High temperature phase relations in the Cu-R-O (R = Dy, Ho, Er, Yb) ternary systems suggest that there exists only one ternary oxide, Cu(2)R(2)O(5)(R = Dy, Ho, Er, Yb). One of the three phase fields in these systems which is of interest consists of Cu2O + R(2)O(3) + Cu(2)R(2)O(5). Chemical potential of oxygen for the co-existence of this three phase assemblage is measured between 1050-1325 K employing the solid-state electrochemical cell, (-)Pt/Cu2O + R(2)O(3) + Cu(2)R(2)O(5)//(CaO)ZrO2//O-2(P = 0.0212 MPa)/Pt(+) Gibbs energy of formation of Cu(2)R(2)O(5) from component oxides is obtained by combining the measured oxygen potential for Cu2O + R(2)O(3) + Cu(2)R(2)O(5) three phase equilibrium and Cu2O + CuO from literature. Based on the present results, Gibbs energy of formation of Cu2Tb2O5, Cu2Tm2O5, Cu2Tm2O5 and Cu2Lu2O5 has been estimated.