The ${}^{28}\mathrm{Si}(\ensuremath{\alpha}{,}^{8}\mathrm{He}{)}^{24}\mathrm{Si}$ reaction has been used to measure the energies of the first two excited states in ${}^{24}$Si. The excitation energies were found to be $1.879\ifmmode\pm\else\textpm\fi{}0.011$ and $3.441\ifmmode\pm\else\textpm\fi{}0.010\mathrm{MeV}$. These data allow for the first time the calculation of the stellar reaction rate of ${}^{23}\mathrm{Al}(p,\ensuremath{\gamma}{)}^{24}\mathrm{Si}$ on the basis of experimental information. This reaction is of considerable interest, since it might lead to a decrease of the ${}^{22}$Na production in nova explosions, and solve the discrepancy between the ${}^{22}$Na yield predictions of nova models and recent COMPTEL observations. We show, however, that the temperatures and densities required for a significantly reduced ${}^{22}$Na yield are not reached in current nova models.