We construct a second order pion-carbon optical potential in momentum space and use it to calculate cross sections for energies between 40 and 280 MeV. We find that the cross sections calculated with this potential depend very strongly on the range of the pion-nucleon interaction for energies below the 3, 3 resonance. For energies above the 3, 3 resonance the main effect of the second order optical potential is to raise the cross sections at large angles by factors of between 2 and 3 independently of the pion-nucleon range. We derive some approximate formulas for the second order term of the optical potential and determine their range of validity. We also study the sensitivity of our results to the use of different relativistic propagators for the pion.