Problem 21 - Chemistry Matter and Change

Question

How many grams of \(\mathrm{CaCl}_{2}\) should be dissolved in 500.0 \(\mathrm{mL}\) of water to make a 0.20 \(\mathrm{M}\) solution of \(\mathrm{CaCl}_{2}\) ?

Step-by-Step Solution

Answer

To make a 0.20 M solution of CaCl₂ in 500.0 mL of water, we need to dissolve approximately 11.098 grams of CaCl₂.

Step 1: Determine the number of moles of CaCl₂ needed for the solution

Using the provided molarity, we can use the formula M = (n / V) to solve for n: n = M × V where M = 0.20 M and V = 500.0 mL. First, we need to convert the volume from milliliters to liters: 500.0 mL × (1 L / 1000 mL) = 0.500 L Now, we can plug in the values for M and V and solve for n: n = (0.20 mol/L) × (0.500 L) n = 0.100 mol

Step 2: Find the molar mass of CaCl₂

To convert moles to grams, we need to know the molar mass of CaCl₂. The molar mass is calculated by adding the molar masses of the elements in the compound. The molar masses are: Ca: 40.08 g/mol, Cl: 35.45 g/mol The molar mass of CaCl₂ = 1 × 40.08 g/mol for Ca + 2 × 35.45 g/mol for Cl Molar mass of CaCl₂ = 40.08 + (2 × 35.45) Molar mass of CaCl₂ = 110.98 g/mol

Step 3: Calculate the grams of CaCl₂ needed

Now that we have the molar mass of CaCl₂ and the number of moles required, we can calculate the grams of CaCl₂ needed: grams of CaCl₂ = (moles of CaCl₂) × (molar mass of CaCl₂) grams of CaCl₂ = (0.100 mol) × (110.98 g/mol) grams of CaCl₂ = 11.098 g We need to dissolve approximately 11.098 grams of CaCl₂ in 500.0 mL of water to make a 0.20 M solution.

Key Concepts

Understanding Moles

In chemistry, a mole is a fundamental concept used to quantify the amount of a substance. It represents a specific number of particles, usually atoms or molecules, and is analogous to counting dozens. Just as a dozen refers to twelve items, one mole refers to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles.
This concept allows chemists to count atoms and molecules by weighing them. For example, if we want to find out how many moles of calcium chloride (\(\text{CaCl}_2\)) are needed to prepare a solution, we multiply the solution's molarity by its volume in liters.
The equation used is \(n = M \times V\), where \(n\) is the number of moles, \(M\) is the molarity, and \(V\) is the volume in liters.

• Molarity (M) is the concentration of the solution, typically given in moles per liter.
• Volume (V) is the space that the solution occupies. It should be converted to liters if it's initially given in milliliters, using the conversion \(1\, \text{L} = 1000\, \text{mL}\).

Applying this equation, you can calculate the moles of \(\text{CaCl}_2\) required for your solution by multiplying its molarity by the volume of the solution in liters.

Calculating Molar Mass

The molar mass of a compound is the mass of one mole of that compound. It's a crucial value for converting moles to grams, thereby helping to determine how much of a substance is present in a given sample.
To find the molar mass of calcium chloride (\(\text{CaCl}_2\)), you add the molar masses of all the atoms in its chemical formula.
Calcium (Ca) has a molar mass of \(40.08\, \text{g/mol}\), and chlorine (Cl) has a molar mass of \(35.45\, \text{g/mol}\). Since there are two chlorine atoms in \(\text{CaCl}_2\), you multiply the molar mass of chlorine by two.

• Molar mass of an element is usually found on the periodic table, listed as grams per mole (g/mol).
• Total molar mass: Combine the mass of all elements present in the formula.
• The molar mass of \(\text{CaCl}_2\) is calculated as follows: \(40.08 + 2 \times 35.45 = 110.98\, \text{g/mol}\).

This value is then used to convert the number of moles of \(\text{CaCl}_2\) into a mass that can be physically measured for use in a lab.

Preparing a Calcium Chloride Solution

Calcium chloride (\(\text{CaCl}_2\)) is a common salt used in various applications, from de-icing roads to making solutions in chemistry labs. Preparing a solution with a specific molarity, like a 0.20 M \(\text{CaCl}_2\) solution, involves precise calculations to ensure the right concentration.
First, calculate the number of moles of \(\text{CaCl}_2\) needed using the formula \(n = M \times V\), where \(M\) is the desired molarity and \(V\) is the volume in liters. For instance, a 0.20 M solution in 500 mL (0.500 L) requires \(n = 0.20 \times 0.500 = 0.100\) moles of \(\text{CaCl}_2\).
Next, convert moles to grams using the molar mass of \(\text{CaCl}_2\), which is 110.98 g/mol. Multiply the moles by the molar mass:

• Grams needed = Moles \(\times\) Molar mass
• \(Grams = 0.100 \times 110.98 = 11.098\) grams

Dissolve approximately 11.098 grams of calcium chloride in 500 mL of water to achieve the desired concentration. Make sure to dissolve completely to ensure uniformity throughout the solution.