For the first order reaction half-life = $${{0.693} \over k}$$

or, $$360 = {{0.693} \over k}$$ $$\therefore$$ $${k_{380^\circ C}} = {{0.693} \over {360}}$$

We know, $$\log {{{k_2}} \over {{k_1}}} = {{{E_a}} \over {2.303R}}\left[ {{1 \over {{T_1}}} - {1 \over {{T_2}}}} \right]$$

$$\therefore$$ $$\log {{{k_{450^\circ C}}} \over {{{0.693} \over {360}}}} = {{200 \times 1000} \over {2.303 \times 8.314}}\left[ {{1 \over {653}} - {1 \over {723}}} \right]$$

or, $${k_{450^\circ C}} = 6.18 \times {10^{ - 2}}$$ min^$$-$$1

For 75% decomposition at 723K (450$$^\circ$$C),

$${k_{450^\circ C}} = {{2.303} \over t}\log {a \over {a - x}}$$

or, $$6.81 \times {10^{ - 2}} = {{2.303} \over t}\log {{100} \over {(100 - 75)}}$$ or, t = 20.358 min