The present invention relates to a sealing system for a pump configured to pressurize a volatile liquid, such as liquid ammonia. The sealing system (2) includes a stuffing box (35) forming a barrier chamber (30) and a pump-side seal chamber (43), a mechanical seal (20) arranged in the barrier chamber (30), and a barrier-gas supply system (32) for supplying a barrier gas into the barrier chamber (30). The barrier gas has a pressure higher than a pressure of the volatile liquid in the pump-side seal chamber (43). The pump-side seal chamber (43) is located between an impeller (7) of the pump (1) and the mechanical seal (20). The barrier-gas supply system (32) includes a pressure control valve (50) configured to maintain a constant difference between pressure in the barrier chamber (30) and pressure in the pump-side seal chamber (43).