We have derived a dynamical equation of shape instability for a spherical bubble，where water vapor evaporation and condensation at a sonoluminescencing bubble wall are considered- Using the derived equation and the mass diffusive equilibrium condition for the bubble vibration, we investigate the bubble instability on those controlled conditions of water temperature and corresponding acoustic frequency (for 14％ of argon concentration dissolved in water with the frequency of 206kHz at 217℃, for a 20kPa 1% argon in nitrogen bubble with the frequency of 319kHz at 0℃ and with the frequency of 338kHz at 20℃)- Comparing the calculated results with the published experimental data, we find that the determination of critical boundaries of the instability can be improved to some extent by considering the effect of vapor-