Calculate the amount of Tris(hydroxlmethyl)aminomethane(Tris) necessary to make 100mL of a 0.100 M Tris buffer that is equimolar in Tris-base (MW=121.1 g/mol) and Tris-HCL (MW= 157.6g/mol)

Let's see.

M = mols/L; therefore,
# mols = M x L
You have M = 0.100 and you have L - 0.100 so you want 0.01 mols of the base and 0.01 mols of the salt (the acid) (since the problem states you want an equimolar solution of base and acid.
After you know mols, then mols = grams/molar mass. You know molar mass and you know the mols, calculate grams of the base and grams of the salt (acid). Voila!

But then if they ask us to predict the pH of this solution, using the Handerson-Haselbach equation...?

To calculate the amount of Tris(hydroxymethyl)aminomethane (Tris) necessary to make a 0.100 M Tris buffer, you need to consider the molar mass and molar ratio of Tris-base and Tris-HCl.

1. Calculate the moles of Tris required:
Moles of Tris = Molarity * Volume (in liters)
Moles of Tris = 0.100 mol/L * 0.100 L
Moles of Tris = 0.010 mol

2. Determine the molar ratio of Tris-base and Tris-HCl:
By looking at the chemical formula of Tris, we can see that it contains three Tris-base molecules (C4H11NO3) and one Tris-HCl molecule (C4H12ClNO3). Therefore, the molar ratio is 3:1.

3. Calculate the moles of Tris-base and Tris-HCl:
Moles of Tris-base = Moles of Tris * (3/4)
Moles of Tris-base = 0.010 mol * (3/4) (since Tris-base accounts for 3/4 parts)
Moles of Tris-base = 0.0075 mol

Moles of Tris-HCl = Moles of Tris * (1/4)
Moles of Tris-HCl = 0.010 mol * (1/4) (since Tris-HCl accounts for 1/4 parts)
Moles of Tris-HCl = 0.0025 mol

4. Calculate the mass of Tris-base and Tris-HCl:
Mass of Tris-base = Moles of Tris-base * Molar mass of Tris-base
= 0.0075 mol * 121.1 g/mol
= 0.908 g

Mass of Tris-HCl = Moles of Tris-HCl * Molar mass of Tris-HCl
= 0.0025 mol * 157.6 g/mol
= 0.394 g

Therefore, to make 100 mL of a 0.100 M Tris buffer that is equimolar in Tris-base and Tris-HCl, you would need to weigh 0.908 grams of Tris-base and 0.394 grams of Tris-HCl.