A zero-order reaction is 25% complete in 30seconds. What time does it take for 50% completion?

Options

A. 40s
B. 70s
C. 50s
D. 60s

Answer

To solve the problem of determining the time it takes for a zero-order reaction to reach 50% completion, we can follow these steps:

### Step 1: Understand the given data
- The reaction is 25% complete in 30 seconds.
- This means that 25% of the initial concentration has reacted, and 75% remains.

### Step 2: Define the initial concentration
Let the initial concentration of the reactant be \( [A_0] = 100 \) (this is an arbitrary value for ease of calculation).

### Step 3: Calculate the concentration after 25% completion
After 25% completion, the concentration remaining is:
\[ [A] = [A_0] - 25\% \text{ of } [A_0] = 100 - 25 = 75 \]

### Step 4: Use the zero-order reaction formula
For a zero-order reaction, the concentration at any time \( t \) can be expressed as:
\[ [A] = [A_0] - kt \]
Where \( k \) is the rate constant and \( t \) is the time.

### Step 5: Substitute known values for 25% completion
Substituting the known values into the equation for when the reaction is 25% complete:
\[ 75 = 100 - k(30) \]
Rearranging gives:
\[ k(30) = 100 - 75 = 25 \]
Thus,
\[ k = \frac{25}{30} = \frac{5}{6} \text{ (units: concentration/time)} \]

### Step 6: Calculate time for 50% completion
Now we need to find the time when the reaction is 50% complete. At 50% completion, the concentration remaining is:
\[ [A] = 100 - 50 = 50 \]
Using the zero-order formula again:
\[ 50 = 100 - kt \]
Substituting the value of \( k \):
\[ 50 = 100 - \left(\frac{5}{6}\right)t \]
Rearranging gives:
\[ \left(\frac{5}{6}\right)t = 100 - 50 = 50 \]
Solving for \( t \):
\[ t = 50 \times \frac{6}{5} = 60 \text{ seconds} \]

### Conclusion
The time taken for 50% completion of the zero-order reaction is **60 seconds**.

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