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.
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Step 1: Identify given values and convert units. The number of moles of ideal gas is n = 1 mol. The initial temperature is T = 25^. Convert this to Kelvin: T = 25 + 273.15 = 298.15 K The initial internal pressure of the gas is P_1 = 5 atm. The constant outside pressure against which the gas expands is P_ext = 1 atm. The final internal pressure of the gas is P_2 = 1 atm. The gas constant R = 0.08206 L atm mol^-1 K^-1 will be used for volume calculations, and 1 L atm = 101.325 J for work conversion. Step 2: Apply the formula for work done in an irreversible expansion. For an irreversible expansion against a constant external pressure, the work done (W) is given by: W = -P_ext V where V = V_2 - V_1 is the change in volume. We assume the temperature remains constant during the expansion for volume calculations, as no information about temperature change is provided. Step 3: Calculate the initial volume (V_1) using the ideal gas law. The ideal gas law is PV = nRT. So, V = (nRT)/(P). V_1 = (nRT)/(P_1) V_1 = (1 mol)(0.08206 L atm mol^-1 K^-1)(298.15 K)5 atm V_1 = 24.466 L atm5 atm V_1 = 4.8932 L Step 4: Calculate the final volume (V_2) using the ideal gas law. V_2 = (nRT)/(P_2) V_2 = (1 mol)(0.08206 L atm mol^-1 K^-1)(298.15 K)1 atm V_2 = 24.466 L atm1 atm V_2 = 24.466 L Step 5: Calculate the change in volume ( V). V = V_2 - V_1 V = 24.466 L - 4.8932 L V = 19.5728 L Step 6: Calculate the work done (W) in L atm. W = -P_ext V W = -(1 atm)(19.5728 L) W = -19.5728 L atm Step 7: Convert the work done from L atm to Joules. Using the conversion factor 1 L atm = 101.325 J: W = -19.5728 L atm × 101.325 J1 L atm W = -1983.10 J The work done is: -1983.10 J What's next?