Multiple Choice
The graph below shows the decay of a radioactive isotope. What is the half-life of the isotope?
15. Chemical Kinetics
Half-Life
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Use the data below to determine the half-life of decomposition of NOCl reaction which follows 2nd order kinetics.
A
1.00×104 s
B
1.80×105 s
C
2.02×104 s
D
1.022×103 s
Verified step by step guidance1
Identify that the reaction follows second-order kinetics. The integrated rate law for a second-order reaction is \( \frac{1}{[A]} = kt + \frac{1}{[A]_0} \), where \([A]\) is the concentration at time \(t\), \([A]_0\) is the initial concentration, and \(k\) is the rate constant.
Use the data provided to calculate the rate constant \(k\). Choose two data points, for example, \(t = 0\) and \(t = 1100\) seconds, and their corresponding concentrations \([NOCl]_0 = 0.2563\, M\) and \([NOCl] = 0.2314\, M\). Substitute these values into the integrated rate law equation to solve for \(k\).
Calculate \(k\) using the equation: \( \frac{1}{0.2314} = k \times 1100 + \frac{1}{0.2563} \). Rearrange to solve for \(k\).
Once \(k\) is determined, use the formula for the half-life of a second-order reaction: \( t_{1/2} = \frac{1}{k[A]_0} \). Substitute the initial concentration \([A]_0 = 0.2563\, M\) and the calculated \(k\) into this formula.
Calculate the half-life \(t_{1/2}\) using the values obtained. This will give you the time required for the concentration of NOCl to decrease to half of its initial value.
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