I own a house with my ex wife worth $450K. she has mortgage in her name only for $350K. if we sell the house, am I responsible for $175K ofthe mortgag

The mortgage is gong to have to be satisfied in order to pass clean title to the property.  I am surprised that the mortgage company would give her a mortgage with your name on the deed and not make you sign anything.  If the house is sold, $350,000 of the proceeds will have to be used to satisfy the mortgage.  You might be able to make a claim that you own half of the value and that she improperly put a lien on your portion of the asset, and/or make a claim to the rest of the proceeds from the sale.