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Calculate the enthalpy of adsorption of benzene vapor on silica gel at 25°C and a pressure of 2.0 atm, given that the mass of adsorbent used is 0.25 g and the adsorption capacity of silica gel for benzene at this temperature and pressure is 0.75 g/g.

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To calculate the enthalpy of adsorption, we first need to determine the amount of benzene adsorbed on the silica gel. The adsorption capacity is given as 0.75 g/g, which means that 0.75 grams of benzene can be adsorbed per gram of silica gel. Given the mass of adsorbent used is 0.25 g, we can calculate the mass of benzene adsorbed:Mass of benzene adsorbed =  mass of adsorbent    adsorption capacity Mass of benzene adsorbed =  0.25 g    0.75 g/g  = 0.1875 gNow, we need to determine the moles of benzene adsorbed. The molecular weight of benzene  C6H6  is 12.01 g/mol  for carbon   6 + 1.01 g/mol  for hydrogen   6 = 78.12 g/mol.Moles of benzene adsorbed =  mass of benzene adsorbed  /  molecular weight of benzene Moles of benzene adsorbed =  0.1875 g  /  78.12 g/mol  = 0.0024 molNext, we will use the Clausius-Clapeyron equation to determine the enthalpy of adsorption. The equation is:ln P2/P1  = -H/R   1/T2 - 1/T1 Where P1 and P2 are the initial and final pressures, T1 and T2 are the initial and final temperatures, H is the enthalpy of adsorption, and R is the gas constant  8.314 J/molK .In this case, we are given the final pressure  P2  as 2.0 atm. We will assume that the initial pressure  P1  is 1 atm, as this is a common assumption for adsorption problems. The initial temperature  T1  is 25C, which is 298.15 K. We will assume that the final temperature  T2  is the same as the initial temperature since there is no mention of a temperature change.Plugging these values into the Clausius-Clapeyron equation:ln 2.0 atm / 1.0 atm  = -H /  8.314 J/molK    1/298.15 K - 1/298.15 K Since the temperature does not change, the term  1/T2 - 1/T1  becomes zero, and the equation simplifies to:ln 2  = 0This means that there is no change in enthalpy during the adsorption process, so the enthalpy of adsorption  H  is 0 J/mol.

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