Final answer:
The pressure in an oxygen tank is most likely to increase due to an increase in the number of gas molecules or temperature. The number of moles at different conditions can be calculated using the Ideal Gas Law, which also allows comparison between different sets of pressure and temperature conditions.
Step-by-step explanation:
The pressure in a patient's oxygen tank after it is filled is greater, primarily because of the increase in the number of gas molecules (moles) within a given fixed volume. When the number of gas molecules increases in a constant volume, the frequency of collisions between the molecules and the container walls increases, thereby increasing the pressure. Another key factor is the temperature of the gas; an increase in temperature will also increase the pressure in a rigid container due to the increased kinetic energy of the gas molecules, leading to more frequent and forceful collisions. However, in this specific scenario, if the volume, temperature, and gas constant (R) remain the same, then a change in the number of moles is the most likely reason for the increase in pressure after filling the oxygen tank.
To calculate the number of moles of oxygen in the tank given its volume, temperature and pressure, you would use the Ideal Gas Law: PV = nRT. Let's calculate the number of moles at the provided condition (105 K and 3.356 atm) using this formula:
n = PV / RT
Where:
P = pressure (3.356 atm)
V = volume (2.5 L)
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (105 K)
Calculating, we find the number of moles in the tank. To compare with standard conditions, you convert to STP (standard temperature and pressure), which is typically 273 K and 1 atm. Assuming the same volume and using the Ideal Gas Law again, you'd find the amount of moles at STP. By comparing the two numbers obtained, you determine if there are fewer, more, or an unchanged number of moles.