Penning trap mass spectrometry (PTMS) can be used to test the Standard Model (SM) and to answer the questions related to the origin and abundance of the elements in the universe. There are several facilities worldwide specialized in PTMS and some of them can measure the masses of isotopes with half-lives in the range of milliseconds. TRIUMF’s ion trap for atomic and nuclear science (TITAN) is one such facility. In mass measurement the precision is linearly proportional to the charge state of the ion of interest. To increase the charge state, ions are charge-bred using an electron beam ion trap (EBIT) at TITAN. However, the charge breeding process introduces an energy spread among the ions which adversely affects the precision of the mass measurement. To overcome this problem a cooler Penning trap (CPET) was designed, assembled and is now being tested off-line. This thesis presents the first systematic test results of CPET. We also present the result of the first Penning trap mass measurement of the isotope 24Al, which is five times more precise than the previous atomic mass evaluation (AME2012) value. The precise and accurate mass of 24Al is important for both astrophysics and for test of the standard model (SM). The resonance energy (E_r) calculated for the 23Mg(p,gamma)24Al reaction using the ground state mass of 24Al reported in this thesis shows a 2s deviation from the direct measurement. On the other hand, tests of the SM by evaluating f_t values using isospin T = 1 nuclides have reached a high precision level. Effort is now shifting towards the T = 2 nuclides, which are far from stability compared to their T = 1 counterparts. For this reason, the ground state masses of T = 2 nuclides and of their decay products are required to be known with high precision. 24Al is the daughter of one such nucleus, 24Si. The ground state mass of 24Al reported in this thesis will be useful to test the SM. / October 2016