The conformation and titration curves of weak polyampholytes are examined using Monte Carlo simulations with screened Coulomb potentials in the Grand Canonical ensemble. Two different types of monomers are considered. Depending on the solution pH, monomers A are weak acidic sites that can either be negatively charged or uncharged (as carboxylic groups), whereas monomers B are weak basic sites that can either be positively charged or uncharged (as amino groups). The influence of the chain stiffness, primary structure, and ionic concentration on the acid/base properties of the polyampholyte chains are systematically investigated. By adjusting the pH values, titration curves and then the fractions of positively and negatively ionized charged monomers are calculated. Stiffness influence is estimated by comparing two models of chain: a fully flexible and a rod-like polyampholyte. Different primary structures such as statistical (diblock, octablock, and alternating) and random polyampholytes are also considered. We demonstrate that the primary structure plays important roles in the acid/base properties as well as the charge distribution along the polymer backbone of a statistical rod-like polyampholyte. When flexible polyampholytes are considered, polyampholyte conformations promote the attractive electrostatic interactions between positively and negatively charged monomers, hence leading to more or less compact conformations and acid/base properties relatively different in comparison to the rod-like polyampholytes. Various conformations such as extended, globular, and pearl-necklace conformations are found in good agreement with the literature by adjusting the interaction parameter between monomers and monomer stoichiometry.