diff --git a/docs/.vitepress/config/sidebar.ts b/docs/.vitepress/config/sidebar.ts index 237474a0..cae5f1d9 100644 --- a/docs/.vitepress/config/sidebar.ts +++ b/docs/.vitepress/config/sidebar.ts @@ -23,7 +23,8 @@ export const sidebar: DefaultTheme.Config['sidebar'] = { collapsed: true, items: [ { text: 'Problem: 02-20', link: '/academic/chemistry/problems/02-20' }, - { text: 'Problem: 03-02', link: '/academic/chemistry/problems/03-02' }, + { text: 'Problem: 03-02-1', link: '/academic/chemistry/problems/03-02' }, + { text: 'Problem: 03-02-2', link: '' }, ], }, ], diff --git a/docs/academic/chemistry/problems/03-02.md b/docs/academic/chemistry/problems/03-02-1.md similarity index 99% rename from docs/academic/chemistry/problems/03-02.md rename to docs/academic/chemistry/problems/03-02-1.md index 5a35dc89..53b70aae 100644 --- a/docs/academic/chemistry/problems/03-02.md +++ b/docs/academic/chemistry/problems/03-02-1.md @@ -1,4 +1,4 @@ -# Problem: 03-02 +# Problem: 03-02-1 ## Question diff --git a/docs/academic/chemistry/problems/03-02-2.md b/docs/academic/chemistry/problems/03-02-2.md new file mode 100644 index 00000000..3289593e --- /dev/null +++ b/docs/academic/chemistry/problems/03-02-2.md @@ -0,0 +1,27 @@ +# Problem: 03-02-2 + +## Question + +The rate law for a particular reaction is rate $=k[\mathrm{XY}]^2$. In an experiment, the initial rate of the reaction is determined to be $0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})$ when the initial concentration of $\mathrm{XY}$ is $0.40 \mathrm{~mol} / \mathrm{L}$. +- What is the value of the rate constant, $k$, for the reaction? + - [ ] $0.10 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})$ + - [ ] $0.40 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})$ + - [x] $1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})$ + - [ ] $2.5 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})$ + +## Solution + +lo tind the value of the rate constant for the reaction, let's first solve the rate law for $k$ : +$$ +k=\frac{\text { rate }}{[\mathrm{XY}]^2} +$$ +Next, let's plug in the initial rate and concentration given in the text: +$$ +\begin{aligned} +k & =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{(0.40 \mathrm{~mol} / \mathrm{L})^2} \\ +& =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{0.16 \mathrm{~mol}^2 / \mathrm{L}^2} \\ +& =1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s}) +\end{aligned} +$$ +So, the value of the rate constant for the reaction is +$1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})$ \ No newline at end of file