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 600K is x × 10^-6. The value of x is_____. (nearest integer).

$[G i v e n R = 8.31 J K^{- 1} m o l^{- 1}; l o g 6.36 \times 1 0^{- 3} = - 2.19, 1 0^{- 4.79} = 1.62 \times 1 0^{- 5}]$

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alok kumar singh | Contributor-Level 10

2 months ago

$K_{700} = 6.36 \times 1 0^{- 3} s^{- 1}$

$K_{600} = x \times 1 0^{- 6} s^{- 1}$

E_a = 209 KJ/mol

$l o g (\frac{K_{2}}{K_{1}}) = \frac{- E a}{2.303 R} [\frac{1}{T_{2}} - \frac{1}{T_{1}}]$

$l o g K_{600} = - 4.79$

$K_{600} = 1 0^{- 4.79} = 1.62 \times 1 0^{- 5}$

= 16.2 × 10^-6

x = 16 (the nearest integer)

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