Problem 74 - Chemistry Matter and Change

Question

IIow much \(\mathrm{CaCl}_{2},\) in grams, is needed to make 2.0 \(\mathrm{L}\) of a 3.5 \(\mathrm{M}\) solution?

Step-by-Step Solution

Answer

776.86 grams of \(\mathrm{CaCl}_2\) are needed.

Step 1: Determine Moles Required

First, we need to calculate the number of moles of calcium chloride (\(\mathrm{CaCl}_2\)) needed for the solution. Given a molarity of 3.5 \(\mathrm{M}\) and a volume of 2.0 \(\mathrm{L}\), use the formula \(\text{moles} = \text{molarity} \times \text{volume}\). So, \(3.5 \text{ M} \times 2.0 \text{ L} = 7.0\text{ moles}\).

Step 2: Find Molar Mass of \(\mathrm{CaCl}_2\)

Calculate the molar mass of \(\mathrm{CaCl}_2\) by adding up the atomic masses of calcium (Ca) and chlorine (Cl). Calcium has an atomic mass of approximately 40.08 \(\text{g/mol}\) and chlorine has an atomic mass of approximately 35.45 \(\text{g/mol}\). Since there are two chlorine atoms, the molar mass is calculated as: \(40.08 + 2 \times 35.45 = 110.98 \text{ g/mol}.\)

Step 3: Calculate Required Mass

Now, calculate the mass of \(\mathrm{CaCl}_2\) needed using the formula \(\text{mass} = \text{moles} \times \text{molar mass}\). Substituting in the values we have: \(7.0 \text{ moles} \times 110.98 \text{ g/mol} = 776.86 \text{ grams}.\)

Key Concepts

Calcium Chloride

Calcium chloride, or \( \text{CaCl}_2 \), is a chemical compound composed of calcium and chlorine. It is a salt that is crystalline and usually appears white when in pure form. Calcium chloride is highly soluble in water, releasing heat upon dissolving, a property that makes it useful in applications like de-icing roads and controlling dust.
Calcium chloride is also used in medicine, food, and various industrial processes. In chemistry, it is often utilized in experiments and reactions due to its ability to form ionic bonds with water, making it a great candidate for molarity calculations and preparing solutions.

• Formula: \( \text{CaCl}_2 \)
• Properties: Highly soluble, generates heat when dissolved
• Uses: De-icing, desiccation, food preservation, and more

Understanding its properties helps in determining its application in solutions and reactions.

Moles Calculation

In chemistry, the concept of a mole is fundamental. A mole is a unit that quantifies substances in terms of their particles, which could be atoms, molecules, or other entities. The mole allows chemists to count particles in a manageable way, akin to how a dozen counts 12 items.
To calculate moles from molarity and volume of a solution, use the formula:
\[ \text{moles} = \text{molarity} \times \text{volume} \]
This formula gives you the number of moles required for a particular solution. For instance, if a solution has a molarity of 3.5 M and a volume of 2.0 L, multiplying these values gives:

• \( 3.5 \ \text{M} \times 2.0 \ \text{L} = 7.0 \ \text{moles} \)

This means you need 7.0 moles of \( \text{CaCl}_2 \) to make the solution.

Molar Mass

Molar mass is crucial in stoichiometric calculations and refers to the mass of one mole of a substance. It is expressed in grams per mole (\( \text{g/mol} \)). To find the molar mass of a compound, you add up the atomic masses of all the atoms in its chemical formula.
Consider calcium chloride (\( \text{CaCl}_2 \)):

• Calcium (Ca) has an atomic mass of about 40.08 \( \text{g/mol} \).
• Chlorine (Cl) has an atomic mass of about 35.45 \( \text{g/mol} \).
• Since there are two chlorines in \( \text{CaCl}_2 \), its molar mass is:
  \[ 40.08 + 2 \times 35.45 = 110.98 \ \text{g/mol} \]

This calculation is essential to find out the mass of \( \text{CaCl}_2 \) required when you know the number of moles. By multiplying the number of moles by the molar mass, you get the weight of \( \text{CaCl}_2 \) needed for your solution.