Calculating Ion Molality In CaCl2 Solution Step By Step Guide

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Hey guys! Having trouble with molality calculations in chemistry? No worries, let's break down this problem together, step by step, so it becomes crystal clear. We're going to tackle a classic question involving calcium chloride (CaCl₂) dissolved in water, and by the end, you'll be a pro at calculating ion molality. Let's dive in!

The Problem: Unpacking the Question

So, here's the question we're tackling: 2.22 grams of calcium chloride (CaCl₂) are dissolved in 100 grams of water. What is the molality of ions in the solution? The molar mass (Mr) of CaCl₂ is given as 111 grams/mol. Sounds intimidating? Don't sweat it! We'll dissect this like seasoned chemists. The key here is understanding what the question is really asking. We aren't just looking for the molality of CaCl₂ itself, but the molality of the ions that result when CaCl₂ dissolves. This means we need to consider how CaCl₂ dissociates in water. Remember, molality is defined as the number of moles of solute per kilogram of solvent. In this case, our solute is CaCl₂, and our solvent is water.

First, let's identify the important information given in the problem. We have the mass of CaCl₂ (2.22 grams), the mass of water (100 grams), and the molar mass of CaCl₂ (111 grams/mol). We need to use these pieces of information to find the number of moles of CaCl₂ and then relate that to the number of moles of ions produced. Don't forget that CaCl₂ dissociates into one calcium ion (Ca²⁺) and two chloride ions (Cl⁻) in water. This is a crucial detail! So, essentially, one mole of CaCl₂ will produce a total of three moles of ions (1 mole of Ca²⁺ + 2 moles of Cl⁻). Understanding this stoichiometry is vital for solving the problem correctly. Now, let's move on to the calculations!

Step 1: Calculating Moles of CaCl₂

Alright, let's get our hands dirty with some calculations! The first step is to figure out how many moles of CaCl₂ we have. Remember the formula: moles = mass / molar mass. We've got the mass of CaCl₂ (2.22 grams) and the molar mass (111 grams/mol). So, let's plug those values in:

Moles of CaCl₂ = 2.22 grams / 111 grams/mol = 0.02 moles

See? That wasn't so bad! We've now determined that we have 0.02 moles of CaCl₂ dissolved in the water. This is a crucial stepping stone to finding the ion molality. But remember, we're not interested in the molality of CaCl₂ itself, but the molality of the ions it produces when it dissolves. This is where the dissociation of CaCl₂ into its constituent ions comes into play. Think about it this way: when CaCl₂ dissolves in water, it doesn't just float around as CaCl₂ molecules. It breaks apart into calcium ions (Ca²⁺) and chloride ions (Cl⁻). And the number of these ions is directly related to the initial number of moles of CaCl₂. So, let's move on to the next step and figure out how many moles of each ion we have.

Step 2: Determining Moles of Ions

This is where the stoichiometry of the dissociation reaction becomes super important. As we discussed earlier, CaCl₂ dissociates into one calcium ion (Ca²⁺) and two chloride ions (Cl⁻). We can represent this with the following equation:

CaCl₂ (s) → Ca²⁺ (aq) + 2Cl⁻ (aq)

This equation tells us that for every one mole of CaCl₂ that dissolves, we get one mole of Ca²⁺ ions and two moles of Cl⁻ ions. This is key to unlocking the next part of the problem. We already know we have 0.02 moles of CaCl₂. So, based on the stoichiometry:

  • Moles of Ca²⁺ = 0.02 moles (same as moles of CaCl₂)
  • Moles of Cl⁻ = 2 * 0.02 moles = 0.04 moles (twice the moles of CaCl₂)

Now, we need the total moles of ions in the solution. This is simply the sum of the moles of Ca²⁺ and the moles of Cl⁻:

Total moles of ions = 0.02 moles + 0.04 moles = 0.06 moles

Great! We've figured out that there are 0.06 moles of ions in total in the solution. We are getting closer to the final answer. Remember, molality is moles of solute per kilogram of solvent. We have the moles of ions (our "solute"), and we have the mass of the water (our solvent). The only thing left to do is convert the mass of water to kilograms and then calculate the molality.

Step 3: Calculating Molality

Okay, we're in the home stretch now! We have all the pieces of the puzzle, and it's time to put them together. Remember, molality is defined as:

Molality (m) = Moles of solute / Kilograms of solvent

We've already calculated the total moles of ions (solute) as 0.06 moles. Now we need to convert the mass of water (solvent) from grams to kilograms. We were given that we have 100 grams of water. To convert this to kilograms, we divide by 1000:

Kilograms of water = 100 grams / 1000 grams/kg = 0.1 kg

Now we have everything we need to calculate the molality of the ions:

Molality (m) = 0.06 moles / 0.1 kg = 0.6 mol/kg

And there you have it! The molality of ions in the solution is 0.6 mol/kg. We've successfully navigated through the problem, step by step, and arrived at the answer. This result means that there are 0.6 moles of ions (Ca²⁺ and Cl⁻ combined) for every kilogram of water in the solution. Understanding molality is super important in chemistry, especially when dealing with colligative properties like boiling point elevation and freezing point depression.

The Final Answer and Key Takeaways

So, the final answer to our problem is 0.6 m. This means the molality of ions in the calcium chloride solution is 0.6 mol/kg. High five! You've just successfully tackled a molality calculation. But beyond just getting the right answer, let's recap the key concepts and takeaways from this problem:

  1. Understanding Molality: Molality is a measure of concentration defined as moles of solute per kilogram of solvent. It's different from molarity, which is moles of solute per liter of solution. Remember the distinction!
  2. Dissociation of Ionic Compounds: When ionic compounds like CaCl₂ dissolve in water, they dissociate into their constituent ions. The stoichiometry of this dissociation is crucial for calculating ion concentrations.
  3. Stoichiometry is Key: Pay close attention to the stoichiometric coefficients in the dissociation equation. They tell you the ratio of ions produced from one mole of the compound.
  4. Step-by-Step Approach: Break down complex problems into smaller, manageable steps. This makes the problem less daunting and reduces the chance of errors.
  5. Units Matter: Always pay attention to units and make sure you're using the correct units in your calculations. Converting grams to kilograms is a common step in molality problems.

By mastering these concepts and practicing similar problems, you'll become a molality calculation master in no time. Keep up the great work, and happy chemistry-ing!

Practice Problems

Want to solidify your understanding? Try these practice problems:

  1. What is the molality of ions in a solution prepared by dissolving 11.7 grams of sodium chloride (NaCl) in 200 grams of water (Mr NaCl = 58.5 g/mol)?
  2. If 5.55 grams of anhydrous calcium chloride, CaCl2, are dissolved in 100.0 g of water, calculate the molality of chloride ions in the solution. (Mr CaCl2 = 111 g/mol)

Work through these problems using the steps we outlined above. If you get stuck, review the explanations and examples. Remember, practice makes perfect! You've got this!

This guide should give you a solid foundation for understanding and calculating molality. Remember to practice and apply these concepts to different problems. With a little effort, you'll be a chemistry whiz in no time! Keep up the great work, and don't hesitate to ask for help when you need it.