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← JEE Main 2022 · 30 Jun · Shift 1
ChemistryInteger+4 / -1Question 84 of 90

JEE Main 2022 · 30 Jun · Shift 1, Chemistry question 84

For the reaction P → B, the values of frequency factor A and activation energy EAE_A are 4×10134\times10^{13} s−1^{-1} and 8.3 kJ mol−1^{-1} respectively. If the reaction is of first order, the temperature at which the rate constant is 2×10−62\times10^{-6} s−1^{-1} is ______ ×10−1\times10^{-1} K

(Given : ln 10 = 2.3, R = 8.3 J K−1^{-1} mol−1^{-1}, log2 = 0.30)

Answer and worked solution

Official answer: 225

Arrhenius. ln⁡kA=ln⁡(5×10−20)=1.61−46=−44.39\ln\frac kA=\ln(5\times10^{-20})=1.61-46=-44.39, and EaR=1000\frac{E_a}R=1000 K.

T =100044.39≈22.5=\frac{1000}{44.39}\approx22.5 K =225×10−1=225\times10^{-1} K.

Answer: 225