetics of the drug decomposition and calculates the rate constant, half-life, and expiry time based on the given information.
- Original concentration of the drug sample = 5 mg/mL
- Concentration after 20 months = 4.2 mg/mL
- Drug becomes ineffective after 30% decomposition
Approach:
To solve this problem, we can use the concept of first-order kinetics. The rate of decomposition of the drug follows a first-order reaction, which means that the rate of decomposition is directly proportional to the concentration of the drug remaining.
Step 1: Calculate the rate constant (k)
We can use the formula for first-order kinetics: ln(Ct/C0) = -kt
Where:
- Ct is the concentration at time t
- C0 is the initial concentration
- k is the rate constant
Rearranging the equation, we get: k = -ln(Ct/C0) / t
Using the given values:
- Ct = 4.2 mg/mL
- C0 = 5 mg/mL
- t = 20 months
Substituting the values into the formula, we can calculate the rate constant (k).
Step 2: Calculate the half-life (T1/2)
The half-life of a first-order reaction is given by the equation: T1/2 = ln(2) / k
Using the calculated value of k, we can find the half-life of the drug.
Step 3: Calculate the expiry time
The drug becomes ineffective after 30% decomposition. This means that the concentration remaining should be 70% of the original concentration (100% - 30% = 70%).
Using the formula for first-order kinetics: Ct = C0 * e^(-kt)
We can rearrange the equation to solve for time (t): t = -ln(Ct/C0) / k
Using the given values:
- Ct = 0.7 * C0
- C0 = 5 mg/mL
- k (calculated from step 1)
- Solve for t to find the expiry time in months.
Step 4: Check the solution
The calculated expiry time should be between 40.7 and 50.3 months.
This approach considers the first-order kinetics of the drug decomposition and calculates the rate constant, half-life, and expiry time based on the given information.
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A drug becomes ineffective after 30% decomposition. The original concentration of a sample was 5mg/mL which becomes 4.2 mg/mL during 20 months. Assuming the decomposition of first order, calculate the expiry time (in months) of the drug in months.Correct answer is between '40.7,50.3'. Can you explain this answer?
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