Question

\(50 \mathrm{~mL}\) of \(20.8 \%(\mathrm{w} / \mathrm{V}) \mathrm{BaCl}_{2}(a q)\) and \(100 \mathrm{~mL}\) of \(9.8 \%(\mathrm{w} / \mathrm{V}) \mathrm{H}_{2} \mathrm{SO}_{4}(a q)\) solutions are mixed. Molarity of \(\mathrm{Cl}^{-}\) ions in the resulting solution is: (At. wt. of \(\mathrm{Ba}=137\) ) (a) \(0.333 \mathrm{M}\) (b) \(0.666 \mathrm{M}\) (c) \(0.1 \mathrm{M}\) (d) \(1.33 M\)

Short answer

The molarity of Cl- ions in the resulting solution is 0.666 M.

Step-by-step solution

Calculate moles of BaCl2

First, calculate the number of moles of BaCl2 in the given volume of solution. Use the percentage concentration to find the mass of BaCl2, then convert it to moles using the molar mass of BaCl2 (which is the sum of the atomic mass of Ba and twice the atomic mass of Cl). The formula for moles is moles = mass / molar mass.

Determine moles of Cl- ions from BaCl2

Each molecule of BaCl2 yields two Cl- ions. Therefore, multiply the moles of BaCl2 by 2 to find the total moles of Cl- ions.

Calculate total volume of the mixed solution

Add the volumes of the two solutions to find the total final volume of the resulting mixture in liters.

Calculate molarity of Cl- ions

Molarity is defined as moles of solute per liter of solution. Divide the total moles of Cl- ions by the total volume in liters of the solution to find the molarity of Cl- ions.

Key concepts

Chemical Concentration

Understanding chemical concentration is fundamental for studying and working with solutions. Simply put, concentration is a measure of how much solute is present in a given amount of solvent or solution. In chemistry, there are several ways to express concentration, such as mass percent, molarity, molality, and normality.

For instance, a solution described as 20.8% (w/v) BaCl2 indicates that there are 20.8 grams of barium chloride (BaCl2) for every 100 milliliters of the solution. This percentage concentration is useful for preparing solutions and is especially relevant in the pharmaceutical industry and other sectors where volumetric measurements are common.

When we mix solutions, as seen in the example with BaCl2 and H2SO4, we need to pay attention to their concentrations since this determines the number of particles, such as ions, in the final mixture. The concentration of these particles affects the solution's properties and reactions it can undergo.

Moles and Molar Mass

Moles and molar mass are two important concepts in stoichiometry that allow chemists to quantify the amount of a substance. A mole is a unit in chemistry that represents an Avogadro's number of particles (approximately 6.022 x 10^23 particles). The molar mass, on the other hand, is the mass of one mole of a substance, usually expressed in grams per mole (g/mol).

The molar mass is obtained by adding up the atomic masses of all atoms in a molecule. For example, in the solution exercise, the molar mass of BaCl2 is calculated by adding the atomic weight of barium (\(137\text{ g/mol}\)) to the combined weight of two chlorine atoms. Once the total mass of the solute is known, you can convert it to moles using the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).

This calculation is the foundation of stoichiometry, which allows us to find out the exact quantity of reactants and products involved in a chemical reaction. Converting between mass and moles using the molar mass aids in understanding the quantitative aspects of the chemical equation.

Stoichiometry in Solutions

Stoichiometry in solutions involves the quantitative relationship between the reactants and products in a chemical solution. When dealing with solutions, it's important not just to understand the individual components but also how they interact with each other. This can help us determine the concentration of ions after chemical reactions have taken place.

In the context of the example problem, the stoichiometry of the dissolution of barium chloride (BaCl2) needs to be considered. Since each BaCl2 molecule dissociates into one Ba^2+ ion and two Cl^- ions, we must account for this stoichiometry when calculating the final concentration of chloride ions in the solution. Knowing that one mole of BaCl2 produces two moles of Cl^- is essential for accurately determining the resulting molarity of the Cl^- ions after mixing the two solutions.

Dilution and Mixing Solutions

Dilution is an important process which involves reducing the concentration of a solute in a solution by adding more solvent. When we mix different solutions, as in the example provided, we're effectively diluting them. The molarity after dilution can be determined using the formula \( M_1V_1 = M_2V_2 \), where \( M_1 \) and \( M_2 \) are the initial and final molarities, while \( V_1 \) and \( V_2 \) are the corresponding volumes.

In the case of mixing two solutions with different volumes and concentrations, we add up the volumes for the total volume, and then use the moles of each solute and this total volume to find the final molarity. This process can be understood in the context of the problem where the total moles of Cl^- ions were divided by the total volume of the mixed solutions to determine the molarity of Cl^- in the resulting mixture.