A chemist needs to prepare a moderately concentrated acid bath. If of a solution is mixed homogeneou — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
A chemist needs to prepare a moderately concentrated acid bath. If $x\text{ mL}$ of a $5.0\text{ M } HCl$ solution is mixed homogeneously with exactly $20\text{ mL}$ of a $2.0\text{ M } HCl$ solution, the final resulting mixture is verified to have a molarity of exactly $2.6\text{ M}$. Calculate the exact integer value of $x$.
💡 Solution & Explanation
Step 1: Apply the standard dilution and mixing equation for solutions of the same solute. $M_{final} = \frac{M_1V_1 + M_2V_2}{V_1 + V_2}$. Step 2: Substitute all known variables into the equation. $2.6 = \frac{(5.0 \times x) + (2.0 \times 20)}{x + 20}$. Step 3: Solve the algebraic equation for $x$. $2.6(x + 20) = 5x + 40$ $2.6x + 52 = 5x + 40$ $52 - 40 = 5x - 2.6x$ $12 = 2.4x \implies x = \frac{12}{2.4} = 5$.