Problem 87 - A Complete Resource Book in Chemistry for JEE Main

Question

Equal volumes of \(0.1 \mathrm{M} \mathrm{AgNO}_{3}\) and \(0.2 \mathrm{M} \mathrm{NaCl}\) are mixed. The concentration of nitrate ions in the mixture will be (a) \(0.1 \mathrm{M}\) (b) \(0.05 \mathrm{M}\) (c) \(0.2 \mathrm{M}\) (d) \(0.15 \mathrm{M}\)

Step-by-Step Solution

Answer

The concentration of nitrate ions in the mixture is (b) \(0.05 \mathrm{M}\).

Step 1: Identify Initial Conditions

We have equal volumes of two solutions: \(0.1 \mathrm{M} \mathrm{AgNO}_{3}\) and \(0.2 \mathrm{M} \mathrm{NaCl}\). When mixed, these will form a solution with new concentrations.

Step 2: Determine Final Volume

Since equal volumes are mixed, the final volume doubles the original volume of each component. If the initial volume of each is \(V\), the final volume becomes \(2V\).

Step 3: Calculate Moles of \(\mathrm{AgNO}_{3}\)

The initial concentration of \(\mathrm{AgNO}_{3}\) is \(0.1 \mathrm{M}\), so the moles of \(\mathrm{AgNO}_{3}\) in volume \(V\) is \(0.1V\). Since \(\mathrm{AgNO}_{3} \) fully dissociates in water, it forms \(\mathrm{NO}_{3}^{-}\) ions in equal molarity.

Step 4: Concentration of \(\mathrm{NO}_{3}^{-}\) in Mixed Solution

Since the solution volume is now \(2V\), the concentration of \(\mathrm{NO}_{3}^{-}\) ions becomes \(\frac{0.1V}{2V} = 0.05 \mathrm{M}\).

Step 5: Final Verification

Check each calculation step to ensure the arithmetic and logic are correctly applied, verifying that the nitrate ions concentration after mixing is indeed \(0.05 \mathrm{M}\).

Key Concepts

Concentration Calculation

When dealing with solutions, concentration calculations are fundamental. Concentration tells us how much solute is dissolved in a given volume of solution. In this exercise, we've mixed equal volumes of two solutions:

• 0.1 molar (M) silver nitrate (AgNO_3)
• 0.2 molar (M) sodium chloride (NaCl)

Concentration is expressed in molarity, which is moles of solute per liter of solution. Since we are mixing equal volumes of both solutions, the total volume doubles. This affects the concentration of each ion in the solution. We initially have a volume, labeled as \(V\), for both solutions. After mixing, the final volume becomes \(2V\). Calculating concentrations after mixing requires dividing the initial moles of solute by the new, larger volume. This is done to find the new molarity, or concentration, of ions in the solution.

Chemical Reactions

Chemical reactions involve the rearrangement of atoms to form new substances. For this exercise, mixing AgNO_3 and NaCl leads to a chemical reaction where they exchange ions to form silver chloride (AgCl) and sodium nitrate (NaNO_3). This is a double displacement reaction represented by the equation: \[AgNO_3 (aq) + NaCl (aq) \rightarrow AgCl (s) + NaNO_3 (aq)\]In the resulting solution:

• AgCl precipitates as a solid due to its low solubility in water.
• NaNO_3 remains in solution, dissociating into ions - Na^+ and NO_3^-, similar to how sodium chloride and silver nitrate fully dissociate when first dissolved.

Understanding this reaction is crucial to predicting and calculating the resulting concentrations of reactants and products post-reaction.

Stoichiometry

Stoichiometry is a key concept in chemistry that involves the calculation of reactants and products in chemical reactions based on their balanced equations. Here, stoichiometry helps us calculate the concentration of ions remaining in solution after mixing our two chemicals. Since AgNO_3 dissociates completely in water to give NO_3^- ions at the same concentration as the original solution, there were initially \(0.1V\) moles of NO_3^- ions from the AgNO_3 solution. After mixing, the total volume is \(2V\). Thus, the nitrate ion concentration is \[ \text{Concentration of } NO_3^- = \frac{0.1V}{2V} = 0.05 \, \text{M} \]This means our final concentration of nitrate ions is half of the initial concentration due to the dilution effect when the solution volumes are combined. Correct stoichiometric calculations ensure accurate predictions of concentrations in chemical solutions.