Based on the experimental data on the ratio of Raman frequencies in isotope-pure diamonds, parameters of the pair potential of interatomic interaction for diamond from 12C and from 13C were determined. Using the obtained parameters, both state equation and baric dependences of the lattice properties of isotope-pure diamonds at a temperature of 300 K were calculated. The Debye temperature; the first, second and third Grüneisen parameters; the isothermal bulk modulus; the coefficient of thermal expansion; the heat capacity; the surface energy; as well as the derivatives with respect to pressure for these functions along the 300 K isotherm were calculated.