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# (Solved): Using calculus, you can obtain the folloming relationship betueen the concentration of $$\mathrm{A ... Using calculus, you can obtain the folloming relationship betueen the concentration of \( \mathrm{A}$$ and the time. $\frac{1}{[\mathrm{~A}]}=k t+\frac{1}{[\mathrm{~A}]} \text { (sowad-onder initguinad mition) }$ Using this equation, you can calculate the conccntration of $$\mathrm{NO}_{2}$$ at any time during its desomposition if you know the rate constant and the initial concentration. At 330 C, the rate constant for the decomposition of $$\mathrm{NO}_{2}$$ is $$0.775 \mathrm{~L}$$ (mol $$\left./ \mathrm{s}\right)$$. Supposo the initial concentration is $$0.0030 \mathrm{~mol} / \mathrm{L}$$. What is the concentration of $$\mathrm{NO}_{2}$$ after $$645 \mathrm{~s}$$ ? By substituting into the previous equation, you get $\frac{1}{\mathrm{INO}, \mathrm{l}}=0.775 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s}) \times 645 \mathrm{~s}+\frac{1}{0.0030 \mathrm{~mol} / \mathrm{L}}=83 \times 10^{2} \mathrm{~L} / \mathrm{mol}$ If you illvert both eider of the equation, you find that $$\left[\mathrm{NO}_{3}\right]=0.0012 \mathrm{Y}_{201 / 1}$$. Thus, alter 645 $$\mathrm{x}$$, the concentration of $$\mathrm{NO}_{2}$$ decresed from $$0.0030 \mathrm{~mol} \mathrm{~L}$$ to $$\{0012$$ mol/L. Zero-Order Reactions These are intanco Whicre reactions are zen-order. As comple iscludes the decomposition of etby alocholia the lintr in the preseact of the enyyme liver alcobol dehydivermane Omic again, fostuder the reaction with the general form

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