A chemistry student needs to calculate the enthalpy of adsorption for NH3 gas onto a silica gel adsorbent. The mass of silica gel used is 5.00g and the initial temperature of the system is 298K. The student also measures the equilibrium pressure of the NH3 gas at 298K to be 0.222atm. To carry out the experiment, the student passes NH3 gas over the silica gel and waits until it reaches equilibrium. The temperature of the system is then measured to be 305K. Using this information, what is the enthalpy of adsorption of NH3 onto the silica gel adsorbent in kJ/mol?

Question

A chemistry student needs to calculate the enthalpy of adsorption for NH3 gas onto a silica gel adsorbent. The mass of silica gel used is 5.00g and the initial temperature of the system is 298K

Answer 1

To calculate the enthalpy of adsorption, we can use the Clausius-Clapeyron equation: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 ideal gas constant  8.314 J/molK .In this case, we have:P1 = 0.222 atm  initial pressure T1 = 298 K  initial temperature T2 = 305 K  final temperature We need to find P2, the final pressure. Since the mass of silica gel is given, we can assume that the amount of NH3 gas adsorbed is proportional to the mass of the silica gel. Therefore, we can write:P2 = P1 *  1 - m_adsorbed/m_total where m_adsorbed is the mass of NH3 adsorbed and m_total is the total mass of silica gel  5.00 g . We can assume that the mass of NH3 adsorbed is small compared to the mass of silica gel, so we can approximate:P2  P1 *  1 - m_adsorbed/m_total Now we can plug the values into the Clausius-Clapeyron equation:ln P2/P1  = -H/R *  1/T2 - 1/T1 ln  P1 - m_adsorbed/m_total /P1  = -H/R *  1/T2 - 1/T1 Since we are interested in the enthalpy of adsorption per mole of NH3, we can divide both sides of the equation by the molar mass of NH3  17.03 g/mol :ln  P1 - m_adsorbed/m_total /P1  /  m_adsorbed/17.03  = -H/ R *  1/T2 - 1/T1  Now we can solve for H:H = -R *  1/T2 - 1/T1  * ln  P1 - m_adsorbed/m_total /P1  *  m_adsorbed/17.03 Since we don't have the value for m_adsorbed, we cannot provide a numerical value for H. However, if the student can measure the mass of NH3 adsorbed, they can use this equation to calculate the enthalpy of adsorption in kJ/mol.