Final answer:
The amount of oxygen in the tank is determined by using the ideal gas law formula PV = nRT after adjusting for atmospheric pressure and converting temperature to Kelvin. By inserting the values for pressure, volume, and temperature, the number of moles can be calculated.
Step-by-step explanation:
To determine the amount of oxygen in the tank, we can use the ideal gas law, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin.
First, adjust the readings of the pressure gauge to account for the atmospheric pressure. Since the gauge pressure is the pressure above atmospheric pressure, the absolute pressure inside the tank is P = gauge pressure + atmospheric pressure = 500 kPa + 97 kPa = 597 kPa.
Next, convert the temperature from degrees Celsius to Kelvin: T = 28°C + 273.15 = 301.15 K.
Now we can use the ideal gas law. Rearrange the formula to solve for n (the number of moles):
n = (PV) / (RT)
Insert the values:
n = (597 kPa * 2.5 m³) / (8.314 kPa·L/mol·K * 301.15 K)
Since 1 m³ = 1000 L, we convert the volume in m³ to L:
n = (597 kPa * 2500 L) / (8.314 kPa·L/mol·K * 301.15 K)
Solve for n to find the number of moles of oxygen in the tank.