1f:I[80107,["/_next/static/chunks/235ad55241b6443f.js","/_next/static/chunks/8337ab1f037b6654.js","/_next/static/chunks/c9e933b5fd1a0afc.js","/_next/static/chunks/848a330faa2461ac.js","/_next/static/chunks/9f2942e368a262d2.js","/_next/static/chunks/92f9e11244990470.js","/_next/static/chunks/a8b867fbb1dfca1a.js","/_next/static/chunks/1100f0390a901fa7.js","/_next/static/chunks/bbe6bd9d3c7b0355.js","/_next/static/chunks/a82195c3e5de7dd4.js"],"default"] 20:I[76763,["/_next/static/chunks/235ad55241b6443f.js","/_next/static/chunks/8337ab1f037b6654.js","/_next/static/chunks/c9e933b5fd1a0afc.js","/_next/static/chunks/848a330faa2461ac.js","/_next/static/chunks/9f2942e368a262d2.js","/_next/static/chunks/92f9e11244990470.js","/_next/static/chunks/a8b867fbb1dfca1a.js","/_next/static/chunks/1100f0390a901fa7.js","/_next/static/chunks/bbe6bd9d3c7b0355.js","/_next/static/chunks/a82195c3e5de7dd4.js"],"default"] 1e:T43e,{"@context":"https://schema.org","@graph":[{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://www.divinejee.com"},{"@type":"ListItem","position":4,"name":"The first order rate constant for the decomposition of CaCO3","item":"https://www.divinejee.com/question/the-first-order-rate-constant-for-the-decomposition-of-caco3-at-700-k-is-636-x-103s1-and-activation"}]},{"@type":"QAPage","mainEntity":{"@type":"Question","name":"Question The first order rate constant for the decomposition of CaCO3 on Topic","text":"The first order rate constant for the decomposition of CaCO₃ at 700 K is 6.36 $\\times$ 10^$-$3s^$-$1 and activation ene...","answerCount":1,"upvoteCount":0,"datePublished":"2026-01-16","author":{"@type":"Organization","name":"DivineJEE"},"acceptedAnswer":{"@type":"Answer","text":"Check the detailed solution on the page.","upvoteCount":0,"url":"https://www.divinejee.com/question/the-first-order-rate-constant-for-the-decomposition-of-caco3-at-700-k-is-636-x-103s1-and-activation"}}}]}21:T41a,K₇₀₀ = 6.36 $$\times$$ 10^$$-$$3s^$$-$$1;

K₆₀₀ = x $$\times$$ 10^$$-$$6s^$$-$$1

E_a = 209 kJ/mol

Applying;

$$\log \left( {{{{K_{{T_2}}}} \over {{K_{{T_1}}}}}} \right) = {{ - {E_a}} \over {2.303R}}\left( {{1 \over {{T_2}}} - {1 \over {{T_1}}}} \right)$$

$$\log \left( {{{{K_{700}}} \over {{K_{600}}}}} \right) = {{ - {E_a}} \over {2.303R}}\left( {{1 \over {700}} - {1 \over {600}}} \right)$$

$$\log \left( {{{6.36 \times {{10}^{ - 3}}} \over {{K_{600}}}}} \right) = {{ + 209 \times 1000} \over {2.303 \times 8.31}}\left( {{{100} \over {700 \times 600}}} \right)$$

log(6.36 $$\times$$ 10^$$-$$3) $$-$$ logK₆₀₀ = 2.6

$$\Rightarrow$$ logK₆₀₀ = $$-$$2.19 $$-$$ 2.6 = $$-$$4.79

$$\Rightarrow$$ K₆₀₀ = 10^$$-$$4.79 = 1.62 $$\times$$ 10^$$-$$5

= 1.62 $$\times$$ 10^$$-$$6

= x $$\times$$ 10^$$-$$6

$$\Rightarrow$$ x = 16