Problem 73 - A Complete Resource Book in Chemistry for JEE Main

Question

If \(0.50\) mole of \(\mathrm{BaCl}_{2}\) is mixed with \(0.20\) mole of \(\mathrm{Na}_{3} \mathrm{PO}_{4}\), the maximum number of moles of \(\mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) that can be formed is (a) \(0.10\) (b) \(0.20\) (c) \(0.30\) (d) \(0.40\)

Step-by-Step Solution

Answer

The maximum number of moles of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \) is 0.10 (option a).

Step 1: Write the Balanced Chemical Equation

To determine the reaction, first write the balanced chemical equation for the reaction between \( \text{BaCl}_2 \) and \( \text{Na}_3\text{PO}_4 \). The equation is: \[ 3 \text{BaCl}_2 + 2 \text{Na}_3\text{PO}_4 \rightarrow \text{Ba}_3\text{(PO}_4\text{)}_2 + 6 \text{NaCl} \] This indicates that 3 moles of \( \text{BaCl}_2 \) react with 2 moles of \( \text{Na}_3\text{PO}_4 \) to produce 1 mole of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \).

Step 2: Determine Mole Ratio and Limiting Reactant

Calculate the mole ratio from the balanced equation:- 1 mole of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \) forms from 3 moles of \( \text{BaCl}_2 \) and 2 moles of \( \text{Na}_3\text{PO}_4 \).Given moles:- \( \text{BaCl}_2 \): 0.50 mole- \( \text{Na}_3\text{PO}_4 \): 0.20 moleDetermine which reacts completely first (limiting reactant). Use the ratio to see which reactant will run out first. For \( \text{BaCl}_2 \): Need 3 moles for each mole of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \). For \( \text{Na}_3\text{PO}_4 \): Need 2 moles for each mole of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \).

Step 3: Calculate Maximum Number of Moles of Product

Using the given moles, determine the actual reaction:- From the equation: \( \frac{0.50}{3} = 0.167 \) possible moles of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \) from \( \text{BaCl}_2 \).- From the equation: \( \frac{0.20}{2} = 0.10 \) possible moles of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \) from \( \text{Na}_3\text{PO}_4 \).\( \text{Na}_3\text{PO}_4 \) produces fewer moles, making it the limiting reactant. Therefore, maximum moles of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \) is 0.10.

Key Concepts

Limiting Reactant

In a chemical reaction, the limiting reactant is the substance that runs out first, halting the progress of the reaction and determining the maximum amount of product that can be formed. It is essential to compare the mole ratios of the reactants provided in the balanced chemical equation to recognize the limiting reactant.

To identify the limiting reactant:

• Calculate and compare the amounts of product each reactant could potentially form.
• The reactant that produces the smallest amount of product is the limiting reactant.

Use these insights when calculating, as in our exercise above, to solve limiting reactant problems. In the provided problem, \( \text{Na}_3\text{PO}_4 \) was the first to deplete, limiting the reaction and thus controlling the yield of \( \text{Ba}_3\text{(PO}_4\text{)}_2 \).

Balanced Chemical Equation

A balanced chemical equation is crucial for understanding how a chemical reaction proceeds. It shows the precise quantities of reactants and products involved, ensuring that matter is neither created nor destroyed during the process. Balance is achieved by adjusting coefficients before chemical formulas to meet the conservation of mass principle.

For our case study, the balanced equation is:\[ 3 \text{BaCl}_2 + 2 \text{Na}_3\text{PO}_4 \rightarrow \text{Ba}_3\text{(PO}_4\text{)}_2 + 6 \text{NaCl} \]Key steps in ensuring the equation is balanced:

• Count atoms of each element in reactants and products.
• Adjust coefficients to balance these counts across the equation.

Using this problem, remember that a balanced equation forms a solid foundation for any stoichiometric calculations, such as determining the limiting reactant or calculating theoretical yields.

Mole Ratio

Mole ratio is a central concept in stoichiometry and refers to the ratio between the amounts of reactants and products derived from a balanced chemical equation. Understanding mole ratios allows us to predict the amounts of products formed or reactants needed in a chemical equation.

In the example provided, the balanced equation dictates that \( 3 \text{ moles of BaCl}_2 \) react with \( 2 \text{ moles of Na}_3\text{PO}_4 \) to form \( 1 \text{ mole of Ba}_3\text{(PO}_4\text{)}_2 \). Analyzing this means:

• To produce \( \text{1 mole\ of } \text{Ba}_3\text{(PO}_4\text{)}_2 \), you need 3 moles of \( \text{BaCl}_2 \).
• The ratio helps determine how much of each reactant is needed or how much product is expected.

By applying mole ratios effectively, as in our example, you can deduce which reactant is limiting and subsequently how much product can be formed.