Final answer:
To find the final pressure in the tank, use the ideal gas law equation PV = nRT. Convert the temperatures from Celsius to Kelvin and calculate the initial number of moles. Plug in the values for the final volume, initial moles, ideal gas constant, and final temperature to solve for the final pressure.
Step-by-step explanation:
To determine the final pressure in the tank, we can use the ideal gas law equation, which states: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the given temperatures from Celsius to Kelvin. The initial temperature is 27°C + 273 = 300K, and the final temperature is 157°C + 273 = 430K.
Next, we can calculate the initial number of moles of nitrogen gas using the ideal gas law equation for the initial conditions: (7.50 * 10^3 Pa) * (0.750 m^3) = n * (8.31 J/(mol * K)) * (300K). Solving for n gives us an initial number of moles of approximately 0.246 moles.
Using the ideal gas law equation for the final conditions, we can solve for the final pressure. (Pf) * (0.480 m^3) = (0.246 moles) * (8.31 J/(mol * K)) * (430K). Solving for Pf gives us a final pressure of approximately 10,104 Pa.