Problem 202 - Introductory Chemistry Atoms First

Question

What is the molarity of \(3.69 \mathrm{~mL}\) of solution containing \(0.0025\) mole of calcium chloride?

Step-by-Step Solution

Answer

The molarity of the calcium chloride solution is approximately \(0.6778 \mathrm{~M}\).

Step 1: Convert the volume from milliliters to liters

To convert the volume of the solution from milliliters (mL) to liters (L), we need to use the conversion factor: 1 L = 1000 mL. Volume in liters = volume in milliliters ÷ 1000 Volume in liters = 3.69 mL ÷ 1000

Step 2: Calculate the molarity

Now, apply the formula for molarity: Molarity (M) = moles of solute ÷ volume of solution in liters Moles of solute (CaCl₂) = 0.0025 moles Volume of solution in liters = 0.00369 L (from Step 1) Molarity = 0.0025 moles ÷ 0.00369 L

Step 3: Compute the molarity

Now, simply divide the moles of solute by the volume of the solution in liters to find the molarity: Molarity = 0.0025 moles ÷ 0.00369 L ≈ 0.6778 M Therefore, the molarity of the calcium chloride solution is approximately 0.6778 M.

Key Concepts

Understanding Calcium Chloride

Calcium chloride is a chemical compound with the formula \( ext{CaCl}_2 \). It is made up of calcium and chlorine and is a salt known for its ability to absorb moisture from the environment.
It is commonly used in the real world for de-icing roads, in food preservation, and in both medicine and laboratory settings.
When dissolved in water, it dissociates into calcium ions \( ( ext{Ca}^{2+}) \) and chloride ions \( ( ext{Cl}^-) \), which are essential in many chemical reactions.
Understanding the behavior of calcium chloride in a solution is crucial when calculating solution concentration, as it impacts the molarity and the ionic strength of the solution.

Defining Solution Concentration

Solution concentration is a measure of how much solute is dissolved in a given volume of solvent. It tells us the strength or intensity of a solution.
Molarity, with the unit \( ext{M} \) or moles per liter, is a common way to express concentration. It gives a direct insight into the number of moles of a solute per liter of solution.

• To calculate molarity, divide the number of moles of solute by the volume of the solution in liters.
• Example: In our exercise, the molarity is determined by dividing 0.0025 moles of calcium chloride by the converted volume in liters.

Knowing the concentration is important in laboratory and industrial processes where precise chemical reactions are needed.

Exploring Moles of Solute

The number of moles of solute represents the amount of a given substance. In chemical solutions, understanding moles is essential as it defines how many molecules or atoms are present.
A mole is a standard unit in chemistry, representing \( 6.022 imes 10^{23} \) entities, based on Avogadro's number.
For our exercise, we know there are 0.0025 moles of calcium chloride in the solution. This small quantity highlights the precision needed in chemical measurements.

• Moles allow chemists to predict how substances will react based on their balanced chemical equations.
• Calculating moles involves knowing the molecular weight and dissolving quantity effectively.

The detailed understanding of moles is fundamental in accurate molarity calculations.

Mastering Volume Conversion

Volume conversion is a necessary step when dealing with molarity calculations. Chemists often work in liters, but sometimes, measurements are given in milliliters. In such cases, converting to liters is essential.
Remember, 1 liter is equal to 1000 milliliters. Therefore, to convert from milliliters to liters, divide the milliliters by 1000.

• In our example, 3.69 mL is converted to 0.00369 L.
• This conversion ensures that the molarity formula accurately accounts for the solution's volume.

Mastering volume conversion ensures that calculations are precise and consistent across various chemical problems.