Answer:
[tex]\large \boxed{4.6 \times 10^{21}\text{ s}}[/tex]
Explanation:
Whenever a question asks you, "What is the concentration after a given time?" or something like that, you must use the appropriate integrated rate law expression.
The reaction is 2nd order, because the units of k are L·mol⁻¹s⁻¹.
The integrated rate law for a second-order reaction is
[tex]\dfrac{1}{\text{[A]}} =\dfrac{1}{\text{[A]}_{0}}+ kt[/tex]
Data:
k = 2.4 × 10⁻²¹ L·mol⁻¹s⁻¹
[A]₀ = 0.0100 mol·L⁻¹
[A] = 0.009 00 mol·L⁻¹
Calculation :
[tex]\begin{array}{rcl}\dfrac{1}{\text{[A]}} & = & \dfrac{1}{\text{[A]}_{0}}+ kt\\\\\dfrac{1}{0.00900 }& = & \dfrac{1}{0.0100} + 2.4 \times 10^{-21} \, t\\\\111.1&=& 100.0 + 2.4 \times 10^{-21} \, t\\\\11.1& = & 2.4 \times 10^{-21} \, t\\t & = & \dfrac{11.1}{ 2.4 \times 10^{-21}}\\\\& = & \mathbf{4.6 \times 10^{21}}\textbf{ s}\\\end{array}\\\text{It will take $\large \boxed{\mathbf{4.6 \times 10^{21}}\textbf{ s}}$ for the HI to decompose}[/tex]
