A 100-mL aqueous HCl solution was made by diluting concentrated HCl 1:20 to 50 mL. A portion of the resulting solution was then diluted 1:4 to make the final solution. What was the volume of concentrated HCl that was diluted?

Question

A 100-mL aqueous HCl solution was made by diluting concentrated HCl 1:20 to 50 mL.  A portion of the resulting solution was then diluted 1:4 to make the final solution.  What was the volume of concentrated HCl that was diluted?

Quizplus · Accepted Answer

11ecba2d_12a5_e7fd_a3bf_15ae8c50562d_MD0008_00 Concentrated solutions may require dilution if the amount needed is smaller than can be accurately measured. The concentration of the solution is reduced by dissolving a small volume in a larger volume of solvent (V_S). The final volume (V_F) of the diluted solution is the sum of the volume transferred (V_T) and V_S. The dilution factor (DF) is the magnitude by which a solution's concentration is decreased and is expressed as the ratio of V_T to V_F. The DF in a multistep dilution can be calculated using the V_T and V_F of each dilution: 11ecba2d_12a6_0f0e_a3bf_218792718ef8_MD0008_00 Two subsequent dilutions were done to make a 100-mL aqueous HCl solution. Concentrated HCl was diluted to 50 mL in a 1:20 dilution. The volume of concentrated HCl can be calculated by plugging in the DF and the V_F of the solution from the first dilution into the DF equation: 11ecba2d_12a6_0f0f_a3bf_b93c69aacb68_MD0008_00 11ecba2d_12a6_0f10_a3bf_d71f3f91f7dd_MD0008_00 Therefore, 2.5 mL of concentrated HCl was diluted to 50 mL by a 1:20 dilution. (Choice A) If V_F1 were 5 mL rather than 50 mL, a V_T1 of 0.25 mL would be obtained. (Choice C) The 25-mL volume is the amount of diluted HCl transferred in the second dilution. (Choice D) A volume of 250 mL would be obtained if 50 mL were divided by a DF of 0.2 rather than 20. This volume is not plausible for V_T1 because the V_F1 is 50 mL and the volume transferred cannot be larger than the final volume of the solution. Educational objective: Dilutions are done to decrease the concentration of a solution when a small amount is needed and cannot be accurately measured. A small volume of concentrated solution (V_T) is transferred to a certain volume of solvent (V_S), and the final volume (V_F) is the sum of V_T and V_S. The dilution factor can be determined by the ratio of V_T to V_F.

A 100-ML Aqueous HCl Solution Was Made by Diluting Concentrated