To calculate the molar mass of the unknown monoprotic base, we can use the information provided in the titration.

Step 1: Calculate the number of moles of HCl used in the titration.

Moles of HCl = Concentration of HCl (M) x Volume of HCl used (L)

Moles of HCl = 1.00 M x 0.0200 L = 0.0200 moles HCl

Step 2: Since the base is monoprotic, the number of moles of base is equal to the number of moles of HCl used.

Moles of Base = Moles of HCl = 0.0200 moles

Step 3: Calculate the molar mass of the unknown base.

Molar mass of Base = Mass of Base (g) / Moles of Base (moles)

Mass of Base = 1.122 g

Moles of Base = 0.0200 moles

Molar mass of Base = 1.122 g / 0.0200 moles = 56.1 g/mol

Therefore, the molar mass of the unknown monoprotic base is 56.1 g/mol.