In this study, the improved Tietz potential was used to describe the internal vibration of a diatomic molecule. With the help of the expression for bound state energy levels, a more generalized equation for the upper bound vibrational quantum number and canonical partition function were obtained for the diatomic system. The obtained partition function was used to derive analytical equation for the prediction of constant pressure (isobaric) molar heat capacity of diatomic molecules. The analytical model was used to predict the constant pressure molar heat capacity data of the ground state CO, BBr, HBr, HI, P2, KBr, Br2, PBr, SiO and Cl2 molecules. The upper bound vibrational quantum number obtained for the molecules are 85, 100, 21, 21, 115, 301, 89, 157, 110 and 67. The computed average absolute deviation are 2.3462%, 1.1342%, 2.3350%, 1.9078%, 0.7268%, 2.4041%, 1.7849%, 1.8989%, 2.5209% and 2.1523%. The present results are in good agreement with available literature data on gaseous molecules.