The first order rate constant for the decomposition of CaCO₃ at 700 K is 6.36 $\times$ 10^$-$3s^$-$1 and activation energy is 209 kJ mol^$-$1. Its rate constant (in s^$-$1) at 600 K is x $\times$ 10^$-$6. The value of x is ___________. (Nearest integer)

[Given R = 8.31 J K^$-$ mol^$-$1; log 6.36 $\times$ 10^$-$3 = $-$2.19, 10^$-$4.79 = 1.62 $\times$ 10^$-$5]

K₇₀₀ = 6.36 $\times$ 10^$-$3s^$-$1;<br><br>K₆₀₀ = x $\times$ 10^$-$6s^$-$1<br><br>E_a = 209 kJ/mol<br><br>Applying;<br><br>$$\log \left( {{{{K_{{T_2}}}} \over {{K_{{T_1}}}}}} \right) = {{ - {E_a}} \over {2.303R}}\left( {{1 \over {{T_2}}} - {1 \over {{T_1}}}} \right)$$<br><br>$$\log \left( {{{{K_{700}}} \over {{K_{600}}}}} \right) = {{ - {E_a}} \over {2.303R}}\left( {{1 \over {700}} - {1 \over {600}}} \right)$$<br><br>$$\log \left( {{{6.36 \times {{10}^{ - 3}}} \over {{K_{600}}}}} \right) = {{ + 209 \times 1000} \over {2.303 \times 8.31}}\left( {{{100} \over {700 \times 600}}} \right)$$<br><br>log(6.36 $\times$ 10^$-$3) $-$ logK₆₀₀ = 2.6<br><br>$\Rightarrow$ logK₆₀₀ = $-$2.19 $-$ 2.6 = $-$4.79<br><br>$\Rightarrow$ K₆₀₀ = 10^$-$4.79 = 1.62 $\times$ 10^$-$5<br><br>= 1.62 $\times$ 10^$-$6<br><br>= x $\times$ 10^$-$6<br><br>$\Rightarrow$ x = 16