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Context. The adiabatic exponent $Γ_1$ is studied as a thermodynamic quantity in the partially ionized plasma of the solar convection zone. Aims. The aim of this study is to understand the impact of heavy elements on the $Γ_1$ profile. We calculated $Γ_1$ with the SAHA-S equation of state for different chemical compositions of plasma, and we analyzed contributions of individual elements to $Γ_1$. Methods. We studied the decrease in $Γ_1$ due to the ionization of heavy elements in comparison with the value obtained for a pure hydrogen-helium plasma. These types of differences are denoted as "Z contributions", and we analyzed them for eight elements (C, N, O, Ne, Mg, S, Si, and Fe) as well as for a mixture of elements corresponding to the solar chemical composition. We compared linear combinations of individual Z contributions with the exact Z contribution. Applying a least-squares technique to the decomposition of the full Z contribution to a basis of individual-element contributions, we obtained the mass fractions of the heavy elements. Results. The Z contribution of heavy elements can be described by a linear combination of individual-element Z contributions with a high level of accuracy of 5e-6 . The inverse problem of estimating the mass fractions of heavy elements from a given $Γ_1$ profile was considered for the example of solar-type mixtures. In ideal numerical simulations, the mass fractions of the most abundant elements could be determined with a relative accuracy better than a few tenths of a percent. In the presence of random or systematic errors in the $Γ_1$ profile, abundance estimations become remarkably less accurate. If the amplitude of the errors does not exceed 1e-4, we can expect a determination of at least the oxygen abundance with a relative error of about 10%.