Problem 139 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

How much \(\mathrm{BaCl}_{2}\) would be needed to make \(250 \mathrm{ml}\) of a solution having the same concentration of \(\mathrm{Cl}^{-}\) as one containing \(\begin{array}{llll}3.78 & \mathrm{~g} & \mathrm{NaCl} \text { per } 100 \mathrm{ml} \text { ? }\end{array}\) \((\mathrm{Ba}=137)\) (a) \(16.8 \mathrm{~g}\) (b) \(67.2 \mathrm{~g}\) (c) \(33.6 \mathrm{~g}\) (d) \(22.4 \mathrm{~g}\)

Step-by-Step Solution

Answer

33.6 g of \text{BaCl}_2 would be needed.

Step 1: Determine the molar mass of NaCl and BaCl2

Find the molar mass of NaCl by adding the atomic masses of sodium (Na) and chlorine (Cl). Then, find the molar mass of BaCl2 by adding the atomic mass of barium (Ba) and twice the atomic mass of chlorine (Cl).

Step 2: Calculate the moles of Cl- from NaCl

Convert the given mass of NaCl to moles by using its molar mass, and deduce the moles of Cl- ions since NaCl provides one Cl- ion per molecule.

Step 3: Determine the concentration of Cl- in NaCl solution

Calculate the concentration of Cl- in the NaCl solution by dividing the number of moles of Cl- ions by the volume of the solution in liters.

Step 4: Calculate the moles of Cl- desired in BaCl2 solution

Using the equivalent concentration of Cl- ions from the NaCl solution, calculate the total moles of Cl- ions required for 250 ml BaCl2 solution.

Step 5: Convert moles of Cl- to moles of BaCl2

Use the ratio of Cl- ions in BaCl2 (2:1) to find the moles of BaCl2 required to achieve the desired moles of Cl- ions.

Step 6: Calculate the mass of BaCl2 required

Find the mass of BaCl2 that needs to be used by multiplying the moles of BaCl2 by its molar mass.

Step 7: Choose the correct answer

Compare the calculated mass of BaCl2 with the given options to choose the correct answer.

Key Concepts

Stoichiometry in Chemical Reactions

Stoichiometry is a fundamental concept in chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. When solving stoichiometry problems, it's important to understand the principle of the conservation of mass, which states that matter is neither created nor destroyed during a chemical reaction. This means the amount of each element is conserved, and the total mass of the products equals the total mass of the reactants.

To apply stoichiometry to a problem, you typically start by writing a balanced chemical equation, which gives you the mole ratio of reactants to products. This ratio allows you to convert between moles of different substances in the reaction. In the context of the exercise provided, stoichiometry is used to relate the moles of Cl⁻ ions in the NaCl solution to the corresponding moles of BaCl₂ needed to achieve the same concentration of Cl⁻ ions.

Solution Concentration

Solution concentration is a measure of the amount of a solute that is dissolved in a given quantity of solvent. Common units of concentration include molarity (M), which is defined as the number of moles of solute per liter of solution. Knowing the concentration is essential when preparing chemical solutions for reactions or for comparison, as seen in the given problem.

To find the concentration, you take the number of moles of solute and divide by the volume of solution in liters. In our example, after finding the moles of Cl⁻ from a given mass of NaCl, you can calculate the concentration by dividing the moles of Cl⁻ by the total volume of the solution. Then, using this concentration, you can determine the amount of BaCl₂ needed for the new volume of solution (250 ml). It is essential to ensure that the volume is in liters to match the units for molarity.

Understanding Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It's a crucial factor in converting between mass and moles, which is a common step in stoichiometry problems. Each element has a unique molar mass, which is approximately equivalent to its atomic mass on the periodic table.

To calculate the molar mass, you need to sum the atomic masses of all atoms in the formula of the compound. For example, NaCl has one sodium atom and one chlorine atom, so you would add the atomic mass of Na to that of Cl. Similarly, for BaCl₂, you add one barium atomic mass to twice the chlorine atomic mass, as there are two chloride ions for every barium ion. This calculation is essential in the step-by-step solution for determining the mass of BaCl₂ required to prepare the new solution.