The first order rate constant for the decomposition of CaCO3 at 700 K is 6.36 × 10-3 s-1 and activation energy is 209 kJ mol-1. Its rate constant (in s-1) at 600 K is x × 10-6[Given R = 8.31 J K-1 mol-1 ; log 6.36 × 10-4.79 = 1.62 × 10-5
K700 = 6.36 x 10-3 s-1
K600 = x x 10-6 s-1
Ea = 209 kJ/mol
Applying
log\(\Big(\frac{K_{T_2}}{K_{T_1}}\Big)\) = \(\frac{-E_a}{2.303 R}\)\(\Big(\frac{1}{T_2} - \frac{1}{T_1}\Big)\)
log\(\Big(\frac{K_{700}}{K_{600}}\Big)\) = \(\frac{-E_a}{2.303 R}\)\(\Big(\frac{1}{700} - \frac{1}{600}\Big)\)
log\(\Big(\frac{6.36 \times 10^{-3}}{K_{600}}\Big)\) = \(\frac{+209 \times 1000}{2.303 \times 8.31}\)\(\Big(\frac{100}{700 \times 600} \Big)\)
log(6.36 × 10-3) – logK600 = 2.6
⇒ logK600 = -2.19 - 2.6 = -4.79
⇒ K600 = 10-4.79 = 1.62 × 10-5
= 1.62 × 10-5
= x x 10-6