A mobile vacuum distillation unit for extracting, condensing, and collecting volatile organic compound vapor emissions from one or more polymer-containing articles includes a shell that defines an enclosed interior space and is mounted to a transportable support platform, a vacuum distillation vessel, a condenser, a condensate storage tank, and a vacuum pump system in fluid communication with a vacuum distillation chamber of the vacuum distillation vessel. The vacuum distillation chamber that includes the one or more polymer-containing articles from which the VOC vapor emissions are extracted may be heated by an exhaust gas heat exchanger if the transportable support platform is connected to and hauled by a tractor unit powered by a diesel engine. A method of using the mobile vacuum distillation unit to extract VOC vapor emissions from one or more polymer-containing article during transportation of the one or more polymer-containing articles between geographically separate destinations is also disclosed.