Seawater Dilution: Calculating Fresh Water Addition

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Have you ever wondered how much fresh water you need to add to seawater to change its salinity? This is a common problem in various fields, from marine biology to desalination. Let's break down the math and figure out how to calculate the amount of fresh water needed to dilute seawater to a specific concentration. We'll use a real-world example to make things clear, and by the end, you'll be a pro at solving these types of problems.

Understanding the Problem

In this article, we're tackling a classic concentration problem. The core concept here is that the amount of solute (in our case, salt) remains constant when we add a solvent (fresh water). We're just changing the overall volume of the solution, which affects the concentration. Our main keywords here are seawater, salt concentration, and fresh water addition. We need to find out how much fresh water to add to a given amount of seawater to reduce its salt concentration from 5% to 2%. This involves understanding the initial amount of salt, the final desired concentration, and how the total volume changes when we add fresh water.

The problem states that we have 80 kg of seawater with a 5% salt concentration. Our goal is to dilute this solution to a 2% salt concentration by adding fresh water. The key to solving this problem is realizing that the amount of salt in the solution remains the same before and after adding fresh water. We're only changing the amount of water, not the amount of salt. So, we'll first calculate the initial amount of salt, then use that to determine the final total weight of the solution at 2% concentration, and finally, find the difference to calculate the amount of fresh water added. This step-by-step approach will make the problem much easier to solve. Remember, understanding the principle of conservation of solute is crucial in these types of problems. Let's dive into the calculations now!

Step-by-Step Solution

1. Calculate the Initial Amount of Salt

The first step in solving this problem is to determine how much salt is initially present in the 80 kg of seawater. We know the seawater has a 5% salt concentration. This means that 5% of the total weight is salt. To find the weight of the salt, we simply calculate 5% of 80 kg. Mathematically, this is expressed as:

Salt weight = 0.05 * 80 kg = 4 kg

So, we have 4 kg of salt in the initial 80 kg of seawater. This is a crucial piece of information because, as we add fresh water, the amount of salt doesn't change. Only the total weight of the solution and the concentration will change. Remember this key principle: the salt content remains constant. This understanding is fundamental to solving dilution problems effectively. This initial calculation gives us a baseline to work with and allows us to determine the final weight of the solution needed to achieve the desired concentration.

2. Determine the Final Total Weight

Now that we know the amount of salt (4 kg) and the desired final concentration (2%), we can calculate the final total weight of the solution. The salt content remains the same, but it now represents 2% of the total weight. Let's denote the final total weight as 'x' kg. We can set up the following equation:

  1. 02 * x = 4 kg

This equation states that 2% of the final weight (x) is equal to the amount of salt (4 kg). To solve for x, we simply divide both sides of the equation by 0.02:

x = 4 kg / 0.02 = 200 kg

Therefore, the final total weight of the solution needs to be 200 kg to achieve a 2% salt concentration. This step is critical because it tells us the target weight we need to reach by adding fresh water. Understanding this final weight helps us determine exactly how much fresh water we need to add to the initial 80 kg of seawater. Remember, this calculation is based on the principle that the amount of salt remains constant, and we're only changing the water content.

3. Calculate the Amount of Fresh Water to Add

We now know the initial weight of the seawater (80 kg) and the final total weight of the solution (200 kg). To find out how much fresh water we need to add, we simply subtract the initial weight from the final weight:

Fresh water added = Final total weight - Initial weight

Fresh water added = 200 kg - 80 kg = 120 kg

So, we need to add 120 kg of fresh water to the 80 kg of seawater to reduce the salt concentration to 2%. This is the final answer to our problem. It's important to remember the units; we're dealing with kilograms here, so our answer is also in kilograms. This calculation provides a clear and precise answer to the original question. By breaking down the problem into these three steps, we've made it much easier to understand and solve. This systematic approach can be applied to various concentration and dilution problems.

Final Answer

The final answer to the question is 120 kg. Therefore, you need to add 120 kg of fresh water to 80 kg of seawater with a 5% salt concentration to obtain a 2% salt concentration. This corresponds to option 1 in the given choices.

Why This Matters

Understanding these types of calculations is crucial in many real-world applications. For instance, in marine aquariums, maintaining the correct salinity level is vital for the health of the marine life. In desalination plants, these calculations are essential for determining the amount of fresh water that can be extracted from seawater. In the food industry, similar calculations are used when preparing brines or other solutions. The principles of concentration and dilution are fundamental in chemistry, biology, and many engineering fields. Mastering these concepts gives you a solid foundation for solving more complex problems in these areas.

Tips and Tricks for Solving Concentration Problems

  • Always start by identifying the knowns and unknowns: What information are you given, and what are you trying to find?
  • Focus on the constant: In dilution problems, the amount of solute (like salt in our example) remains constant. This is a key piece of information.
  • Set up clear equations: Use variables to represent unknown quantities and write equations that relate the knowns and unknowns.
  • Check your units: Make sure your units are consistent throughout the problem. If you're working with kilograms, stick to kilograms.
  • Think logically about the answer: Does your answer make sense in the context of the problem? For instance, you should expect to add water to reduce the concentration.

By following these tips and practicing regularly, you'll become more confident in solving concentration problems. These problems may seem daunting at first, but with a systematic approach and a clear understanding of the principles involved, you can tackle them effectively.

Practice Problems

To further solidify your understanding, try solving these practice problems:

  1. You have 100 kg of a solution with a 10% sugar concentration. How much water do you need to add to reduce the concentration to 4%?
  2. You have 50 kg of a solution with a 20% alcohol concentration. How much pure alcohol do you need to add to increase the concentration to 30%?
  3. If you mix 30 kg of a solution with a 15% salt concentration with 70 kg of a solution with a 5% salt concentration, what is the final salt concentration of the mixture?

Work through these problems, applying the steps and principles we discussed. The more you practice, the better you'll become at solving these types of problems. Remember, consistent practice is key to mastering any mathematical concept.

Conclusion

Calculating the amount of fresh water to add to seawater to achieve a specific salt concentration is a practical problem with applications in various fields. By understanding the principle of constant solute, setting up clear equations, and following a step-by-step approach, you can confidently solve these problems. We hope this article has clarified the process and provided you with the tools you need to tackle similar challenges. So go ahead, give it a try, and become a master of concentration calculations! Guys, you've got this!