Question

Orange juice is packaged aseptically and stored under ambient conditions. The degradation of vitamin C in the juice occurs during storage following first-order reaction kinetics. The degradation rate constant is $5.2 \times 10^{-3}$ day$^{-1}$. The half-life of vitamin C in days is ............. (in integer).

Hint:

For first-order degradation of nutrients, use $t_{1/2} = 0.693/k$. Always keep units consistent (here days).

Answer 1

Correct Answer: 132

Step 1: Recall half-life formula for first-order reactions.
\[ t_{1/2} = \frac{0.693}{k} \]
Step 2: Substitute values.
\[ k = 5.2 \times 10^{-3} \ \text{day}^{-1} \] \[ t_{1/2} = \frac{0.693}{5.2 \times 10^{-3}} = \frac{0.693}{0.0052} \]
Step 3: Simplify.
\[ t_{1/2} \approx 133.27 \ \text{days} \]
Step 4: Round to integer.
\[ t_{1/2} \approx 133 \ \text{days} \] Final Answer: \[ \boxed{133 \ \text{days}} \]