The volume of a manifold (tubing and glassware of small volume) used in transferring gases is calibrated using Boyle's law. Deduce the total volume of the manifold from the following data:
A 0.251 dm^3 flask containing nitrogen at 697 torr is attached to the manifold. With the stopcock bteween the flask and the manifold closed, the manifold is pumped down to a pressure of 21 mTorr. When the stopcock between the manifold and the flask is opened, the pressure in the system is 287 torr. Assuming no temperature changes, what is the volume of the manifold?