Barium Hydroxide: Calculating Mass Fraction After Oxide Addition

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Barium Hydroxide: Calculating Mass Fraction After Oxide Addition

Hey guys! Today, we're diving into a fun chemistry problem involving barium hydroxide. Specifically, we're going to figure out how to calculate the mass fraction of the alkali (that's the barium hydroxide, Ba(OH)₂) in a solution after we've added some barium oxide (BaO). It might sound a little complex, but trust me, we'll break it down step by step so it's super easy to understand. So, grab your calculators and let's get started!

Understanding the Problem

Okay, so here's the scenario. We start with 30 grams of a barium hydroxide solution. This solution is 20% barium hydroxide by mass, meaning 20% of the solution's weight is pure Ba(OH)₂. Then, we add 15 grams of barium oxide (BaO) to this solution. Now, the key thing to remember is that barium oxide reacts with water to form more barium hydroxide. This means we're not just adding a solid; we're actually creating more of our alkali in the solution. Our mission, should we choose to accept it, is to calculate the new mass fraction of barium hydroxide in the final solution. This involves a few steps, but don't worry, we'll tackle each one methodically.

Step 1: Calculate the Initial Mass of Barium Hydroxide

First things first, we need to figure out how much barium hydroxide we have at the beginning. We know we have 30 grams of solution, and 20% of that is Ba(OH)₂. To calculate this, we simply multiply the total mass of the solution by the mass fraction:

Initial mass of Ba(OH)₂ = 30 g (solution) * 0.20 (mass fraction) = 6 grams

So, we start with 6 grams of barium hydroxide in our solution. This is our baseline, the starting point from which we'll calculate the change after adding barium oxide. Remembering this initial mass is crucial for the next steps. It's like the foundation of our calculation, so make sure you've got this part down!

Step 2: Calculate the Mass of Barium Oxide That Reacts

Now, let's think about the barium oxide we're adding. 15 grams of BaO is going to react with water (H₂O) in the solution to form more Ba(OH)₂. To figure out how much Ba(OH)₂ is formed, we first need to look at the balanced chemical equation for this reaction:

BaO + H₂O → Ba(OH)₂

This equation tells us that one mole of barium oxide reacts with one mole of water to produce one mole of barium hydroxide. To use this information, we need to convert the mass of BaO to moles. To do that, we'll need the molar mass of BaO.

The molar mass of BaO is 137.33 g/mol (for Ba) + 16.00 g/mol (for O) = 153.33 g/mol. Now we can calculate the moles of BaO:

Moles of BaO = 15 g / 153.33 g/mol ≈ 0.0978 moles

Since one mole of BaO produces one mole of Ba(OH)₂, we know that 0.0978 moles of Ba(OH)₂ will be formed. This is a key conversion, linking the amount of BaO added to the amount of Ba(OH)₂ produced. It's like the bridge between our reactant and our product.

Step 3: Calculate the Mass of Barium Hydroxide Formed

We know we've formed 0.0978 moles of Ba(OH)₂. To find out the mass of this Ba(OH)₂, we need to use its molar mass. The molar mass of Ba(OH)₂ is 137.33 g/mol (for Ba) + 2 * (16.00 g/mol (for O) + 1.01 g/mol (for H)) = 171.34 g/mol. Now we can calculate the mass of Ba(OH)₂ formed:

Mass of Ba(OH)₂ formed = 0.0978 moles * 171.34 g/mol ≈ 16.76 grams

So, the reaction of barium oxide with water produces approximately 16.76 grams of barium hydroxide. This is a significant addition to the amount of Ba(OH)₂ already present in the solution. Think of it as adding fuel to the fire – we're boosting the concentration of our alkali!

Step 4: Calculate the Total Mass of Barium Hydroxide in the Solution

Now we need to add the mass of Ba(OH)₂ formed to the initial mass of Ba(OH)₂ we calculated in step 1:

Total mass of Ba(OH)₂ = Initial mass of Ba(OH)₂ + Mass of Ba(OH)₂ formed

Total mass of Ba(OH)₂ = 6 grams + 16.76 grams = 22.76 grams

So, after the reaction, we have a total of 22.76 grams of barium hydroxide in the solution. This represents the total amount of our alkali after the reaction has taken place. We're getting closer to our final answer – we've figured out the total mass of Ba(OH)₂.

Step 5: Calculate the Total Mass of the Solution

To calculate the mass fraction, we also need the total mass of the solution. We started with 30 grams of solution and added 15 grams of BaO. So, the total mass of the solution is:

Total mass of solution = Initial mass of solution + Mass of BaO added

Total mass of solution = 30 grams + 15 grams = 45 grams

Okay, so our final solution weighs 45 grams. This is the denominator in our mass fraction calculation. We now have both the mass of the solute (Ba(OH)₂) and the mass of the solution – we're in the home stretch!

Step 6: Calculate the Mass Fraction of Barium Hydroxide in the Final Solution

Finally, we can calculate the mass fraction of Ba(OH)₂ in the final solution. The mass fraction is the mass of the solute (Ba(OH)₂) divided by the total mass of the solution:

Mass fraction of Ba(OH)₂ = (Total mass of Ba(OH)₂) / (Total mass of solution)

Mass fraction of Ba(OH)₂ = 22.76 grams / 45 grams ≈ 0.5058

To express this as a percentage, we multiply by 100:

Mass fraction of Ba(OH)₂ = 0.5058 * 100 ≈ 50.58%

So, the mass fraction of barium hydroxide in the final solution is approximately 50.58%. That's our final answer! We've successfully navigated through all the steps, from calculating initial masses to determining the final concentration. High five!

Final Answer

Therefore, the mass fraction of barium hydroxide in the obtained solution is approximately 50.58%. This means that about half of the final solution's mass is barium hydroxide.

Key Takeaways and Summary

Alright guys, let's recap what we've learned! Calculating the mass fraction of a solution after a reaction involves a few key steps:

  1. Determine the initial mass of the solute (in our case, barium hydroxide). This is your starting point.
  2. Calculate the moles of the added reactant (barium oxide) using its mass and molar mass.
  3. Use the balanced chemical equation to determine the moles of product (barium hydroxide) formed.
  4. Convert the moles of product to mass using its molar mass.
  5. Add the mass of the product formed to the initial mass of the solute to get the total mass of solute.
  6. Calculate the total mass of the solution by adding the mass of the added reactant to the initial mass of the solution.
  7. Divide the total mass of the solute by the total mass of the solution to find the mass fraction.

Remember, paying close attention to units and molar masses is crucial for accurate calculations. Each step builds upon the previous one, so it's important to tackle them in order and double-check your work.

Practice Makes Perfect

Chemistry problems like this can seem tricky at first, but with practice, you'll become a pro! Try working through similar problems with different compounds and concentrations. The more you practice, the more comfortable you'll become with the concepts and calculations.

So there you have it! We've successfully calculated the mass fraction of barium hydroxide in a solution after adding barium oxide. I hope this breakdown was helpful and made the process a little less daunting. Keep practicing, and you'll be a chemistry whiz in no time! Until next time, keep those beakers bubbling!