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:T43c,{"@context":"https://schema.org","@graph":[{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://www.divinejee.com"},{"@type":"ListItem","position":4,"name":"t875 is the time required for the reaction to undergo 875 co","item":"https://www.divinejee.com/question/t875-is-the-time-required-for-the-reaction-to-undergo-875-completion-and-t50-is-the-time-required"}]},{"@type":"QAPage","mainEntity":{"@type":"Question","name":"Question t875 is the time required for the reaction to undergo 875 co on Topic","text":"

$\\mathrm{t}_{87.5}$ is the time required for the reaction to undergo $87.5 \\%$ completion and $\\mathrm{t}_{50}$ is the time required for the reacti...","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/t875-is-the-time-required-for-the-reaction-to-undergo-875-completion-and-t50-is-the-time-required"}}}]}21:T438,For a first-order reaction, the relation between the reaction rate constant (k) and time (t) for a given percentage of completion (p) is:

$$\ln\left(\frac{1}{1-p}\right) = kt$$

For t₅₀ (50% completion), p = 0.5:

$$\ln\left(\frac{1}{1-0.5}\right) = k\cdot t_{50}$$

$$\ln\left(\frac{1}{0.5}\right) = k\cdot t_{50}$$

$$\ln(2) = k\cdot t_{50}$$

For t₈₇.₅ (87.5% completion), p = 0.875:

$$\ln\left(\frac{1}{1-0.875}\right) = k\cdot t_{87.5}$$

$$\ln\left(\frac{1}{0.125}\right) = k\cdot t_{87.5}$$ $$\ln(8) = k\cdot t_{87.5}$$

Now, we need to find the relationship between t₈₇.₅ and t₅₀:

$$\frac{k\cdot t_{87.5}}{k\cdot t_{50}} = \frac{\ln(8)}{\ln(2)}$$

Since the k's cancel out, we have:

$$\frac{t_{87.5}}{t_{50}} = \frac{\ln(8)}{\ln(2)}$$

Using the property of logarithms, we get:

$$\frac{t_{87.5}}{t_{50}} = \frac{\ln(2^3)}{\ln(2)}$$

$$\frac{t_{87.5}}{t_{50}} = 3$$

So, the value of x is 3.