Question

A solution contains 19 grams of \(\mathrm{MgCl}_2\) in \(0.5\) liters of distilled water. If \(\mathrm{MgCl}_2\) totally dissociates, what is the concentration of chloride ions in the solution? A. \(0.1 \mathrm{M}\) B. \(0.2 \mathrm{M}\) C. \(\quad 0.4 M\) D. \(0.8 \mathrm{M}\)

Short answer

D. \ \ 0.8 \text{ M}\

Step-by-step solution

Molar Mass Calculation

Calculate the molar mass of \(\text{MgCl}_2\). The molar mass of Mg is 24.305 g/mol and Cl is 35.453 g/mol. Therefore, \(\text{MgCl}_2 = 24.305 + 2 \times 35.453 = 95.211 \text{ g/mol}\).

Calculate Moles of \(\text{MgCl}_2\)

Use the given mass of \(\text{MgCl}_2\) to find the number of moles: \(\frac{19 \text{ g}}{95.211 \text{ g/mol}} \approx 0.2 \text{ moles}\).

Determine Moles of Chloride Ions

Since \(\text{MgCl}_2\) dissociates into one \(\text{Mg}^{2+}\) ion and two \(\text{Cl}^-\) ions, the moles of chloride ions are \(\text{moles of} \ \text{MgCl}_2 \times 2 = 0.2 \times 2 = 0.4 \text{ moles} \).

Calculate Concentration of Chloride Ions

The concentration of chloride ions is found by dividing the moles of chloride ions by the volume of the solution in liters: \(\frac{0.4 \text{ moles}}{0.5 \text{ liters}} = 0.8 \text{ M}\).

Key concepts

molar mass calculation

To start calculating the concentration of chloride ions, we need to first determine the molar mass of the compound \(\text{MgCl}_2\). Understanding molar mass is crucial because it helps convert grams into moles, which are needed for further calculations.

The molar mass (molecular weight) is the sum of the masses of all atoms in a chemical formula. For \(\text{MgCl}_2\):

* Magnesium (Mg) has a molar mass of 24.305 g/mol.
* Chlorine (Cl) has a molar mass of 35.453 g/mol.

Since the formula for magnesium chloride has one magnesium atom and two chlorine atoms, the molar mass is calculated as:

\[24.305 \text{ g/mol} + 2 \times 35.453 \text{ g/mol} = 95.211 \text{ g/mol}\]

This total mass allows us to convert any given mass of \(\text{MgCl}_2\) into moles, a key step in solving concentration problems.

ion dissociation in solutions

When \(\text{MgCl}_2\) dissolves in water, it completely dissociates into its ions. Dissociation is the process where an ionic compound breaks apart into ions when dissolved.

For \(\text{MgCl}_2\), the process looks like this:

\[\text{MgCl}_2(s) \rightarrow \text{Mg}^{2+}(aq) + 2\text{Cl}^-(aq)\]

This means each formula unit of \(\text{MgCl}_2\) splits into one magnesium ion (\(\text{Mg}^{2+}\)) and two chloride ions (\(\text{Cl}^-\)).

Understanding this dissociation is essential because it helps calculate the total amount of each ion present in the solution. For instance, if you have 0.2 moles of \(\text{MgCl}_2\), after dissociation, you will end up with 0.2 moles of \(\text{Mg}^{2+}\) ions and 0.4 moles of \(\text{Cl}^-\) ions.

chloride ion concentration

Now that we know the moles of chloride ions, we can calculate the concentration. Concentration refers to how much of a substance is present in a certain volume of solution. It's typically measured in moles per liter (Molarity, M).

From our dissociation, we have calculated that there are 0.4 moles of chloride ions. The solution volume given is 0.5 liters.

To find the concentration of chloride ions in the solution, use the formula:

\[ \text{Concentration} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]

Substituting in the known values:

\[ \frac{0.4 \text{ moles}}{0.5 \text{ liters}} = 0.8 \text{ M} \]

Therefore, the concentration of chloride ions in the solution is \(0.8 \text{ M}\).

moles and molarity

Understanding moles and molarity is fundamental in chemistry. A mole is a unit that measures the amount of substance, which is particularly useful for counting entities like atoms, ions, or molecules.

One mole of any substance contains exactly \(6.022 \times 10^{23} \) entities (Avogadro's number).

Molarity, on the other hand, is a measure of the concentration of a solute in a solution. It is expressed as moles of solute per liter of solution (M). The formula for molarity is:

\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]

For our problem, to find moles of \(\text{MgCl}_2\) from grams, we use:

\[ \text{moles of } \text{MgCl}_2 = \frac{19 \text{ g}}{95.211 \text{ g/mol}} \approx 0.2 \text{ moles} \]

Using these moles and given volume, we calculate the molarity of the chloride ions in the solution, which ultimately equals \(0.8 \text{ M}\).