Analytical expressions for the low-field mobility of two-dimensional electron gas (2DEG) are obtained on the basis of quantum kinetic approach. Calculations and experimental data show that the acoustic and polar optical phonons and ionized impurities are the dominant scattering mechanisms in AlGaN, Al0.3Ga0.7As, and In0.53Ga0.47As heterostructures. In the temperature range under consideration, there are three regions in which mobility is determined by the scattering of electrons on ionized impurities (T < 40 K), acoustic phonons (40 < T < 200 K), and polar optical phonons (T < 200 K). Two analytical expressions for calculating the acoustic phonon limited mobility in 2DEG are examined: the widely used semi-empirical formula and the formula derived from the proposed quantum kinetic approach. A comparison of the calculated temperature dependences of mobility with experimental data allows us to determine the type of the phonons and their interaction constants with electrons and gives the values of the polar optical phonon energy that limits the electron mobility at temperature T > 200 K. New values of polar optic phonons are proposed to describe temperature dependences of electron mobility.