A solution contains 5% salt. How much water must be evaporated from 200 liters of this solution to make a 10% salt solution?
["How to Convert a 5% Salt Solution to a 10% Salt Solution by Evaporating Water: A Step-by-Step Guide", "When working with saltwater solutions, adjusting the salt concentration is a common task in industries like food processing, chemical manufacturing, and water treatment. One frequent challenge is transforming a 5% salt solution—specifically 200 liters of it—into a more concentrated 10% salt solution. But how much water must be carefully evaporated to achieve this? Let’s break down the solution with clear math, science, and practical tips.", "### Understanding the Problem", "We start with 200 liters of a 5% salt solution, which means:", "- Salt content = 5% of 200 liters = ( 0.05 \ imes 200 = 10 ) liters of salt\n- Water content = 200 L – 10 L = 190 liters", "To increase the salt concentration to 10%, the amount of salt stays constant (10 liters), but the total volume (now mostly salt-rich solution) must decrease.", "### Let’s Define:\nLet ( x ) = the amount of water (in liters) to evaporate.", "After evaporating ( x ) liters of water:\n- Remaining water = ( 190 - x ) liters\n- Total solution volume = ( 10 + (190 - x) = 200 - x ) liters", "We want the final concentration to be 10%, so:", "[\n\frac{\ ext{salt\ content}}{\ ext{total volume}} = 10%\n]\n[\n\frac{10}{200 - x} = 0.10\n]", "### Solve for ( x ):", "[\n10 = 0.10 \ imes (200 - x)\n]\n[\n10 = 20 - 0.10x\n]\n[\n0.10x = 20 - 10 = 10\n]\n[\nx = \frac{10}{0.10} = 100\n]", "### Conclusion:\nYou must evaporate 100 liters of water from the original 200 liters to concentrate the 5% salt solution to a 10% salt solution.", "### Why This Works\nEvaporating water increases the proportion of salt in the mixture without changing the total salt mass. By removing 100 liters of water, the salt percentage rises from 5% to 10%, achieving the desired concentration efficiently and precisely.", "---", "Practical Tip: Use a precise evaporative system or controlled heat to remove water evenly and avoid contamination or overheating, especially in large-scale applications.", "---", "This straightforward concentration process is essential in many real-world scenarios—ensuring safety, quality, and efficiency in liquid formulation."]
