Describe and show your calculations on how you would prepare 1.00L of a 0.50M solution of each of the following

a.) HCl from "concentrated" (12M) reagent.
b.) Sodium Carbonate from the pure solid

a) To prepare 1.00L of a 0.50M solution of HCl from a concentrated (12M) reagent, we need to calculate the volume of the concentrated reagent required.

The definition of molarity (M) is moles of solute per liter of solution. We can use this definition to calculate the amount of solute (HCl) needed.

Molarity (M) = moles of solute / volume of solution (in liters)

Rearranging the formula, moles of solute = Molarity (M) * volume of solution (in liters)

First, we need to calculate the moles of solute required for a 0.50M solution of HCl:
moles of HCl = 0.50 M * 1.00 L = 0.50 moles

Now, we can use the equation: Moles = Volume (in liters) * Concentration (in M)

Volume (in liters) of concentrated HCl = moles of HCl / Concentration (in M)
Volume (in liters) of concentrated HCl = 0.50 moles / 12 M

Volume (in liters) of concentrated HCl = 0.0417 L or 41.7 mL

Therefore, to prepare 1.00L of a 0.50M HCl solution using a concentrated HCl reagent (12M), you would need to measure and dilute 41.7 mL of the concentrated HCl with distilled water.

b) To prepare 1.00L of a 0.50M solution of Sodium Carbonate (Na2CO3) from the pure solid, we need to calculate the amount of solid needed and how to dissolve it in water.

The molar mass of Sodium Carbonate is:
Na2CO3 = (2 * 22.99 g/mol) + 12.01 g/mol + (3 * 16.00 g/mol)
Na2CO3 = 105.99 g/mol

To calculate the amount of solid needed, we can use the formula:
Amount (in moles) = Molarity (M) * Volume (in liters)

Amount (in moles) of Sodium Carbonate = 0.50 M * 1.00 L = 0.50 moles

Now, we can use the equation: Mass = Amount (in moles) * Molar mass

Mass of Sodium Carbonate = 0.50 moles * 105.99 g/mol
Mass of Sodium Carbonate = 52.995 g

Therefore, to prepare 1.00L of a 0.50M solution of Sodium Carbonate using the pure solid, you would need to measure 52.995 grams of Sodium Carbonate, dissolve it in distilled water, and then make up the final volume to 1.00L.