Final answer:
To find the new partial pressure of oxygen in a scuba tank, the ideal gas law is used along with the temperature conversion from Celsius to Kelvin. The number of moles of oxygen is calculated first from initial conditions and then the ideal gas law gives the partial pressure in the new tank volume.
Step-by-step explanation:
To calculate the new partial pressure of oxygen in a scuba tank, we can use the ideal gas law formula in the context of Dalton's Law of Partial Pressures. According to Dalton's Law, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases.
The ideal gas law is given by: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we will convert the temperature from degrees Celsius to Kelvin by adding 273.15:
25.0 °C + 273.15 = 298.15 K.
For oxygen, we calculate the number of moles (n) using its initial conditions:
(0.900 atm) * (27.0 L) = n * (0.0821 L*atm/(mol*K)) * (298.15 K).
Solving for n gives us the number of moles of oxygen.
After finding the number of moles, we use the ideal gas law again to find the partial pressure of oxygen in the new volume (5.70 L) at the same temperature:
(P_new) * (5.70 L) = n * (0.0821 L*atm/(mol*K)) * (298.15 K).
Solving for P_new gives us the new partial pressure of oxygen.