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ap_chem:rate_of_reaction [2021/01/20 05:28] – created epix | ap_chem:rate_of_reaction [2021/01/21 06:39] (current) – [Integrated Rate Laws] added epix | ||
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====== Rate of Reaction and Rate Law ====== | ====== Rate of Reaction and Rate Law ====== | ||
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For most equations you can write a rate law in the form of $r = k[X]^m[Y]^n$, | For most equations you can write a rate law in the form of $r = k[X]^m[Y]^n$, | ||
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===== Finding Orders ===== | ===== Finding Orders ===== | ||
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+ | Take the example diagram here for the reaction $2NO_{(g)} + 2H_{2 (g)} -> N_{2 (g)} + 2H_2O_{(g)}$. To determine $m$ and $n$ for the rate law, you have to find pairs of trials that only modify **1** of the reactant compound' | ||
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+ | ^Muliplier^Order^Unit| | ||
+ | |No difference|0th order|$M^1*s^{-1}$| | ||
+ | |2x|1st order|$M^0*s^{-1}$ or $s^{-1}$| | ||
+ | |4x|2nd order|$M^{-1}*s^{-1}$| | ||
+ | |8x|3rd order|$M^{-2}*s^{-1}$| | ||
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+ | As $H_2$ has a 2:2 difference, $H_2$ is a **1st order** reaction, consequently, | ||
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+ | ===== Solving for $k$ ===== | ||
+ | We can use one of the table entries to solve for $k$ using the rate law we just created. The rate of production would be $r$ and the values for $NO$ and $H_2$ would be placed in their respective slots. | ||
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+ | - $r = k[H_2][NO]^2$ | ||
+ | - $1.8 \times 10^{-4} = k[0.001][0.006]^2$((when solving treat the brackets as parentheses)) | ||
+ | - $\frac{1.8 \times 10^{-4}}{3.6 \times 10^{-8}} = k$ | ||
+ | - $k = 5000$ $M^{-2}*s^{-1}$ | ||
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+ | The unit for each order is given to the right of the previously mentioned table, and the sum of the rate law's orders corresponding unit would be the $k$ value' | ||
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+ | ===== Solving Rate of Production or $r$ ===== | ||
+ | Now that we have an equation and $k$ value, we can estimate rates of production of $N_2$ by plugging and chugging values into our new rate law. Take trial 5 for example: | ||
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+ | - $r = k[H_2][NO]^2$ | ||
+ | - $r = 5000[0.002][0.002]^2$ | ||
+ | - $r = 4 \times 10^{-5}$ $\frac{\text{mol}}{L}*\text{min}$ | ||
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+ | ===== Rate of Disappearance ===== | ||
+ | Rate of Disappearance is similar to Production, after solving for the production of $N_2$, use [[ap_chem: | ||
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+ | $ 4 \times 10^{-5} * \frac{2NO}{1N_2} = -8 \times 10^{-5}$ $\frac{\text{mol}}{L}*\text{min}$((the negative is there because it is a rate of disappearance!)) which is our rate of disappearance of $NO$ for trial 5. | ||
+ | ===== Integrated Rate Laws ===== | ||
+ | Use the below chart to determine for each order. Note that half life problems on the AP test will always be given with first order for simplicity. | ||
+ | {{: |