Question

A closed vessel with rigid walls contains 1 mol of U²³⁸₉₂ and 1 mol of air at 298 K. Considering complete decay of U²³⁸₉₂ to Pb²⁰⁶₈₂ , the ratio of the final pressure to the initial pressure of the system at 298 K is:

Answer 1

The ratio of the final pressure to the initial pressure is 2:1.

Step-by-step explanation:

Given that the vessel contains 1 mole of U²³⁸₉₂ and 1 mole of air, and considering the complete decay of U²³⁸₉₂ to Pb²⁰⁶₈₂, we can use the ideal gas law to determine the ratio of the final pressure to the initial pressure. The ideal gas law equation is 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.

Since the volume and temperature are constant, we can simplify the equation to P₁ / P₂ = n₁ / n₂, where P₁ is the initial pressure, P₂ is the final pressure, n₁ is the initial number of moles, and n₂ is the final number of moles. In this case, n₁ is 1 mole of U²³⁸₉₂ and n₂ is 1 mole of U²³⁸₉₂ plus 1 mole of air.

Therefore, the ratio of the final pressure to the initial pressure is 2:1, or 2.