Problem 136 - A Complete Resource Book in Chemistry for JEE Main

Question

14..How many milliliters of \(0.05 \mathrm{M} \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) solution are required for titration of \(60 \mathrm{ml}\) of \(0.01\) M \(\mathrm{ZnSO}_{4}\) solution, when the product of reaction is \(\mathrm{K}_{2} \mathrm{Zn}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]_{2} ?\)

Step-by-Step Solution

Answer

8 mL of 0.05 M \(\text{K}_4[\text{Fe(CN)}_6]\) is needed.

Step 1: Write the Balanced Equation

First, we need to write the balanced chemical equation for the reaction:\[\text{3 ZnSO}_4 + 2 \text{K}_4[\text{Fe(CN)}_6] \rightarrow \text{K}_2\text{Zn}_3[\text{Fe(CN)}_6]_2 + 3 \text{K}_2\text{SO}_4\]This shows that 2 moles of \(\text{K}_4[\text{Fe(CN)}_6]\) react with 3 moles of \(\text{ZnSO}_4\).

Step 2: Determine Moles of ZnSO4

We need to calculate the number of moles of \(\text{ZnSO}_4\) in the solution. Use the molarity formula, which is moles = molarity \(\times\) volume (in liters):\[\text{Moles of ZnSO}_4 = 0.01 \frac{\text{mol}}{\text{L}} \times 0.060 \text{ L} = 0.0006 \text{ mol}\]

Step 3: Use Stoichiometry to Find Moles of K4[Fe(CN)6]

From the balanced equation, we see that 3 moles of \(\text{ZnSO}_4\) react with 2 moles of \(\text{K}_4[\text{Fe(CN)}_6]\). So, the moles of \(\text{K}_4[\text{Fe(CN)}_6]\) required are:\[\text{Moles of } \text{K}_4[\text{Fe(CN)}_6] = \frac{2}{3} \times 0.0006 \text{ mol} = 0.0004 \text{ mol}\]

Step 4: Calculate Volume of K4[Fe(CN)6] Solution Required

Now, find the volume (in liters) of the 0.05 M \(\text{K}_4[\text{Fe(CN)}_6]\) solution needed. Use the molarity formula rearranged:\[\text{Volume} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.0004 \text{ mol}}{0.05 \frac{\text{mol}}{\text{L}}}\]This gives:\[\text{Volume} = 0.008 \text{ L} = 8 \text{ mL}\]

Step 5: Final Solution

Thus, you need 8 milliliters of 0.05 M \(\text{K}_4[\text{Fe(CN)}_6]\) solution to titrate 60 milliliters of 0.01 M \(\text{ZnSO}_4\) solution.

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is crucial for understanding the proportions in which reactants combine to form products. In the context of titration, a balanced equation helps determine the exact amount of reactants needed for a complete reaction. For the given reaction:
\[3 \text{ZnSO}_4 + 2 \text{K}_4[\text{Fe(CN)}_6] \rightarrow \text{K}_2\text{Zn}_3[\text{Fe(CN)}_6]_2 + 3 \text{K}_2\text{SO}_4\]This indicates that 3 moles of zinc sulfate \((\text{ZnSO}_4)\) react with 2 moles of potassium hexacyanoferrate \((\text{K}_4[\text{Fe(CN)}_6])\). The coefficients in front of the chemical formulas tell us the ratio of the substances needed to react completely.
Understanding and calculating these ratios correctly is essential for finding out how much of each reactant is needed to completely participate in a reaction. Without this step, errors in measurement and calculation can occur, leading to inaccurate resultant products.

Stoichiometry

Stoichiometry is the aspect of chemistry that deals with the calculation of reactants and products in chemical reactions. It relies heavily on balanced chemical equations to quantify how much of each reactant is used and how much of each product is formed.
In the example exercise, we determined the moles of \(\text{ZnSO}_4\) involved by using its molarity and volume:

• Molarity of \(\text{ZnSO}_4\) = 0.01 M
• Volume of \(\text{ZnSO}_4\) = 60 mL = 0.060 L (converted to liters)

The calculation of moles is:
\[\text{Moles of ZnSO}_4 = 0.01 \times 0.060 = 0.0006 \text{ mol}\]
Understanding these relationships helps ensure that chemical reactions are executed accurately, with no excess of one reactant over another, unless purposely designed to do so.

Molarity Formula

Molarity is a measure of the concentration of a solute in a solution, expressed as moles per liter \((\text{mol/L})\). The molarity formula is fundamental in reactions involving solutions and is often used in titrations to calculate the amount of reactant needed to reach an endpoint.
Consider our need to find the volume of \(\text{K}_4[\text{Fe(CN)}_6]\) solution required:

• Moles of \(\text{K}_4[\text{Fe(CN)}_6]\) needed = 0.0004 mol
• Molarity of \(\text{K}_4[\text{Fe(CN)}_6]\) = 0.05 M

Using the rearranged molarity formula:
\[\text{Volume} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.0004}{0.05} = 0.008 \text{ L} = 8 \text{ mL}\]
This calculation is vital in titration, ensuring the correct amount of titrant is used to completely react with the analyte.

Chemical Reaction

A chemical reaction involves the transformation of substances through the breaking and formation of bonds, resulting in new substances with different properties. Understanding chemical reactions is key to mastering titration and other chemical processes.
In our example, we observe a typical exchange reaction where zinc sulfate reacts with potassium hexacyanoferrate. During this reaction:

• Bonds between atoms in the original compounds are broken
• New bonds form to create the products
• No atoms are lost or gained, just rearranged

Watching these transformations helps us predict the paths of reactions and the quantities of substances needed or produced. Keeping track of the reactants and products ensures that the chemical equations remain balanced, crucial for precise and accurate chemical analyses.