This problem can be solved using Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases:

`P_(Total) = P_A + P_B + P_C +....`

In this case,

`8.00 atm = P_(Total) = P_O_2 + P_N_2 + P_H_2`

so

`P_H_2 =P_(Total) - P_O_2 - P_N_2`

The partial pressure of nitrogen must be converted to atmospheres to be consistent with the other two pressure values:

2.50 torr x (1 atm/760 torr) = 0.00329 atm

The partial pressure of hydrogen is:

8.00 atm - 3.00 atm - 0.00329 atm = 4.9967 atm

Rounded to 3 significant digits: 5.00 atm

The partial pressure of an individual gas in a gas mixture is the pressure the gas would exert if it was the only gas in the container. When a gas mixture behaves ideally, each gas in the mixture obeys the ideal gas law independently, regardless of other gases present.