A solution is made by mixing 3 liters of a 20% salt solution with 2 liters of a 50% salt solution. What is the concentration of the resulting mixture?

["How to Calculate the Concentration of a Mixed Salt Solution: A Step-by-Step Guide", "When mixing solutions of different salt concentrations, understanding how to compute the final concentration is essential—especially in chemistry, cooking, and industrial applications. In this article, we’ll explore a practical example: mixing 3 liters of a 20% salt solution with 2 liters of a 50% salt solution, and determine the concentration of the resulting mixture.", "### Step 1: Understand What Concentration Means\nSalt concentration is expressed as a percentage, representing grams (or milliliters) of salt per total volume of solution. For instance, a 20% salt solution means 20 grams of salt dissolved in 100 mL of solution.", "### Step 2: Calculate Salt Amount in Each Solution\nTo find the total salt in the final mixture, calculate the amount of salt from each individual solution:", "- For the 3 liters (3000 mL) of 20% solution:\n Salt = Volume × Concentration = 3000 mL × 20% = 3000 × 0.20 = 600 grams of salt", "- For the 2 liters (2000 mL) of 50% solution:\n Salt = 2000 mL × 50% = 2000 × 0.50 = 1000 grams of salt", "### Step 3: Add Salt Amounts and Total Volume\nNow, sum the salt from both solutions and combine their volumes:", "- Total salt = 600 g + 1000 g = 1600 grams\n- Total volume = 3 L + 2 L = 5 liters", "### Step 4: Compute the Final Concentration\nConcentration is the ratio of total salt to total solution volume, expressed as a percentage:", "[\n\ ext{Final concentration} = \left( \frac{\ ext{Total salt (g)}}{\ ext{Total volume (L)}} \right) \ imes 100 = \left( \frac{1600\ \ ext{g}}{5\ \ ext{L}} \right) \ imes 100 = 32,000% \ ext{ (by mass, when converted properly)} \quad \ ext{or simply } 32%\n]", "Wait — let's clarify units: since grams of salt are proportional to kilograms of solution (assuming density ~1 g/mL), we can treat grams salt per liter of solution.", "Actually, a more accurate approach:\nSalt concentration is typically by mass/weight (g/kg), but when volumes are mixed heterogeneously and densities differ slightly, using mass/volume (g/L) is better.", "But in standard practice, especially with dilute aqueous solutions, concentration by mass/volume (%) is directly calculated as:", "[\n\ ext{Concentration (%)} = \frac{\ ext{Total mass of salt}}{\ ext{Total volume of solution (in mL or L)}} \ imes 100\n]", "Because 1 liter of water ≈ 1,000 grams, and if densities are close, we can use volume directly in percentage terms when diluted properly.", "So total salt = 1600 g\nTotal solution volume = 5 L", "[\n\ ext{Final concentration} = \frac{1600\ \ ext{g}}{5000\ \ ext{mL}} \ imes 100 = \frac{1600}{5} = 32% \ ext{ (by mass/volume)}\n]", "But note: this assumes all solutions behave identically. A more precise method uses weighted average by mass:", "Let’s do it rigorously:", "- Salt from 20% solution: 600 g in 3 L → mass = 600 g\n- Salt from 50% solution: 1000 g in 2 L → mass = 1000 g\n- Total salt = 1600 g\n- Total volume = 5 L\n- Since salt mass is additive and assuming negligible volume change, final concentration is:", "[\n\frac{1600\ \ ext{g}}{5000\ \ ext{mL}} = 0.32 \ ext{ g/mL} = 320\ \ ext{g/L}\n]", "But since concentration is usually reported per liter, and 1 L = 1000 mL, then:", "[\n\frac{1600\ \ ext{g}}{5\ \ ext{L}} = 320\ \ ext{g/L}\n]", "But if “20% salt solution” means 20 grams salt per 100 mL of solution, then volume scaling is key.", "Let’s standardize:", "Assume both solutions are dilute enough that volume mixing is approximately additive:", "[\n\ ext{Total salt} = 3\ \ ext{L} \ imes 20% = 600\ \ ext{g} \quad (\ ext{in 3 L})\n]\n[\n\ ext{Total salt} = 2\ \ ext{L} \ imes 50% = 1000\ \ ext{g} \quad (\ ext{in 2 L})\n]\nTotal salt = 1600 g\nTotal volume = 5 L\nFinal concentration = (1600 g ÷ 5000 mL) × 100 = 32%", "Yes — because when you mix 3 L of 20% and 2 L of 50%, the salt adds linearly, and the final concentration depends only on total salt and total volume, assuming no volume change.", "### Final Answer:\nThe resulting mixture has a concentration of 32% salt by mass (or volume, since densities are similar).", "### Why This Matters\nUnderstanding solution mixing is critical in labs, food preparation, water treatment, and chemical manufacturing. Proper calculation ensures accurate formulations, safety, and efficiency.", "Key Takeaway:\nTo find the concentration of a mixed salt solution:\n1. Calculate salt mass from each component\n2. Sum salt and total volume\n3. Compute concentration as (total salt ÷ total volume) × 100 (in % by mass/volume)", "The final mixture made from 3 L of 20% and 2 L of 50% salt solutions is 32% concentrated salt solution.", "---", "Keywords: salt solution concentration, mixing solutions, salt concentration calculation, 3L 20% solution 2L 50% solution, final mixture percentage, chemistry dilution, how to calculate mixing concentrations."]