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1.4.2 - Molarity Calculations and Dilutions

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Understanding Molarity

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0:00
Teacher
Teacher

Today, we will talk about molarity. Can anyone tell me what molarity represents?

Student 1
Student 1

Is it the concentration of a solution?

Teacher
Teacher

Exactly! Molarity, often abbreviated as 'M', is defined as the number of moles of solute per liter of solution. To calculate it, we use the formula M = moles of solute / liters of solution.

Student 2
Student 2

Can you give an example of how we would calculate the molarity of a solution?

Teacher
Teacher

Sure! If we dissolve 0.50 moles of NaCl in 1 liter of water, what is the molarity?

Student 3
Student 3

That would be 0.50 M, right?

Teacher
Teacher

Correct! Remember, the goal is to have the right number of moles for the volume of the solution. Let's move onto how we can prepare a solution with a specific molarity next.

Preparing Solutions

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0:00
Teacher
Teacher

To prepare a solution of known molarity, we need to calculate the mass of solute needed. Can anyone tell me what information we need to do this?

Student 1
Student 1

We need the molarity we want and the volume of the solution.

Teacher
Teacher

"Correct! Also, we need the molar mass of the solute. The formula we will use is:

Dilution Process

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0:00
Teacher
Teacher

Let's shift our focus to the dilution process. What happens when we dilute a solution?

Student 2
Student 2

We are adding more solvent, right?

Teacher
Teacher

"Absolutely! When we dilute, we maintain the amount of solute but increase the volume, which decreases the concentration. We use the formula:

Introduction & Overview

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Quick Overview

This section explores how to prepare solutions of known molarity and perform dilutions using established formulas.

Standard

In this section, you will learn to calculate the mass of solute needed to achieve a specific molarity in a solution and understand the dilution process through the formula C1V1 = C2V2. Different examples illustrate practical applications of these concepts.

Detailed

Molarity Calculations and Dilutions

This section focuses on the calculation of molarity (M) and the process of diluting solutions.

Preparing a Solution of Known Molarity

To prepare a solution with a specified molarity, you can use the formula:

mass of solute (g) = M(mol/L) ร— V(L) ร— Mm(g/mol)

Where:
- M is the molarity in moles per liter (mol/L)
- V is the volume of solution in liters (L)
- Mm is the molar mass of the solute in grams per mole (g/mol)

Procedure to Prepare a Molarity Solution:

  1. Weigh the calculated mass of the solute.
  2. Transfer the solute into a volumetric flask.
  3. Add distilled water to about two-thirds of the flask.
  4. Swirl until the solute is completely dissolved.
  5. Fill the flask to the calibration mark with more distilled water.
  6. Invert the flask several times to ensure uniform concentration.

Dilution of Solutions

The dilution process allows for the adjustment of the concentration of a solution by adding more solvent. The relationship between the concentration and the volumes of two solutions involved in a dilution is given by:

C1V1 = C2V2

Where:
- C1 is the concentration of the stock solution
- V1 is the volume of the stock solution to be diluted
- C2 is the final concentration after dilution
- V2 is the final total volume of the diluted solution

Example: Preparing a Dilution

To prepare 250 mL of a 0.100 M HCl solution from a 1.00 M stock solution, you would calculate:
- V1 = (C2ร—V2) รท C1 = (0.100 M ร— 0.250 L) รท 1.00 M = 0.0250 L = 25.0 mL
You would therefore measure 25.0 mL of the stock solution and dilute it to a final volume of 250 mL.

Overall, mastering molarity calculations and dilutions is essential for accurate preparation of chemical solutions critical in various laboratory settings.

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Preparing a Solution of Known Molarity

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  1. To prepare an M solution of a solute with molar mass Mm (g/mol), weigh out:

mass of solute (g) = M (mol/L) ร— V (L) ร— Mm (g/mol).

  1. Procedure:
  2. Weigh the calculated mass of solute.
  3. Transfer the solute to a volumetric flask.
  4. Add distilled water to dissolve the solute, filling to about two-thirds of the flask.
  5. Swirl or stir until the solute is fully dissolved.
  6. Add water until the bottom of the meniscus rests exactly at the calibration mark.
  7. Invert the flask several times to ensure uniform concentration.

Detailed Explanation

To prepare a solution of a specific molarity (M), you first need to know the molarity required and the volume of the solution you want to prepare. The formula for calculating the mass of solute required is mass of solute (g) = M (mol/L) ร— V (L) ร— Mm (g/mol), where Mm is the molar mass of the solute.

  1. Weigh the solute: Start by calculating the amount of solute necessary using the formula. For example, if you want to prepare a 1 M solution and your molar mass is 58.44 g/mol (like NaCl), for 1 liter, you would need 58.44 g of the solute.
  2. Transfer to a volumetric flask: Put the weighed solute into a volumetric flask, which is designed to hold a specific volume.
  3. Dissolution: After adding the solute, fill the flask with distilled water up to about two-thirds full and stir it until fully dissolved.
  4. Complete to volume: Add more distilled water until the liquid reaches the calibration line on the flask, which indicates the exact volume you wished to prepare.
  5. Mix well: Finally, invert the flask several times to ensure the solution is homogeneous.

Examples & Analogies

Think of preparing a fruit punch. You wouldn't just throw in random amounts of fruit and water; you'd measure how much fruit to add for the desired flavor. Similarly, you're measuring precise amounts of solute (like measuring fruit) to achieve the perfect flavor (concentration) in the solution.

Dilution Formula

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  1. When a stock solution of concentration C1 is diluted to a new concentration C2, the relationship is:

C1 ร— V1 = C2 ร— V2,

where C1 and C2 are in the same concentration units (e.g., mol/L) and V1 and V2 are in the same volume units (e.g., L).

  1. Example: To prepare 250 mL of 0.100 M HCl from a 1.00 M stock:
  2. C1 = 1.00 M, C2 = 0.100 M, V2 = 0.250 L.
  3. V1 = (C2 ร— V2) รท C1 = (0.100 M ร— 0.250 L) รท 1.00 M = 0.0250 L = 25.0 mL.
  4. Measure 25.0 mL of 1.00 M HCl and dilute to 250 mL.

Detailed Explanation

The dilution formula helps you calculate how much of a concentrated solution (stock solution) is needed to create a less concentrated solution. The equation C1 ร— V1 = C2 ร— V2 expresses this relationship, where:

  • C1 is the initial concentration of the stock solution.
  • V1 is the volume of the stock solution you need.
  • C2 is the final concentration of the diluted solution.
  • V2 is the final volume of the diluted solution.

In practice, to make a diluted solution like a 0.100 M HCl from a stronger 1.00 M stock, you need to identify how much from the stock solution (V1) is needed. So, calculating using the formula involves plugging in the C1, C2, and V2 values, allowing you to find V1, the volume you must use.

Examples & Analogies

Imagine you have a very strong drink concentrate and you need to serve a party full of friends. You wouldn't serve them the concentrate straight; instead, you would measure out a certain amount and mix it with water so that itโ€™s enjoyable. This is similar to how you dilute a stock solution to achieve a desired concentration.

Solution Concentration Calculations

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  1. Example 7: Solution concentration to moles of solute

Problem: How many moles of Naโ‚‚SOโ‚„ are present in 200 mL of a 0.250 M solution?

  1. Convert 200 mL to liters: 200 mL = 0.200 L.
  2. Use moles = M ร— V: Number of moles = 0.250 mol/L ร— 0.200 L = 0.0500 mol.

Answer: 0.0500 mol Naโ‚‚SOโ‚„.

Detailed Explanation

To calculate the number of moles in a solution, you can use the formula M = moles / V, where M is the molarity, and V is the volume in liters. Rearranging gives moles = M ร— V.

In this example, you first convert 200 mL to liters so that you can use the formula. After converting, you multiply the molarity of the solution (0.250 M) by the volume in liters (0.200 L) to find the total moles of Naโ‚‚SOโ‚„ present in that solution.

Examples & Analogies

Itโ€™s like trying to find out how many servings are in a container of juice. If the container has a specific volume and you know how much of that volume makes a serving (akin to molarity in a solution), you can simply calculate the total number of servings available in that full container.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Molarity: Defined as moles of solute per liter of solution, crucial for solution preparation.

  • Preparation of Solution: Involves calculating the mass of solute needed for a desired molarity.

  • Dilution Process: Refers to making a less concentrated solution from a more concentrated one using the formula C1V1 = C2V2.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Example of preparing a solution: For a 0.200 M NaCl solution in 1 L, weigh 11.69 g of NaCl.

  • Example of dilution: From a 1.00 M HCl stock solution, to prepare 250 mL of 0.100 M, measure 25.0 mL of HCl and dilute.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

๐ŸŽต Rhymes Time

  • To find Molarity, just take a gander, divide moles by liters with great candor.

๐Ÿ“– Fascinating Stories

  • Imagine a chef mixing ingredients. The more ingredients he mixes (the solute), the larger the pot (the volume) becomes. The goal is to make the dish just right โ€“ not too salty (concentration)!

๐Ÿง  Other Memory Gems

  • M for Molarity means Moles over Mixers (liters).

๐ŸŽฏ Super Acronyms

M.E.D. (Molarity = moles solute / liters of solution).

Flash Cards

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Glossary of Terms

Review the Definitions for terms.

  • Term: Molarity (M)

    Definition:

    A measure of concentration defined as the number of moles of solute per liter of solution.

  • Term: Mass of Solute

    Definition:

    The amount of solute measured in grams needed to achieve the desired molarity.

  • Term: Dilution

    Definition:

    The process of reducing the concentration of a solute in a solution, often by adding more solvent.

  • Term: C1V1 = C2V2

    Definition:

    The formula that relates the concentrations and volumes of two solutions before and after dilution.