In acidic medium dichromate oin osxidizes stannous ion as :
`xSn^(2+)+yCr_(2)O_(7)^(2-)+zH^(+) to aSn^(4+)+bCr^(3+)cH_(2)O`

Options

A. "the value of x:y is " 1:3
B. the value of x+y+z is 18
C. a:b " is " 3:2
D. the value of z-c is 7

Answer

To solve the given stoichiometry problem involving the oxidation of stannous ions by dichromate ions in acidic medium, we will follow these steps:

### Step 1: Write the unbalanced reaction
The unbalanced reaction can be written as:
\[ x \text{Sn}^{2+} + y \text{Cr}_2\text{O}_7^{2-} + z \text{H}^+ \rightarrow a \text{Sn}^{4+} + b \text{Cr}^{3+} + c \text{H}_2\text{O} \]

### Step 2: Identify oxidation and reduction half-reactions
- **Oxidation half-reaction**: Stannous ion (\(\text{Sn}^{2+}\)) is oxidized to stannic ion (\(\text{Sn}^{4+}\)):
\[ \text{Sn}^{2+} \rightarrow \text{Sn}^{4+} + 2e^- \]

- **Reduction half-reaction**: Dichromate ion (\(\text{Cr}_2\text{O}_7^{2-}\)) is reduced to chromium ion (\(\text{Cr}^{3+}\)):
\[ \text{Cr}_2\text{O}_7^{2-} + 14 \text{H}^+ + 6e^- \rightarrow 2 \text{Cr}^{3+} + 7 \text{H}_2\text{O} \]

### Step 3: Balance the electrons in both half-reactions
To balance the electrons, we need to multiply the oxidation half-reaction by 3:
\[ 3 \text{Sn}^{2+} \rightarrow 3 \text{Sn}^{4+} + 6e^- \]

### Step 4: Combine the balanced half-reactions
Now we can combine the half-reactions:
\[ 3 \text{Sn}^{2+} + \text{Cr}_2\text{O}_7^{2-} + 14 \text{H}^+ \rightarrow 3 \text{Sn}^{4+} + 2 \text{Cr}^{3+} + 7 \text{H}_2\text{O} \]

### Step 5: Identify the coefficients
From the balanced equation, we can identify the coefficients:
- \( x = 3 \)
- \( y = 1 \)
- \( z = 14 \)
- \( a = 3 \)
- \( b = 2 \)
- \( c = 7 \)

### Step 6: Verify the options
Now we can check the options given in the question:
1. \( x : y = 3 : 1 \) (Correct)
2. \( x + y + z = 3 + 1 + 14 = 18 \) (Correct)
3. \( a : b = 3 : 2 \) (Correct)
4. \( z - c = 14 - 7 = 7 \) (Correct)

### Final Coefficients
Thus, the final values are:
- \( x = 3 \)
- \( y = 1 \)
- \( z = 14 \)
- \( a = 3 \)
- \( b = 2 \)
- \( c = 7 \)

### Summary of Correct Options
The correct options are the second, third, and fourth.

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