3.7.A.2  Molarity: Solution Composition:

1. Definition of Molarity:

Molarity (M) is a measure of the concentration of a solution. It is defined as the number of moles of solute dissolved in one liter of solution.

Formula:

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

Explanation:

• Moles of solute: This refers to the amount of the substance (solute) dissolved in the solution, measured in moles.
• Liters of solution: This is the total volume of the solution, including both the solute and the solvent, measured in liters.

Example:

If you dissolve 1 mole of NaCl (salt) in 1 liter of water, the molarity of the solution is 1 M (1 mole per liter).

So, molarity tells you how much solute is present in a specific volume of solution. It’s commonly used to express concentrations in chemistry, especially in solutions for reactions.

2. Moles:

i. Moles and Avogadro’s Number:

When we talk about a mole, we’re referring to a quantity, similar to how we might talk about a “dozen,” which is 12 items. For a mole, that number is 6.022 × 10²³. This is called Avogadro’s number, and it tells us how many individual particles (atoms, molecules, or ions) are in one mole of a substance.

• For example: If you have 1 mole of water (H₂O), you have 6.022 × 10²³ molecules of water.

ii. Molarity and Concentration

Next, we talk about molarity, which is a way to describe the concentration of a solution. Concentration is how much solute (like salt or sugar) is dissolved in a certain amount of solvent (like water).

Molarity (M) is defined as:

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

So, molarity tells us how many moles of solute (substance being dissolved) are present in 1 liter of solution.

• For example: If you dissolve 1 mole of NaCl (salt) in 1 liter of water, the molarity of the salt solution would be 1 M (1 mole per liter).

iii. How Moles and Molarity Relate:

• If you know the number of moles of a substance and the volume of the solution, you can calculate its molarity (concentration).
• Conversely, if you know the molarity and volume, you can calculate how many moles of solute are in the solution.

iv. Why is this important?

Understanding moles and molarity helps chemists perform calculations for reactions, predict amounts of products, and work out the concentration of different solutions. It’s essential for designing experiments or creating solutions with precise concentrations, which is often required in labs.

3. Solution Preparation:

i. Calculate the Required Moles of Solute:

First, you need to figure out how many moles of solute are required to make a solution of a specific molarity (M). The formula for molarity is:

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

Molarity (M)=liters of solution moles of solute​

So, to find the moles of solute, you can rearrange this formula:

$$\text{moles of solute}=\text{Molarity (M)}\times \text{liters of solution}$$

For example:

• If you want to prepare 2 liters of a 1 M NaCl (sodium chloride) solution, you need:
  $$\text{moles of NaCl}=1\text{ M}\times 2\text{ L}=2\text{moles of NaCl}$$

ii. Convert Moles to Grams Using the Molar Mass:

Now that you know how many moles of solute you need, the next step is to convert moles into grams, since you will measure the solute in grams. To do this, you use the molar mass of the solute (the mass of 1 mole of the substance).

The molar mass is typically given in units of grams per mole (g/mol). For NaCl, the molar mass is:

• Na (sodium) = 23.0 g/mol
• Cl (chlorine) = 35.5 g/mol
• So, the molar mass of NaCl = 23.0 g/mol + 35.5 g/mol = 58.5 g/mol.

Now, you can convert moles to grams using this formula:

$$\text{grams of solute} = \text{moles of solute} \times \text{molar mass of solute (g/mol)}$$

grams of solute = moles of solute × molar mass of solute (g/mol)

For our example:

• If you need 2 moles of NaCl, you can convert it to grams:
  $$\text{grams of NaCl} = 2\ \text{moles} \times 58.5\ \text{g/mol} = 117\ \text{grams of NaCl}$$

  grams of NaCl=2 moles×58.5 g/mol=117 grams of NaCl

iii. Prepare the Solution:

Once you’ve calculated the grams of solute required, you can now prepare the solution:

1. Weigh out 117 grams of NaCl.
2. Dissolve the NaCl in a volume of solvent (usually water). Since you need 2 liters of solution, make sure the final volume of the solution (after dissolving) is exactly 2 liters.

4. Dilution:

i. What is Dilution?

Dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent (like water). When you dilute a solution, you don’t change the number of moles of solute — you’re just increasing the total volume of the solution, which makes the solution less concentrated (i.e., the molarity decreases).

So, if you have a concentrated solution and want to make it less concentrated, you would dilute it by adding more solvent.

ii. How Does the Dilution Equation Work?

The dilution equation is:

$$M_1 V_1 = M_2 V_2$$

Where:

• M₁ = initial molarity (concentration) of the solution
• V₁ = initial volume of the solution
• M₂ = final molarity (concentration) after dilution
• V₂ = final volume of the solution after dilution

This equation tells us that the number of moles of solute before and after dilution must be the same. So, as the volume increases (because you’re adding more solvent), the molarity must decrease to keep the number of moles constant.

iii. How to Use the Equation:

a. Start with your concentrated solution (you know the molarity and volume).

b. Decide how much of the solution you want and what the new molarity should be.

c. Use the equation to find the missing information.

5. Real-world Applications:

i. Chemical Reactions in Laboratories:

In a chemistry lab, chemical reactions often require specific concentrations of reactants. Molarity plays a huge role in determining how much of each reactant is needed.

a. Example: Suppose you’re performing a titration (a type of reaction to determine the concentration of a solution). You need to know the exact molarity of your titrant (the solution being added) and the analyte (the solution being tested) to calculate how much of each reactant is required for the reaction to occur completely.

b. Why it matters: Knowing the molarity of your solutions allows you to control the reaction rates, predict how much product will form, and ensure that the reaction happens with the right amount of each substance involved.

ii. Medicine Preparation (Pharmaceuticals):

In medicine, molarity is essential when preparing solutions for medical use, such as intravenous (IV) fluids, drug formulations, or lab tests. Precise concentrations are necessary for patient safety.

a. Example: When making a saline solution (commonly used in hospitals for hydration), it needs to be at a precise molarity, often around 0.9% NaCl, to match the body’s natural salt concentration. If the solution is too concentrated or too dilute, it can be harmful to the patient.

b. Why it matters: Many drugs must be delivered at a specific molarity for effective treatment. For instance, the molarity of a chemotherapeutic drug or antibiotic solution must be accurately calculated to ensure the right dose is administered. Too much or too little of a drug can lead to adverse effects or ineffectiveness.

iii. Industrial Processes:

In industrial settings, molarity is crucial for various manufacturing processes that involve solutions, such as cleaning, metal processing, or food and beverage production.

a. Example: In the food industry, molarity is used to prepare acidic solutions for things like pickling or to control the acidity (pH) of products like soda or fruit juices. In the chemical manufacturing industry, molarity helps in the synthesis of chemicals, where precise concentrations are needed to ensure the desired chemical reactions happen efficiently.

b. Why it matters: In manufacturing, consistent and accurate concentrations help improve the efficiency of reactions, reduce waste, and ensure that the end product is of high quality. In large-scale operations, even small variations in concentration can lead to significant issues in product quality and cost.

iv. Environmental Applications:

Molarity is also crucial in environmental science for analyzing pollutants in water, air, or soil. Scientists use molarity to measure how much of a certain pollutant is present in a sample and determine how to treat it or regulate its levels.

a. Example: If a factory is discharging wastewater, regulators will often test the concentration of chemicals (like heavy metals or acids) in the water. The molarity of these pollutants will determine how much cleaning or neutralizing is needed to meet environmental safety standards.

b. Why it matters: Monitoring molarity helps in ensuring that chemical levels in the environment are safe for humans, animals, and plant life. It also aids in making informed decisions on the appropriate treatment or filtration methods to reduce pollutants.