A quantitative mixture of $\rm MnO_2$, $\rm NH_4H_2PO_4$, and $\rm H_3PO_4$ is heated together to 300 $\rm \degree C$ (Reaction 1). After washing with water and drying, a purple powder $\bf A$ is obtained, which contains no water of crystallization and has a molecular weight of 246.9. If it is dissolved in dilute sulfuric acid, the solution color does not change significantly, but a precipitate is formed (Reaction 2), while dissolving it in concentrated sulfuric acid yields a clear red solution.

Researchers performed thermogravimetric analysis on $\bf A$, and the intermediate products exhibited a variety of colors (the weight loss ratios here are all theoretical values): $\bf A$ is heated to 340 $\rm \degree C$ in an inert atmosphere, with a weight loss of 3.65%, yielding a blue substance (Reaction 3); continuing to heat to 460 $\rm \degree C$, it loses another 10.14% of its weight, yielding a white substance $\bf B$ (Reaction 4); subsequently, heating to 800 $\rm \degree C$ does not result in any noticeable weight loss, $\bf B$ melts and completely transforms into a pink liquid $\bf C$. The formula weight of $\bf C$ is 1.5 times that of $\bf B$.

The following statements exist:
1. The sum of the coefficients on the right side of the chemical equation for Reaction 1 is 15.
2. The sum of the coefficients on the left side of the chemical equation for Reaction 2 is less than 8.
3. The sum of all the atoms in the chemical formula of the blue product obtained in Reaction 3 is 27.
4. The sum of the coefficients on both sides of the chemical equation for Reaction 4 is less than or equal to 12.
5. The ideal point group of the anion of $\bf C$ is $\rm C_{3v}$.

The option containing all the correct statements is:
将定量的$\rm MnO_2$、$\rm NH_4H_2PO_4$与$\rm H_3PO_4$混合共热至300 $\rm \degree C$（反应1），经水洗、干燥可以得到一种紫色粉末$\bf A$，其不含结晶水，分子量为246.9。若将其溶于稀硫酸，溶液颜色无显著变化但有沉淀生成（反应2），而将其溶于浓硫酸则会得到澄清的红色溶液。

研究人员对$\bf A$进行了热重分析，其中间产物具有多种多样的颜色（这里的失重比例均为理论值）：$\bf A$于惰性气氛中加热至340 $\rm \degree C$，失重3.65%，得到蓝色物质（反应3）；继续加热至460 $\rm \degree C$，又失重10.14%，得到白色物质$\bf B$（反应4）；随后加热至800 $\rm \degree C$，未观察到明显失重，$\bf B$发生熔化并完全转化为粉色液体$\bf C$。$\bf C$的式量为$\bf B$的1.5倍。

存在下列说法：
1. 反应1的化学方程式右侧系数和为15
2. 反应2的化学方程式左侧系数和小于8
3. 反应3得到的蓝色产物，其化学式中所有原子数目之和为27
4. 反应4的化学方程式左右两侧系数之和小于等于12
5. $\bf C$的阴离子的理想点群为$\rm C_{3v}$

包含所有正确说法的选项是：
All other options are incorrect
2
5
4
1,2,3,4
2,3,5
1,2,4
2,4,5
1,3,5
2,5
1,3
3,4,5
1,2,4,5
2,3
1,5
4,5
3,5
1
1,2,3,5
其他选项均不正确
2
5
4
1,2,3,4
2,3,5
1,2,4
2,4,5
1,3,5
2,5
1,3
3,4,5
1,2,4,5
2,3
1,5
4,5
3,5
1
1,2,3,5
$\bf A$ should contain at least 1 $\rm Mn$, 1 $\rm NH_4^+$ and 1 $\rm PO_4^{3-}$. Subtracting these from the molecular weight of $\bf A$, 246.9, leaves approximately 79, which is $\rm P+3O$. Therefore, $\bf A$ is $\rm NH_4MnP_2O_7$.

<Checkpoint>[$\bf A$ is $\rm NH_4MnP_2O_7$](1)</Checkpoint>

Reaction 1: $\rm Mn$ is reduced, and the only element that can be oxidized is $\rm O$, producing $\rm O_2$. The equation is: $\rm 4MnO_2 + 4NH_4H_2PO_4 + 4H_3PO_4 \rightarrow 4NH_4MnP_2O_7 + 10H_2O + O_2$. The sum of the coefficients on the right side is 15, so statement 1 is correct.

<Checkpoint>[Reaction 1 equation is: $\rm 4MnO_2 + 4NH_4H_2PO_4 + 4H_3PO_4 \rightarrow 4NH_4MnP_2O_7 + 10H_2O + O_2$](1)</Checkpoint>

Reaction 2: Dissolving in dilute sulfuric acid produces a precipitate, corresponding to the disproportionation of trivalent $\rm Mn$ to produce $\rm Mn^{2+}$ and $\rm MnO_2$. The equation is: $\rm 2NH_4MnP_2O_7 + 2H_2SO_4 + 4H_2O \rightarrow (NH_4)_2SO_4 + MnSO_4 + MnO_2 + 4H_3PO_4$. Statement 2 is incorrect.

<Checkpoint>[Reaction 2 equation is: $\rm 2NH_4MnP_2O_7 + 2H_2SO_4 + 4H_2O \rightarrow (NH_4)_2SO_4 + MnSO_4 + MnO_2 + 4H_3PO_4$](1)</Checkpoint>

First step weight loss: $\rm M_1 = w_1 \times M = 3.65 \times 10^{-2} \times 246.922~g\cdot mol^{-1} = 9.01~g\cdot mol^{-1}$, corresponding to 0.5 $\rm H_2O$ molecules.

<Checkpoint>[First step weight loss corresponds to 0.5 $\rm H_2O$ molecules](2)</Checkpoint>

Second step weight loss: $\rm M_2 = w_2 \times M = 10.14 \times 10^{-2} \times 246.922~g\cdot mol^{-1} = 25.04~g\cdot mol^{-1}$, corresponding to $\rm N+3H+0.5O$ (what is lost may be $\rm N_2$, $\rm H_2O$, $\rm NH_3$).

<Checkpoint>[Second step weight loss corresponds to $\rm N+3H+0.5O$, what is lost may be $\rm N_2$, $\rm H_2O$, $\rm NH_3$](2)</Checkpoint>

Therefore, in the two steps of weight loss, 1 molecule of $\rm NH_4MnP_2O_7$ loses 1 $\rm N$, 4 $\rm H$, and 1 $\rm O$, corresponding to the simplest formulas of $\bf B$ and $\bf C$ being $\rm MnP_2O_6$.

<Checkpoint>[$\bf B$ and $\bf C$ simplest formulas are $\rm MnP_2O_6$](2)</Checkpoint>

Since the formula weight of $\bf C$ is 1.5 times that of $\bf B$, we can deduce from the simplest case that $\bf B$:
$\rm Mn_2P_4O_{12}$, $\bf C$: $\rm Mn_3P_6O_{18}$

<Checkpoint>[$\bf B$:   $\rm Mn_2P_4O_{12}$, $\bf C$: $\rm Mn_3P_6O_{18}$](1)</Checkpoint>

Reaction 3: Two molecules of $\bf A$ produce one molecule of $\rm H_2O$, and also produce $\rm Mn_2(NH_3)_2P_4O_{13}$. The equation is: $\rm 2NH_4MnP_2O_7 \rightarrow Mn_2(NH_3)_2P_4O_{13} + H_2O$. Statement 3 is correct.

<Checkpoint>[Reaction 3 equation is: $\rm 2NH_4MnP_2O_7 \rightarrow Mn_2(NH_3)_2P_4O_{13} + H_2O$](1)</Checkpoint>

Reaction 4: $\rm Mn_2(NH_3)_2P_4O_{13}$ is converted to $\rm Mn_2P_4O_{12}$, losing $\rm NH_3$, $\rm N_2$ and $\rm H_2O$. The equation is: $\rm 3Mn_2(NH_3)_2P_4O_{13} \rightarrow 3Mn_2P_4O_{12} + 4NH_3 + N_2 + 3H_2O$. Statement 4 is incorrect.

<Checkpoint>[Reaction 4 equation is: $\rm 3Mn_2(NH_3)_2P_4O_{13} \rightarrow 3Mn_2P_4O_{12} + 4NH_3 + N_2 + 3H_2O$](1)</Checkpoint>

The anion of $\bf C$ is $\rm P_3O_9^{3-}$, and its structure is O=P(OP(O1)([O-])=O)([O-])OP1([O-])=O, the ideal point group is $\rm C_{3v}$. Statement 5 is correct.

<Checkpoint>[$\bf C$ anion is $\rm P_3O_9^{3-}$, ideal point group is $\rm C_{3v}$](1)</Checkpoint>

<MultiModal>![$\bf C$ anion structure is O=P(OP(O1)([O-])=O)([O-])OP1([O-])=O](/media/uploads/531a7942-f939-4bca-bdda-62efc0cf81fd.png)</MultiModal>

Statements 1, 3, and 5 are correct, choose I
$\bf A$中应该至少含1个$\rm Mn$、1个$\rm NH_4^+$和1个$\rm PO_4^{3-}$，$\bf A$的分子量246.9减去这些还剩下约79，即$\rm P+3O$，故$\bf A$为$\rm NH_4MnP_2O_7$

<Checkpoint>[$\bf A$为$\rm NH_4MnP_2O_7$](1)</Checkpoint>

反应1：$\rm Mn$被还原了，被氧化的元素只能是$\rm O$，产生$\rm O_2$。方程式为：$\rm 4MnO_2 + 4NH_4H_2PO_4 + 4H_3PO_4 \rightarrow 4NH_4MnP_2O_7 + 10H_2O + O_2$，右侧系数和为15，说法1正确

<Checkpoint>[反应1方程式为：$\rm 4MnO_2 + 4NH_4H_2PO_4 + 4H_3PO_4 \rightarrow 4NH_4MnP_2O_7 + 10H_2O + O_2$](1)</Checkpoint>

反应2：溶解在稀硫酸产生沉淀，对应于三价$\rm Mn$发生歧化产生$\rm Mn^{2+}$和$\rm MnO_2$。方程式为：$\rm 2NH_4MnP_2O_7 + 2H_2SO_4 + 4H_2O \rightarrow (NH_4)_2SO_4 + MnSO_4 + MnO_2 + 4H_3PO_4$，说法2错误

<Checkpoint>[反应2方程式为：$\rm 2NH_4MnP_2O_7 + 2H_2SO_4 + 4H_2O \rightarrow (NH_4)_2SO_4 + MnSO_4 + MnO_2 + 4H_3PO_4$](1)</Checkpoint>

第一步失重：$\rm M_1 = w_1 \times M = 3.65 \times 10^{-2} \times 246.922~g\cdot mol^{-1} = 9.01~g\cdot mol^{-1}$，对应0.5个$\rm H_2O$分子

<Checkpoint>[第一步失重对应0.5个$\rm H_2O$分子](2)</Checkpoint>

第二步失重：$\rm M_2 = w_2 \times M = 10.14 \times 10^{-2} \times 246.922~g\cdot mol^{-1} = 25.04~g\cdot mol^{-1}$，对应$\rm N+3H+0.5O$（失去的可能是$\rm N_2$、$\rm H_2O$、$\rm NH_3$）

<Checkpoint>[第二步失重对应$\rm N+3H+0.5O$，失去的可能是$\rm N_2$、$\rm H_2O$、$\rm NH_3$](2)</Checkpoint>

因此两步失重中1分子$\rm NH_4MnP_2O_7$失去1个$\rm N$、4个$\rm H$、1个$\rm O$，对应$\bf B$、$\bf C$最简式均为$\rm MnP_2O_6$

<Checkpoint>[$\bf B$、$\bf C$最简式均为$\rm MnP_2O_6$](2)</Checkpoint>

由于$\bf C$的式量为$\bf B$的1.5倍，由最简单情况可推知$\bf B$：  
$\rm Mn_2P_4O_{12}$，$\bf C$：$\rm Mn_3P_6O_{18}$

<Checkpoint>[$\bf B$：   $\rm Mn_2P_4O_{12}$，$\bf C$：$\rm Mn_3P_6O_{18}$](1)</Checkpoint>

反应3：两分子的$\bf A$产生一分子的$\rm H_2O$，还产生了$\rm Mn_2(NH_3)_2P_4O_{13}$，方程式为：$\rm 2NH_4MnP_2O_7 \rightarrow Mn_2(NH_3)_2P_4O_{13} + H_2O$，说法3正确

<Checkpoint>[反应3方程式为：$\rm 2NH_4MnP_2O_7 \rightarrow Mn_2(NH_3)_2P_4O_{13} + H_2O$](1)</Checkpoint>

反应4：$\rm Mn_2(NH_3)_2P_4O_{13}$转变为$\rm Mn_2P_4O_{12}$，失去了$\rm NH_3$、$\rm N_2$和$\rm H_2O$，方程式为：$\rm 3Mn_2(NH_3)_2P_4O_{13} \rightarrow 3Mn_2P_4O_{12} + 4NH_3 + N_2 + 3H_2O$，说法4错误

<Checkpoint>[反应4方程式为：$\rm 3Mn_2(NH_3)_2P_4O_{13} \rightarrow 3Mn_2P_4O_{12} + 4NH_3 + N_2 + 3H_2O$](1)</Checkpoint>

$\bf C$的阴离子为$\rm P_3O_9^{3-}$，其结构为O=P(OP(O1)([O-])=O)([O-])OP1([O-])=O，理想点群为$\rm C_{3v}$，说法5正确

<Checkpoint>[$\bf C$的阴离子为$\rm P_3O_9^{3-}$，理想点群为$\rm C_{3v}$](1)</Checkpoint>

<MultiModal>![$\bf C$的阴离子结构为O=P(OP(O1)([O-])=O)([O-])OP1([O-])=O](/media/uploads/531a7942-f939-4bca-bdda-62efc0cf81fd.png)</MultiModal>

说法1、3、5正确，选I