This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Identify given values and convert units. The number of moles of gas is n = 1 mol. The process is reversible and isothermal, meaning the temperature is constant. The temperature is T = 25^. Convert this to Kelvin: T = 25 + 273.15 = 298.15 K The gas constant R = 8.314 J mol^-1 K^-1. The problem states the gas is "expanded reversibly and isothermally from 5 atm to 10 atm". An expansion implies that the volume increases and the pressure decreases. Therefore, the initial pressure (P_1) should be greater than the final pressure (P_2). The given pressures "from 5 atm to 10 atm" suggest an increase in pressure, which would be a compression, not an expansion. To be consistent with the term "expanded", we will assume the initial pressure was P_1 = 10 atm and the final pressure was P_2 = 5 atm. Step 2: Apply the formula for work done in a reversible isothermal process. For a reversible isothermal process involving an ideal gas, the work done (W) is given by: W = -nRT ((V_2)/(V_1)) For an isothermal process, P_1V_1 = P_2V_2, which means (V_2)/(V_1) = (P_1)/(P_2). Substituting this into the work equation: W = -nRT ((P_1)/(P_2)) Step 3: Substitute the values and calculate the work done. Using n = 1 mol, R = 8.314 J mol^-1 K^-1, T = 298.15 K, P_1 = 10 atm, and P_2 = 5 atm: W = -(1 mol