A gas leak has led to the presence of 1.00 mole% carbon monoxide in a 350-m^3 laboratory. The leak was discovered and sealed, and the laboratory is to be purged with clean air to a point at which the air contains less than the OSHA (Occupational Safety and Health Administration)-specified Permissible Exposure Level (PEL) of 35 ppm (molar basis). Assume that the clean air and the air in the laboratory are at the same temperature and pressure and that the laboratory air is perfectly mixed throughout the purging process.

a. Let tr (h) be the time required for the specified reduction in the carbon monoxide concentration. Write a differential CO mole balance, letting N equal the total moles of gas in the room (assume constant), x the mole fraction of CO in the room air, and v (m/h) the flow rate of purge air entering the room (and also the flow rate of laboratory air leaving the room). Convert the balance into an equation for dxldt and provide an initial condition.
b. Integrate the balance to derive an equation for tr in terms of vp.
c. If the volumetric flow rate is 700 m^3/h (representing a turnover of two room volumes per hour), how long will the purge take? What would the volumetric flow rate have to be to cut the purge time in half?