To find the molarity of the mixed HCl solution, we need to calculate the total number of moles of HCl from both solutions and divide by the total volume of the mixture.

Step 1: Calculate moles from first solution
Moles = Molarity × Volume (in liters)
For 750 mL of 0.5 M HCl:
Volume = 750 mL = 0.75 L
Moles₁ = 0.5 mol/L × 0.75 L = 0.375 mol

Step 2: Calculate moles from second solution
For 250 mL of 2 M HCl:
Volume = 250 mL = 0.25 L
Moles₂ = 2 mol/L × 0.25 L = 0.5 mol

Step 3: Total moles of HCl
Total moles = Moles₁ + Moles₂ = 0.375 mol + 0.5 mol = 0.875 mol

Step 4: Total volume of mixture
Total volume = 750 mL + 250 mL = 1000 mL = 1 L

Step 5: Molarity of mixed solution
Molarity = Total moles / Total volume (in L) = 0.875 mol / 1 L = 0.875 M

Therefore, the molarity of the mixed solution is 0.875 M.

Related Topics and Formulae

Molarity (M): It is defined as the number of moles of solute per liter of solution.
Formula: $M=\frac{n}{V}$ where n is moles of solute and V is volume in liters.

Dilution and Mixing: When mixing solutions of the same solute, the total moles remain conserved. The molarity after mixing can be found using:
$M_{\mathrm{mix}}=\frac{M_1{V}_1+M_2{V}_2}{V_1+V_2}$ (ensure volumes are in same units).