Question

\(0.2\) mole of \(\mathrm{HCl}\) and \(0.2\) mole of barium chloride were dissolved in water to produce a \(500 \mathrm{~mL}\) solution. The molarity of the \(\mathrm{Cl}^{-}\) ions is : (a) \(0.06 \mathrm{M}\) (b) \(0.09 \mathrm{M}\) (c) \(1.2 \mathrm{M}\) (d) \(0.80 \mathrm{M}\)

Short answer

The molarity of the Cl- ions in the solution is 1.2 M.

Step-by-step solution

Calculate Total Moles of Cl- Ions

First, calculate the total moles of Cl- ions from both HCl and BaCl2. Since HCl is a strong acid, it dissociates completely into H+ and Cl- ions in solution. Thus, 0.2 moles of HCl will produce 0.2 moles of Cl- ions. Barium chloride (BaCl2) is also a strong electrolyte and will dissociate completely into Ba2+ ions and 2 Cl- ions for each BaCl2 molecule. Therefore, 0.2 moles of BaCl2 will produce 0.4 moles of Cl- ions (2 x 0.2). The total moles of Cl- ions are 0.2 (from HCl) + 0.4 (from BaCl2) = 0.6 moles.

Calculate the Molarity of Cl- Ions

The molarity (M) is defined as moles of solute per liter of solution. Since the solution's volume is 500 mL, which is equal to 0.5 L, we can use the formula Molarity (M) = Moles of solute / Liters of solution. Using the total moles of Cl- ions from step 1, we calculate the molarity as follows: Molarity of Cl- = 0.6 moles / 0.5 liters = 1.2 M.

Choose the Correct Answer

As calculated in Step 2, the molarity of the Cl- ions is 1.2 M. Therefore, the correct answer from the given options is (c) 1.2 M.

Key concepts

Dissociation of Electrolytes

To understand how electrolytes like hydrochloric acid (HCl) and barium chloride (BaCl₂) behave in water, it's essential to grasp the concept of dissociation. Dissociation is the process by which ionic compounds separate into their individual ions when dissolved in a solvent like water.

For example, take hydrochloric acid, a strong acid and electrolyte. It dissociates completely in water to form hydrogen ions (H⁺) and chloride ions (Cl^-). Barium chloride also fully dissociates into barium (Ba²⁺) and twice the number of chloride ions given its formula BaCl₂. The chemical equation for the dissociation of HCl and BaCl₂ are as follows:
HCl → H⁺ + Cl^-
BaCl₂ → Ba²⁺ + 2Cl^-

This knowledge helps to calculate the concentration of ions in a solution and is the basis for understanding molarity in chemistry.

Moles and Molarity

The mole is a basic unit in chemistry that quantifies the amount of a substance. One mole corresponds to Avogadro's number (6.022 \times 10^{23}) of particles, be they molecules, atoms, ions, etc. Molarity, on the other hand, is a measure of concentration, more precisely, the concentration of a solute in a solution.

It is defined by the formula:
Molarity (M) = \[\frac{{Text{Moles of solute}}}{{Text{Liters of solution}}}\]
Understanding this allows chemists to mix solutions with precise concentrations necessary for reactions or other processes. For instance, when preparing a solution or evaluating the outcome of a reaction, knowing the molarity is often crucial. It is also a building block for more advanced concepts in chemical reactions and stoichiometry.

Chemistry Problem Solving

When solving chemistry problems, especially those involving molarity and concentration, a systematic approach is best. The first step is usually to identify the relevant information, which is moles of the solute and the volume of the solution in the case of molarity calculations. Next, you'll need to perform the correct calculations, often including conversion between units, such as milliliters to liters or grams to moles based on molar mass.

For our example, understanding the complete dissociation of strong electrolytes like HCl and BaCl₂ guides us to calculate the total number of moles of each type of ion accurately. Always remember to check that your final answer makes sense both numerically and in the context of the chemical reaction or solution you're working with.

Concentration of Ions

The concentration of ions in a solution is directly affected by the dissociation of electrolytes. In our textbook example, the determination of chloride ion concentration stems from the complete dissociation of HCl and BaCl₂. Due to their full dissociation, it’s quite straightforward to calculate the individual ion's concentrations.

The calculation becomes a bit more complex when dealing with salts like BaCl₂, which produce more than one mole of an ion for each mole of compound dissolved. It's vital to remember that for each mole of BaCl₂, we end up with two moles of Cl^- ions. This concept underscores the importance of recognizing the formula of the compound and knowing how many of each ion will be produced upon dissociation to properly calculate ion concentrations.