In the following reaction sequence in aqueous solution, the species X,Y and Z, respectively
`S_(2)O_(3)^(2-)overset(Ag^(+))(rarr)underset("clear solution")(X)overset(Ag^(+))(rarr)underset("white precipitate")(Y)overset("withtime")(rarr)underset(" black precipitate")(Z)`

Options

A. `[Ag(S_2O_3)_2]^(3-), Ag_(2)S_(2)O_(3), Ag_(2)S`
B. `[Ag(S_2O_3)_3]^(5-), Ag_(2)SO_(3), Ag_(2)S`
C. `[Ag(SO_3)_2]^(3-), Ag_(2)S_(2)O_(3), Ag`
D. `[Ag(SO_3)_3]^(3-), Ag_(2)SO_(4), AgS`

Answer

To solve the problem, we need to identify the species X, Y, and Z in the given reaction sequence involving \( S_2O_3^{2-} \) and \( Ag^+ \).

### Step 1: Identify Species X
The first reaction involves \( S_2O_3^{2-} \) reacting with \( Ag^+ \) to form a clear solution. The product formed is a complex ion, which is \( Ag_2S_2O_3^{3-} \). This complex is soluble in water, hence it appears as a clear solution.

**Species X:**
\[ X = Ag_2S_2O_3^{3-} \]

### Step 2: Identify Species Y
Next, the clear solution \( X \) reacts again with \( Ag^+ \). This reaction leads to the formation of a white precipitate, which is \( Ag_2S_2O_3 \). This compound is insoluble in water, resulting in a white precipitate.

**Species Y:**
\[ Y = Ag_2S_2O_3 \]

### Step 3: Identify Species Z
Finally, the white precipitate \( Y \) undergoes a change over time to form a black precipitate. This transformation is due to the decomposition of \( Ag_2S_2O_3 \) into \( Ag_2S \), which is known to be a black precipitate.

**Species Z:**
\[ Z = Ag_2S \]

### Summary of Species
- **X:** \( Ag_2S_2O_3^{3-} \) (clear solution)
- **Y:** \( Ag_2S_2O_3 \) (white precipitate)
- **Z:** \( Ag_2S \) (black precipitate)

### Final Answer
The species X, Y, and Z respectively are:
- \( X = Ag_2S_2O_3^{3-} \)
- \( Y = Ag_2S_2O_3 \)
- \( Z = Ag_2S \)