Ask Mr. Smarty Plants

it sounds to me as if your Clematis pitcheri (Purple clematis) has experienced a mutation in the biochemical pathway that is responsible for the flower pigmentation.  The mutation itself probably didn't happen in your particular plant but happened generations ago.   Generally, mutations affecting flower color are recessive, i.e., both the pollen and the ovum of the plant that produced the seed that grew into the plant with white flowers had to have the mutant copy of the gene to produce this plant with white flowers.  A plant with one normal gene and one mutant gene would still have purple flowers.  You could see how it would take several generations to enable a mutant pollen grain to fertilize a mutant ovum.

There isn't really any nutrient or fertilizer that will change the color of this particular plant to purple.  However, if these white flowers receive pollen from a purple leatherflower, the plant that grows from the resultant seed will likely be purple.  Or, if the plant can and does self-pollinate, then its seeds will produce a plant with white flowers again.

The bottom line is that you will either need to wait for offspring of this plant (plants produced from its seeds)  to potentially have purple flowers or buy another plant.