Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with `t_(1//2)=3.00hr.` What fraction of sample of sucrose remains after `8 hr` ?

Explanation

To solve the problem of how much sucrose remains after 8 hours of decomposition in an acid solution, we will follow these steps:

### Step 1: Determine the rate constant (k)
The half-life (t₁/₂) for a first-order reaction is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]

Given that \( t_{1/2} = 3.00 \, \text{hr} \), we can rearrange the formula to solve for k:
\[ k = \frac{0.693}{t_{1/2}} = \frac{0.693}{3.00 \, \text{hr}} \]
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