The rate constant for a first order reaction is `4.606 xx 10^(-3) s^(-1)`. The time required to reduce 2.0g of the reactant to 0.2g is:

Options

A. 100s
B. 200 s
C. 500 s
D. 1000 s

Answer

To solve the problem, we need to determine the time required to reduce the mass of a reactant from 2.0 g to 0.2 g in a first-order reaction with a given rate constant. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Rate constant (K) = \(4.606 \times 10^{-3} \, s^{-1}\)
- Initial mass of the reactant (m₀) = 2.0 g
- Final mass of the reactant (m) = 0.2 g

### Step 2: Use the first-order reaction formula
For a first-order reaction, the relationship between the rate constant, time, and concentrations (or masses in this case) can be expressed as:
\[ K = \frac{2.303}{T} \log\left(\frac{[A]_0}{[A]}\right) \]
Where:
- \([A]_0\) = initial concentration (or mass)
- \([A]\) = final concentration (or mass)

### Step 3: Substitute the values into the equation
In this case, we can substitute the masses directly since the molecular mass cancels out:
\[ K = \frac{2.303}{T} \log\left(\frac{2.0}{0.2}\right) \]

### Step 4: Calculate the logarithm
Calculate the ratio:
\[ \frac{2.0}{0.2} = 10 \]
Now, find the logarithm:
\[ \log(10) = 1 \]

### Step 5: Substitute back into the equation
Now substitute the values back into the equation:
\[ K = \frac{2.303}{T} \cdot 1 \]
Rearranging gives:
\[ T = \frac{2.303}{K} \]

### Step 6: Substitute the value of K
Now substitute the value of K:
\[ T = \frac{2.303}{4.606 \times 10^{-3}} \]

### Step 7: Calculate T
Calculating the above expression:
\[ T = \frac{2.303}{4.606 \times 10^{-3}} \approx 500 \, s \]

### Conclusion
The time required to reduce 2.0 g of the reactant to 0.2 g is approximately **500 seconds**.

---