Asample of hydrogen gas is collected over water at 25°c. the vapor pressure of water at 25°c is 23.8 mmhg. if the total pressure is 523.8 mmhg, what is the partial pressure of the hydrogen?

The partial pressure of the gas will be the total pressure minus the vapor pressure.  523.8-23.8=500mmHg.  This makes sense due to the fact that the idea of partial pressures still works even with vapor pressure since vapor pressure is just the partial pressure of water vapor (23.8mmHg) in the container which is added to the partial pressure of hydrogen gas (500mmHg) to make a total pressure of 523.8mmHg.
I hope this helps.  Let me know in the comments if anything is unclear.