From 4a51bd863c159e8bb61620ee5ef91313efc9bb41 Mon Sep 17 00:00:00 2001
From: andatoshiki <101481353+andatoshiki@users.noreply.github.com>
Date: Thu, 2 Mar 2023 14:54:09 +0800
Subject: [PATCH] doc: addd new problem set for chemistry and update sidebars
 and titles

---
 docs/.vitepress/config/sidebar.ts             |  3 ++-
 .../problems/{03-02.md => 03-02-1.md}         |  2 +-
 docs/academic/chemistry/problems/03-02-2.md   | 27 +++++++++++++++++++
 3 files changed, 30 insertions(+), 2 deletions(-)
 rename docs/academic/chemistry/problems/{03-02.md => 03-02-1.md} (99%)
 create mode 100644 docs/academic/chemistry/problems/03-02-2.md

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