A chemistry lab needs to prepare a solution by mixing 15 liters of a 20% acid solution with enough water to make the final concentration 10%. How many liters of water are needed?
["How to Dilute a 20% Acid Solution to a 10% Solution: A Step-by-Step Chemistry Example", "When preparing solutions in a chemistry lab, accurate dilution is essential for achieving precise concentrations. One common task is diluting a more concentrated acid solution—such as a 20% acid solution—by adding water to reduce the concentration to a safer, target level—like 10%. In this article, we walk through the calculations needed to determine how much water to add when combining 15 liters of a 20% acid solution with water for a final 10% concentration.", "### The Problem: Mixing a 20% Acid Solution with Water", "We start with 15 liters of a 20% acid solution. This means the total amount of pure acid in this solution is:", "[\n\ ext{Amount of acid} = 15~\ ext{liters} \ imes 0.20 = 3~\ ext{liters}\n]", "Our goal is to dilute this solution with water so that the final concentration is 10%. Let ( x ) be the amount of water (in liters) added. Since water contains no acid, the total volume of the final solution becomes:", "[\n15~\ ext{liters} + x~\ ext{liters}\n]", "The concentration of acid in the final solution must be 10%, so the concentration equation is:", "[\n\frac{3~\ ext{liters of acid}}{15 + x} = 0.10\n]", "### Solving for ( x )", "Multiply both sides by ( 15 + x ):", "[\n3 = 0.10(15 + x)\n]", "Distribute the 0.10:", "[\n3 = 1.5 + 0.10x\n]", "Subtract 1.5 from both sides:", "[\n1.5 = 0.10x\n]", "Divide both sides by 0.10:", "[\nx = \frac{1.5}{0.10} = 15~\ ext{liters}\n]", "### Conclusion: How Much Water Is Needed?", "To reduce the concentration of a 15-liter 20% acid solution to a 10% solution, you must add 15 liters of water.", "This means the final solution will be:", "- Total volume: 15 + 15 = 30 liters\n- Acid content: still 3 liters\n- Final concentration: ( \frac{3}{30} = 0.10 = 10% ) ✓", "### Why This Matters in Chemistry Labs", "Accurate dilution ensures safety, consistency, and reliability in experiments. Underestimating water needed could lead to overly concentrated acidic solutions, increasing the risk of chemical burns or unwanted reactions. Overestimating may dilute the solution too much, affecting experimental accuracy. Using precise calculations like this is fundamental in laboratory practice.", "### Summary", "- Starting volume: 15 L of 20% acid\n- Desired final concentration: 10%\n- Water to add: 15 liters\n- Final volume: 30 liters\n- Key formula: ( C_1V_1 = C_fV_f ) (where ( C ) = concentration, ( V ) = volume)", "For any solution dilution, always use:", "[\nV_1 \ imes C_1 = V_2 \ imes C_f\n]", "This ensures correct concentration without guesswork—critical for safe and effective lab work.", "---", "Keywords: chemistry lab, dilution calculation, acid solution, 20% acid dilution, 10% acid solution, concentration formula, water addition in lab, lab safety, chemical dilution, stoichiometry."]
