Brine Solution: Dilution, Concentration, And Final Percentage

Hey guys! Today, we're diving deep into a classic chemistry problem that might seem a bit tricky at first glance, but trust me, it's super straightforward once you break it down. We're talking about a scenario where we heat up a brine solution, specifically 50g of a 10% concentration, until a quarter of the water evaporates. The big questions on the table are: is the solution getting diluted or concentrated, and what's the final concentration going to be? Let's get our lab coats on and figure this out together!

Understanding the Initial Setup: 50g of 10% Brine

Alright, let's start with the basics, shall we? We have 50 grams of a brine solution that has a 10% concentration. What does that 10% actually mean? In simple terms, it means that 10% of the total mass of the solution is salt (solute), and the remaining 90% is water (solvent). So, in our initial 50g solution, we have:

• Salt: 10% of 50g = 0.10 * 50g = 5 grams
• Water: 90% of 50g = 0.90 * 50g = 45 grams

It's super important to get these initial amounts clear because everything we do next builds on this foundation. This initial 50g is our starting point, the whole enchilada. We've got our salt perfectly dissolved in our water, chilling at a nice 10% concentration. Remember these numbers, guys: 5g of salt and 45g of water. They're going to be crucial for our calculations moving forward.

Think of it like making a salty drink. If you have 100ml of water and you add 10g of salt, you get a solution where the salt makes up about 9% of the total mass (assuming the density of water is roughly 1g/ml, so 100ml is about 100g. Total mass would be 110g, and salt is 10g. 10/110 is about 9%). Our brine is similar, just that we're starting with a total mass and a percentage. The key takeaway here is that the amount of salt doesn't change unless we add more salt or remove it. In this case, we're only dealing with evaporation, which affects the water part of the solution.

So, to recap our initial state: we have a total mass of 50g, composed of 5g of salt and 45g of water. This gives us our starting concentration of 10%. Easy peasy, right? Now, let's see what happens when things get a little steamy.

The Evaporation Process: Removing Water

Now, here's where the action happens, guys! We're taking our 50g brine solution and heating it up. The goal is to evaporate one-quarter of the water. Remember, we started with 45 grams of water. So, one-quarter of that water is:

• Water evaporated: (1/4) * 45 grams = 11.25 grams

This is the amount of water that's going to turn into steam and float away into the atmosphere. What's left behind? Well, the salt doesn't evaporate. Salt is a solid at these temperatures, so it stays right there in the pot, faithfully waiting for the water to come back (which it won't, because it's evaporating!).

So, after evaporation, we'll have:

• Salt remaining: 5 grams (this stays the same!)
• Water remaining: 45 grams (initial water) - 11.25 grams (evaporated water) = 33.75 grams

This is the critical part, folks. The amount of solute (salt) remains constant, while the amount of solvent (water) decreases. This is the fundamental principle behind concentration changes in solutions due to evaporation. When you remove the solvent, the solute becomes more 'crowded' in the remaining liquid, leading to a higher concentration.

Think about making pasta. When you boil pasta, the water evaporates, and the salt you added to the water doesn't. If you let too much water evaporate, the water that's left becomes saltier. It's the same principle here, just with a precise calculation. We're not adding anything new, and we're not removing the salt. We're just taking away some of the liquid that the salt is dissolved in.

This process directly leads to a concentration of the solution. The ratio of salt to water is increasing. If you have 5 grams of salt trying to dissolve in less and less water, that means each gram of water is holding onto more salt. It's like trying to fit the same number of people into a smaller room – they're going to be more crowded!

So, to answer the first part of our question: the solution is becoming more concentrated. The evaporation of water without the removal of the solute is the definition of concentrating a solution. We're making it 'stronger' in terms of saltiness.

Calculating the Final Concentration: The New Percentage

Now for the grand finale, guys! We need to figure out the final concentration of our brine solution after evaporation. We know our two key components now: the amount of salt and the amount of water remaining.

• Salt (solute): 5 grams
• Water (solvent): 33.75 grams

To find the concentration, we need to calculate the percentage of salt in the new total mass of the solution. The new total mass is simply the sum of the salt and the remaining water:

• New total mass: 5 grams (salt) + 33.75 grams (water) = 38.75 grams

Now, we can calculate the final concentration (percentage by mass) using the standard formula:

• Concentration (%) = (Mass of solute / Total mass of solution) * 100

Plugging in our numbers:

• Final Concentration = (5 grams / 38.75 grams) * 100

Let's do the math:

• 5 / 38.75 ≈ 0.12903
• 0.12903 * 100 ≈ 12.90%

So, our final concentration is approximately 12.90%. Pretty neat, right? We started at 10% and ended up with a more concentrated solution at about 12.90%.

This calculation clearly shows the effect of evaporation. By removing a portion of the water, the proportion of salt within the solution increases. It's a direct consequence of the solute's mass remaining constant while the solvent's mass decreases. The final concentration is higher because the same amount of salt is now dissolved in a smaller amount of water, making the solution 'saltier' or more concentrated.

It's always a good practice to double-check your work, especially with these types of problems. Did we use the correct initial amounts? Yes, 5g salt and 45g water. Did we calculate the evaporated water correctly? Yes, 1/4 of 45g is 11.25g. Did we find the correct remaining water? Yes, 45g - 11.25g = 33.75g. Is the new total mass correct? Yes, 5g salt + 33.75g water = 38.75g. And finally, the concentration calculation: (5g / 38.75g) * 100 = 12.90%. All steps seem solid!

Conclusion: Concentration Achieved!

So, there you have it, chemistry whizzes! To wrap things up, when we heat 50g of a 10% brine solution until a quarter of the water evaporates, the solution becomes more concentrated. It does not dilute; dilution happens when you add more solvent (water in this case). Evaporation, by definition, removes solvent, thus increasing the concentration of the solute.

Our calculations showed that the initial solution contained 5g of salt and 45g of water. After evaporating 11.25g of water, we were left with 5g of salt and 33.75g of water. This resulted in a new total mass of 38.75g. The final concentration of the brine solution is approximately 12.90%. This is significantly higher than the initial 10%, confirming that the process was indeed one of concentration.

This principle is fundamental in many chemical and industrial processes, from food preservation to manufacturing. Understanding how evaporation affects solution concentration is a key skill for any aspiring chemist. So, next time you see water boiling away, remember that if there's anything dissolved in it, that substance is becoming more concentrated! Keep experimenting, keep asking questions, and keep learning, guys!