We report on the use of first-principles molecular dynamics calculations to examine properties of liquid carbon dioxide in the pressure-temperature range of 0-1 TPa and 200-100 000 K. The computed equations of state points are used to predict a series of shock Hugoniots with initial starting conditions that are relevant to existing and ongoing shock-wave experiments. A comparison with published measurements up to 70 GPa shows excellent agreement. We find that the liquid undergoes a gradual phase transition along the Hugoniot and have characterized this transition based on changes in bonding and structural properties as well as the conductivity and reflectivity of the fluid.