1e: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"] 1f: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"] 1d:T437,{"@context":"https://schema.org","@graph":[{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://www.divinejee.com"},{"@type":"ListItem","position":4,"name":"A first order reaction has the rate constant k46x103s1 The ","item":"https://www.divinejee.com/question/a-first-order-reaction-has-the-rate-constant-k46x103s1-the-number-of-correct-statements-from-the"}]},{"@type":"QAPage","mainEntity":{"@type":"Question","name":"Question A first order reaction has the rate constant k46x103s1 The on Topic","text":"

A first order reaction has the rate constant, $\\mathrm{k=4.6\\times10^{-3}~s^{-1}}$. The number of correct statement/s from the following is/are ___...","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/a-first-order-reaction-has-the-rate-constant-k46x103s1-the-number-of-correct-statements-from-the"}}}]}20:T49f,(A) $\underset{1-\alpha}{\mathrm{A}} \longrightarrow$ Products

$\mathrm{k}=4.6 \times 10^{-3} \mathrm{~s}^{-1}$

$\mathrm{kt}=\ln \frac{1}{1-\alpha}$

$\alpha=1-\mathrm{e}^{-\mathrm{kt}}$

Reaction completes at infinite time.

(B) For first order reaction,

Half-life $=\frac{0.693}{4.6 \times 10^{-3}}=150.65 \mathrm{~s}$

(C) For $10 \%$ completion, $t=t_1$

$$ \begin{aligned} & a=100, a-x=100-10=90 \\\\ & k=\frac{2.303}{t_1} \log \frac{100}{90}=4.6 \times 10^{-3} \\\\ & t_1=\frac{2.303}{4.6 \times 10^{-3}} \times 0.04575 \end{aligned} $$

For $90 \%$ completion $t=t_2, a=100, a-x=100-90=10$

$$ \begin{aligned} & k=\frac{2.303}{t_2} \log \frac{100}{10}=4.6 \times 10^{-3} \\\\ & \frac{2.303}{t_2} \times 1=4.6 \times 10^{-3} \Rightarrow t_2=\frac{2.303}{4.6 \times 10^{-3}} \\\\ & \frac{t_2}{t_1}=\frac{1}{0.04575}=21.85 \quad \text { (Incorrect) } \end{aligned} $$

(E) Unit of rate = mol L^–1s^–1

Unit of rate constant = s^–1

Both have different units.

$\therefore$ Number of correct statements $=1$