If 20 " mL of " 0.1 M `K_(2)Cr_(2)O_(7)` is required to titrate 10 " mL of " a liquid iron supplement, then the concentration of iron in the the the vitamin solution is

Options

A. 1.2 M
B. 2.4 M
C. 0.6 N
D. 1.56 M

Explanation

To find the concentration of iron in the vitamin solution, we will follow these steps:

### Step 1: Write the balanced chemical equation for the reaction.
The reaction between dichromate ions and iron ions can be represented as:
\[ \text{Cr}_2\text{O}_7^{2-} + 6 \text{Fe}^{2+} \rightarrow 2 \text{Cr}^{3+} + 3 \text{Fe}^{3+} \]

### Step 2: Determine the number of equivalents of \( \text{Cr}_2\text{O}_7^{2-} \).
Given:
- Volume of \( \text{K}_2\text{Cr}_2\text{O}_7 \) solution = 20 mL = 0.020 L
- Molarity of \( \text{K}_2\text{Cr}_2\text{O}_7 \) = 0.1 M

The number of equivalents of \( \text{Cr}_2\text{O}_7^{2-} \) can be calculated using the formula:
\[ \text{Equivalents} = \text{Molarity} \times \text{Volume (L)} \times n \]
where \( n \) is the number of electrons transferred (n-factor). For \( \text{Cr}_2\text{O}_7^{2-} \), \( n = 6 \).

Calculating:
\[ \text{Equivalents of } \text{Cr}_2\text{O}_7^{2-} = 0.1 \, \text{mol/L} \times 0.020 \, \text{L} \times 6 = 0.012 \, \text{equivalents} \]

### Step 3: Set up the equivalence relationship.
According to the equivalence principle:
\[ \text{Equivalents of } \text{Cr}_2\text{O}_7^{2-} = \text{Equivalents of Fe}^{2+} \]

### Step 4: Calculate the concentration of iron.
Given:
- Volume of iron supplement = 10 mL = 0.010 L
Let \( M \) be the molarity of the iron solution.

Using the equivalence relationship:
\[ 0.012 \, \text{equivalents} = M \times 0.010 \, \text{L} \times 1 \]
(where \( n \) for \( \text{Fe}^{2+} \) is 1)

Rearranging gives:
\[ M = \frac{0.012}{0.010} = 1.2 \, \text{M} \]

### Final Answer:
The concentration of iron in the vitamin solution is **1.2 M**.

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