I need 500 ml of 0.10 m HCL solution. I have a 3.785 liter container of HCL at 31.45% concentration. How do I acheive my objective?

Is that 31.45% by mass. If so, then the solution is 12.58 m.

31.45 g HCl(31.45 g HCl + 68.55 g H2O) and
31.45/36.46 = 0.8625 moles HCl in 0.06855 kg solvent which makes the solution 12.58%.
Then m x grams soln = m wanted x grams wanted
12.58 m x grams soln = 0.1 m x 500
Solve for grams of the 31.45% solution. This will not give you exactly 500 mL since the density is not known but it should be close.

the solution is 31.45% by weight. I am trying to find out how much of the HCL i use as a base and how much water I need to add to make 500 ml or more at 0.10 m HCL

also the hcl is liquid form.

So you follow the equation I gave above and solve for grams stock solution.

12.58 m x grams soln = 0.1 m x 500
grams soln = 0.1 x 500/12.58 = 3.97 g

If you know the density you can convert 3.97g to mL. The density of 31% HCl is about 1.16 in my tables. Again, that won't be exactly 500 mL and it won't be exactly 0.1 m but close.

Thank you very much ... extremely helpful and very generous of you to volunteer your time and knowledge for this project.

To achieve your objective of obtaining 500 ml of 0.10 M HCl solution from a 3.785 liter container of HCl at 31.45% concentration, you need to follow these steps:

Step 1: Determine the volume of the concentrated HCl solution you need.
The concentration is given as 31.45%, which means that 100 ml of the solution contains 31.45 grams of HCl. To find the volume of the 31.45% HCl solution needed, you can use the formula:
Volume (ml) = (Desired concentration (mol/L) * Desired volume (L) * Molar mass (g/mol)) / Percent concentration (%)
Plug in the values:
Volume (ml) = (0.10 mol/L * 0.500 L * 36.46 g/mol) / 31.45%
So, the volume of the concentrated HCl solution needed is approximately 183.8 ml.

Step 2: Dilute the concentrated HCl solution to obtain the desired concentration.
To dilute the concentrated HCl solution, you can use the equation:
C1V1 = C2V2
where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.

Rearrange the equation to solve for V2:
V2 = (C1V1) / C2
Plug in the values:
V2 = (31.45% * 183.8 ml) / 0.10 M
V2 ≈ 57.7 ml

So, you need to measure 57.7 ml of the concentrated HCl solution and then add water to make a total volume of 500 ml to achieve your objective of obtaining 500 ml of 0.10 M HCl solution.