The decomposition of `AB_2` to AB and B is first-order with `k = 2.8 xx 10^(-7)s^(-1)` at `1000^@C`
`AB_2 to AB + B`
Atomic weights of A and B are 12 and 32 respectively.
(i) Find the half-life of this reaction at `1000^@C`.
(ii) How many days would pass before 1 g of `AB_2` had decomposed to the extent that 0.60 g of `AB_2` remained?
(iii) With reference to (ii), how many grams of AB would be present after this length of time?
(iv) How much of a 1-g sample of `AB_2` would remain after 35 days?

Explanation

Let's solve the problem step by step.

### Given:
- Reaction: \( AB_2 \rightarrow AB + B \)
- Rate constant, \( k = 2.8 \times 10^{-7} \, s^{-1} \)
- Atomic weights: \( A = 12 \, g/mol \), \( B = 32 \, g/mol \)

### (i) Find the half-life of this reaction at \( 1000^\circ C \).
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