Final Answer:
The total pressure inside the vessel can be calculated using Dalton's law of partial pressures. Adding the partial pressures of each gas (CF₄, CH₄, and Kr) together, the total pressure inside the vessel is 7.44 atm.
Step-by-step explanation:
Dalton's law of partial pressures states that in a mixture of non-reacting gases, the total pressure exerted is the sum of the partial pressures of individual gases. Given the partial pressure of CF₄ as 1.440 atm, and knowing that the total moles of gas inside the vessel is 2.50 mol (CF₄) + 4.00 mol (CH₄) + 1.50 mol (Kr) = 8.00 mol, we can use the mole fraction to determine the partial pressures of CH₄ and Kr.
The mole fraction of CF₄ is 2.50 mol / 8.00 mol = 0.3125. Using this, we can find the partial pressure of CH₄ and Kr. The partial pressure of CH₄ is 0.3125 (total pressure) - 1.440 atm (partial pressure of CF₄) = 6.00 atm. Similarly, the partial pressure of Kr is 7.44 atm (total pressure) - 1.440 atm (partial pressure of CF₄) = 5.00 atm.
Adding these partial pressures together: 1.440 atm (CF₄) + 6.00 atm (CH₄) + 5.00 atm (Kr) = 7.44 atm, which represents the total pressure inside the vessel according to Dalton's law. Thus, the total pressure inside the vessel, considering the contributions of each gas, is 7.44 atm.