Using the dilution formula \( C_1V_1 = C_2V_2 \), where \( C_1 = 0.5 \) M, \( V_1 = 300 \) mL, \( V_2 = 500 \) mL, solve for \( C_2 \).
["How to Use the Dilution Formula ( C_1V_1 = C_2V_2 ): A Step-by-Step Guide", "When working with chemical solutions, dilution is a fundamental technique used to reduce the concentration of a solution while preserving its volume. The core of this process lies in the dilution formula:", "[\nC_1 V_1 = C_2 V_2\n]", "Where:\n- ( C_1 ) = Initial concentration (Molarity)\n- ( V_1 ) = Initial volume (mL)\n- ( C_2 ) = Final concentration (Molarity, to solve for)\n- ( V_2 ) = Final volume after dilution (mL)", "Understanding how to apply this formula ensures accurate and reproducible results, especially in laboratory settings, pharmaceuticals, and industrial processes.", "---", "### Step-by-Step Example Using ( C_1 = 0.5 ) M, ( V_1 = 300 ) mL, ( V_2 = 500 ) mL", "Suppose you have 300 mL of a 0.5 M solution, and you want to dilute it to achieve a final volume of 500 mL. Let’s solve for the final concentration ( C_2 ).", "---", "### Step 1: Write the dilution equation", "[\nC_1 V_1 = C_2 V_2\n]", "Substitute known values:", "[\n0.5 , \ ext{M} \ imes 300 , \ ext{mL} = C_2 \ imes 500 , \ ext{mL}\n]", "---", "### Step 2: Calculate the product of initial concentration and volume", "[\n0.5 \ imes 300 = 150 , \ ext{M·mL}\n]", "---", "### Step 3: Set up the equation to solve for ( C_2 )", "[\n150 , \ ext{M·mL} = C_2 \ imes 500 , \ ext{mL}\n]", "---", "### Step 4: Isolate ( C_2 ) by dividing both sides by 500 mL", "[\nC_2 = \frac{150}{500} , \ ext{M}\n]", "[\nC_2 = 0.3 , \ ext{M}\n]", "---", "### Conclusion: Final Diluted Concentration", "Using the dilution formula ( C_1V_1 = C_2V_2 ), when ( C_1 = 0.5 ) M, ( V_1 = 300 ) mL, and ( V_2 = 500 ) mL, the final concentration is:", "[\n\boxed{C_2 = 0.3 , \ ext{M}}\n]", "This precise calculation ensures your diluted solution meets exact requirements, highlighting the power of basic algebra in practical laboratory applications and beyond.", "---", "Why Learn This Formula?\nMastering the dilution formula ( C_1V_1 = C_2V_2 ) is essential for accurate solution preparation, making it a cornerstone of chemistry, biology, pharmacy, and many industrial fields. Always verify units and maintain stoichiometric balance for reliable results."]
