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For a first-order reaction, the plot of ₁₀[R] versus time t (in minutes) is a straight line passing through the points (0, 2) and (50, 0.5) . The half-life of the reaction is _____ minutes. [Given : 2 = 0.3 ]

Correct answer

10

Step-by-step solution

For a first-order reaction, the integrated rate law is: k t = 2.303 ( [R]₀ [R] ) ₁₀[R] = ₁₀[R]₀ - k 2.303 t The plot of ₁₀[R] versus t is a straight line with slope m = - k 2.303 . Using the given points (0, 2) and (50, 0.5) , the slope is: m = 0.5 - 2 50 - 0 = - 1.5 50 = -0.03 Equating the slopes: - k 2.303 = -0.03 k = 0.03 2.303 The half-life t_ 1/2 is given by: t_ 1/2 = 2.303 2 k Substituting the value of k and 2 = 0.3 : t_ 1/2 = 2.303 0.3 0.03 2.303 = 0.3 0.03 = 10 minutes. Answer: 10

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