Final answer:
To find the total pressure in the 2.0 L tank, we can use Dalton's law of partial pressures. We calculate the partial pressure of N₂(g) and Ar(g) using the ideal gas law, and then add them together to get the total pressure in the tank.
Step-by-step explanation:
In this problem, we are given a 2.0 L sample of N₂(g) and a 6.0 L sample of Ar(g), each originally at 1 atm and 0°C, which are combined in a 2.0 L tank. Since the temperature is held constant, the total pressure in the tank can be calculated using Dalton's law of partial pressures. According to Dalton's law, the total pressure in a mixture of gases is equal to the sum of the partial pressures of each individual gas.
First, we need to calculate the partial pressure of N₂(g):
Using the ideal gas law, PV = nRT, we can rearrange the equation to solve for the pressure:
P = (nRT) / V
For N₂(g), n = moles of N₂(g), R = gas constant, T = temperature in Kelvin, and V = volume of N₂(g) sample. Since the number of moles of N₂(g) is not provided, we cannot calculate the partial pressure directly. However, since the volume is halved from 2.0 L to 1.0 L when combined with Ar(g) in the 2.0 L tank, we can assume that the moles of N₂(g) are also halved. Hence, the volume becomes 1.0 L and the number of moles of N₂(g) becomes half of the original number of moles. Now, we can plug in the values into the ideal gas law equation to calculate the partial pressure of N₂(g).
Next, we need to calculate the partial pressure of Ar(g):
Following the same reasoning as above, the volume of Ar(g) becomes 1.0 L and the number of moles of Ar(g) remains the same. We can use the ideal gas law equation with the given values to calculate the partial pressure of Ar(g).
Finally, we can add the partial pressures of N₂(g) and Ar(g) to get the total pressure in the 2.0 L tank.