Stable water-soluble transition metal complexes for catalytic and biomedical purposes are an important research area in modern coordination chemistry. In ethanol, the reaction of $\mathrm{CoCl_2\cdot 6H_2O}$ with $\mathrm{P(CH_2OH)_3, H_2S}$ yielded a complex $\mathbf{A}\cdot yH_2O$ with a molecular weight of 1444.6. $\mathbf{A}$ is a multinuclear complex with octahedral symmetry, containing only two types of ligands, and the chemical environment of the same element in the complex is completely identical except for hydrogen. It is known that $y\in[4,8]$. Let $a, b$ be the sum of the coefficients on the left and right sides of the chemical equation for the synthesis of $\mathbf{A}$ (reaction coefficients are the simplest integer ratio), then the value of $log_y(\frac{b-a}{b+a})$ is (considered correct only when the error is within 0.01):
用于催化和生物医学目的的稳定水溶性过渡金属配合物是现代配位化学的重要研究领域。在乙醇中，用 $\mathrm{CoCl_2\cdot 6H_2O}$ 与 $\mathrm{P(CH_2OH)_3，H_2S}$共同反应得到了分子量为1444.6的配合物$\mathbf{A}\cdot yH_2O$。$\mathbf{A}$为多核配合物，具有八面体对称性，仅含两种配体，配合物中除氢元素外，同种元素的化学环境完全相同。已知$y\in[4,8]$。设$a，b$为合成$\mathbf{A}$的化学方程式（反应系数为最简整数比）左侧和右侧系数之和，则$log_y(\frac{b-a}{b+a})$的值为（只有误差在0.01之内时视为正确）：
All other options are incorrect
-1.08
-0.95
-0.89
-0.76
-0.61
0.18
0.39
0.58
0.94
1.23
1.50
-0.44
-0.32
-0.14
其他选项均不正确
-1.08
-0.95
-0.89
-0.76
-0.61
0.18
0.39
0.58
0.94
1.23
1.50
-0.44
-0.32
-0.14
Considering multinuclearity, octahedral symmetry, and identical chemical environments for the same element, $\mathrm{P(CH_2OH)_3}$ must be the terminal group, which implies that there should be 6 nuclei and $\mathrm{S^{2-}}$ must be the bridging ligand.

<Checkpoint>[$\mathrm{S^{2-}}$ as a bridging ligand](1)</Checkpoint>

Therefore, the number of $\mathrm{P(CH_2OH)_3}$ may be 6, 12, etc., and the number of $\mathrm{S^{2-}}$ may be 8, 12, etc.

After simple calculation, it is found that the molecular weight can only be less than 1444.6 when both numbers take the minimum values. Therefore, the number of $\mathrm{P(CH_2OH)_3}$ is 6, and the number of $\mathrm{S^{2-}}$ is 8. The core chemical formula is $\mathrm{Co_6S_8(P(CH_2OH)_3)_6}$.

<Checkpoint>[$\mathbf{A}$ is $\mathrm{Co_6S_8(P(CH_2OH)_3)_6}$](2)</Checkpoint>

$M(\mathbf{A})=1354.57~g/mol$

$yM(\mathrm{H_2O})=1444.6-1354.57=90.03~g/mol$

Therefore $y=5$

<Checkpoint>[$y=5$](1)</Checkpoint>

The equation for the synthesis of $\mathbf{A}$ is:

$\mathrm{6CoCl_2\cdot 6H_2O+6P(CH_2OH)_3+8H_2S+O_2\to Co_6S_8(P(CH_2OH)_3)_6\cdot 5H_2O+33H_2O+12HCl}$

Therefore $a=21，b=46$.

<Checkpoint>[$a=21，b=46$](1)</Checkpoint>

$log_y(\frac{b-a}{b+a})=log_5\frac{25}{67}\approx-0.61$

<MultiModal>![配合物结构](/media/uploads/e9ce986b-0ddd-40a0-944e-0a650769f3fe.png)</MultiModal>
考虑到多核，八面体对称性，同种元素化学环境相同，$\mathrm{P(CH_2OH)_3}$必须作为端基，可以推出应该为6核并且$\mathrm{S^{2-}}$必须作桥。

<Checkpoint>[$\mathrm{S^{2-}}$为桥连配体](1)</Checkpoint>

故$\mathrm{P(CH_2OH)_3}$的个数可能为6、12等，$\mathrm{S^{2-}}$的个数可能为
8、12等。

经过简单计算发现只有当二者的数目均取最小值时，分子量才可以小于1444.6，因此$\mathrm{P(CH_2OH)_3}$的个数为6，$\mathrm{S^{2-}}$的个数为
8。核心的化学式为$\mathrm{Co_6S_8(P(CH_2OH)_3)_6}$。

<Checkpoint>[$\mathbf{A}$为$\mathrm{Co_6S_8(P(CH_2OH)_3)_6}$](2)</Checkpoint>

$M(\mathbf{A})=1354.57~g/mol$

$yM(\mathrm{H_2O})=1444.6-1354.57=90.03~g/mol$

因此$y=5$

<Checkpoint>[$y=5$](1)</Checkpoint>

合成$\mathbf{A}$的方程式为：

$\mathrm{6CoCl_2\cdot 6H_2O+6P(CH_2OH)_3+8H_2S+O_2\to Co_6S_8(P(CH_2OH)_3)_6\cdot 5H_2O+33H_2O+12HCl}$

因此$a=21，b=46$。

<Checkpoint>[$a=21，b=46$](1)</Checkpoint>

$log_y(\frac{b-a}{b+a})=log_5\frac{25}{67}\approx-0.61$

<MultiModal>![配合物结构](/media/uploads/e9ce986b-0ddd-40a0-944e-0a650769f3fe.png)</MultiModal>