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 K₄[Fe(CN)₆] solution are required.

Step 1: Write the Balanced Reaction Equation

First, let's write the balanced chemical reaction between ZnSO₄ and K₄[Fe(CN)₆]. The balanced reaction is: \[ 3 ext{ZnSO}_4 + 2 ext{K}_4[ ext{Fe(CN)}_6] ightarrow ext{K}_2 ext{Zn}_3[ ext{Fe(CN)}_6]_2 + 3 ext{K}_2 ext{SO}_4 \] This equation shows us that 3 moles of ZnSO₄ react with 2 moles of K₄[Fe(CN)₆].

Step 2: Calculate Moles of ZnSO₄

We need to find how many moles of ZnSO₄ are present in the given solution. The concentration of ZnSO₄ is 0.01 M, and the volume is 60 mL or 0.060 L. Therefore, the moles of ZnSO₄ are: \[ 0.01 imes 0.060 = 0.0006 ext{ moles} \]

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

Using the stoichiometry of the reaction, 3 moles of ZnSO₄ react with 2 moles of K₄[Fe(CN)₆]. Therefore, the moles of K₄[Fe(CN)₆] required are: \[ rac{2}{3} imes 0.0006 = 0.0004 ext{ moles} \]

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

The concentration of the K₄[Fe(CN)₆] solution is 0.05 M. The volume (in Liters) required to provide 0.0004 moles is: \[ rac{0.0004}{0.05} = 0.008 ext{ L} \] Convert this into mL by multiplying by 1000: \[ 0.008 imes 1000 = 8 ext{ mL} \]

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry, allowing us to predict the amounts of reactants and products required in a chemical reaction. It is based on the principle that atoms are conserved in reaction processes. Whenever we react chemical substances, stoichiometry helps us determine the relationship between the amounts of substances involved.

In our exercise, stoichiometry is applied to calculate the amount of titrant needed to completely react with a given amount of analyte. This involves using the coefficients from the balanced chemical reaction, which tell us the ratio of the moles of each reactant and product involved.

For example, if 3 moles of ZnSO₄ react with 2 moles of K₄[Fe(CN)₆], using stoichiometry, we can determine how many moles of K₄[Fe(CN)₆] are needed to react with the ZnSO₄ present in the solution.

Balanced Chemical Reaction

A balanced chemical reaction is crucial as it ensures that the law of conservation of mass is upheld. This means that the number of atoms for each element is the same on both the reactant and product sides of the equation. Balanced equations provide the necessary stoichiometric coefficients for calculations.

In the given exercise, balancing the chemical reaction between ZnSO₄ and K₄[Fe(CN)₆] gives us the equation:

• \[ 3 \text{ZnSO}_4 + 2 \text{K}_4[\text{Fe(CN)}_6] \rightarrow \text{K}_2\text{Zn}_3[\text{Fe(CN)}_6]_2 + 3 \text{K}_2\text{SO}_4 \]

Importance of a Balanced Reaction

Without this balanced equation, it would be impossible to correctly compute the quantities of each compound needed in the reaction, making stoichiometry calculations inaccurate.
Always ensure you balance the equation first to reflect true stoichiometric relationships.

Molar Calculations

Molar calculations are needed to understand how many moles of a substance are present in a solution based on its given concentration and volume. Given that concentration (usually in Molarity, M) is defined as moles of solute per liter of solution, this relationship allows us to determine the moles of a substance if we know the concentration and the volume of the solution.

For the exercise at hand, we first determine how many moles of ZnSO₄ are present by multiplying its concentration by the volume of the solution:

\[ \text{Moles of ZnSO}_4 = 0.01 \times 0.060 = 0.0006 \text{ moles} \]

Using stoichiometric ratios from the balanced equation, these moles are then used to find how many moles of K₄[Fe(CN)₆] are necessary to complete the reaction.

Solution Concentration

Solution concentration informs us of the amount of solute dissolved in a given volume of solvent, typically expressed in terms of molarity (M). Molarity is calculated by dividing the number of moles of solute by the volume of solution in liters.

In our problem, you're given the concentrations of both ZnSO₄ and K₄[Fe(CN)₆], which are 0.01 M and 0.05 M, respectively. Knowing the concentration is crucial in titration because:

• It helps identify how much of the titrant is needed to react completely with the analyte.
• It ensures the stoichiometric calculations are based on accurate initial data.

In the solution part, to calculate how much 0.05 M K₄[Fe(CN)₆] is needed, the moles required are divided by the concentration:

• \[ \text{Volume required} = \frac{0.0004}{0.05} = 0.008 \text{ L} \]

Converting this to milliliters gives the volume required for complete titration.