75% of the first order is completed in 30min calculate the rate consta

1.	75% of the first order is completed in 30min calculate the rate constant of the reaction
Answer» $\huge\underline{\underline{\bf \orange{Question-}}}$ 75% of the first order is completed in 30min calculate the rate constant of the reaction. $\huge\underline{\underline{\bf \orange{Solution-}}}$ $\large\underline{\underline{\sf Given:}}$ a = 100% a - X = 100 - 75 ➝ 25% time (t) = 30 × 60 ➝ 1800sec $\large\underline{\underline{\sf To\:Find:}}$ Rate Constant (K) $\large{\rm We \:know\:that\:for\:1^{st}\:order\: Reaction- }$ ✪ $\large{\boxed{\bf \blue{K=\dfrac{2.303}{t}log\dfrac{a}{a-x}} }}$ $\implies{\sf \dfrac{2.303}{1800}×log\dfrac{100}{25}}$ $\implies{\sf \dfrac{2.303}{1800}×log4}$ $\implies{\sf \dfrac{2.303}{1800}×2log2}$ { log2 = 0.303 } $\implies{\sf\dfrac{2.303}{1800}×2×0.303 }$ $\implies{\sf \dfrac{1.39}{1800}}$ $\implies{\bf \red{Rate\: Constant (K)=7.7×10^{-4}sec^{-1}} }$ $\huge\underline{\underline{\bf \orange{Answer-}}}$ Rate constant of the reaction is ${\bf \red{7.7×10^{-4}sec^{-1}}}$ .