The rate constant for a first order reaction is 4.606×10−3s−14.606 \times 10^{-3} s^{-1}4.606×10−3s−1. The time required to reduce 2.0 g of the reactant to 0.2 g is :
100 s
200 s
500 s
1000 s
For a first order reaction, t=2.303klog[A]0[A]tt = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}t=k2.303log[A]t[A]0. Given k=4.606×10−3s−1k = 4.606 \times 10^{-3} s^{-1}k=4.606×10−3s−1, [A]0=2.0g[A]_0 = 2.0 g[A]0=2.0g, [A]t=0.2g[A]_t = 0.2 g[A]t=0.2g. t=2.3034.606×10−3log2.00.2=2.3034.606×10−3log10=2.3034.606×10−3×1=10002=500st = \frac{2.303}{4.606 \times 10^{-3}} \log \frac{2.0}{0.2} = \frac{2.303}{4.606 \times 10^{-3}} \log 10 = \frac{2.303}{4.606 \times 10^{-3}} \times 1 = \frac{1000}{2} = 500 st=4.606×10−32.303log0.22.0=4.606×10−32.303log10=4.606×10−32.303×1=21000=500s.
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