2. (25 pts) An adiabatic stirred tank reactor is used to carry out an irreversible, exothermic reaction, Aproduct(s). The mole balance for the reactant A and the corresponding system energy balance are given below, CA,0CAkCA=0,C^p(TT0)=kCA(Hr) where CA is the molar concentration of A in the reactor, CA,0 is the molar concentration of A in the feed, is the fluid residence time in the reactor, k is the reaction rate constant, is the fluid density, C^p is the fluid heat capacity, T is the reactor temperature, T0 is the feed temperature, and (Hr) is the heat of reaction. The reaction rate constant is a function of temperature as given below. k=k0exp(RTEA) - Note: the rate constant is not one of the equations that you are solving. It is a function of the temperature (one of the variables you are determining), so it will change as Solver changes the temperature to find a solution. This system of equations is known to possess three possible solutions. Using Solver with the initial guesses and parameter values given below, determine the three different steady-state reactant concentrations (CA) and reactor temperatures (T). You should use the following reformulated forms of the equations in your solution: 1kCACA,0CA=0,1kCA(Hr)C^p(TT0)=0 You will also have to set up three different Solver models on three separate worksheets to solve each part of the problem. CA,0=4.0LmolT0=325Kk0=2.21015min1REA=13500KC^p=3785LKJ(Hr)=85,000molJVr=2100LV=700minL=VVr a. Use initial guess T=325,CA=4.0 b. Use initial guess T=325,CA=4.0, and constrain T350 c. Use initial guess T=325,CA=4.0, and constrain T400 nework 4 - Solving Nonlinear Equations Monday, March 27, 2023 ructions: Name your file HW4_LastName. Work each homework problem on separate ksheets in the same Excel file. The numbers appearing in your workbook should be neatly nized and clearly labeled. Upload your Excel workbook to the HW4 Dropbox on Moodle n you are finished. (10 pts) The vapor pressure (Pvap) of a substance is the pressure in the vapor phase of a substance that is equilibrium with the liquid phase. For example, the vapor pressure of water at 100C is atmospheric pressure; stated another way, any substance has a vapor pressure of atmospheric pressure at its normal boiling point. The vapor pressure for a substance is often determined from the Antoine equation, which takes the form: log10Pvap=AT+CB where the temperature (T) is in C and the vapor pressure is in torr. The constants A,B, and C are substance specific constants that are typically valid over a range of temperatures. Notice the log10 on the left-hand side (LHS). Create a worksheet where A,B,C, and T all have their own cells, and Pvap (in torr) is calculated from those quantities. In another cell, the vapor pressure will be converted from torr to kPa. Your conversion must use the CONVERT function for full credit. (NOTE: kPa does not show up as an option, but it is built in.) Once your worksheet is setup, use Goal Seek to determine the temperature of water if the vapor pressure is 500kPa. The Antoine constants for water are: A=8.05573B=1723.64C=233.076 2. (25 pts) An adiabatic stirred tank reactor is used to carry out an irreversible, exothermic reaction, Aproduct(s). The mole balance for the reactant A and the corresponding system energy balance are given below, CA,0CAkCA=0,C^p(TT0)=kCA(Hr) where CA is the molar concentration of A in the reactor, CA,0 is the molar concentration of A in the feed, is the fluid residence time in the reactor, k is the reaction rate constant, is the fluid density, C^p is the fluid heat capacity, T is the reactor temperature, T0 is the feed temperature, and (Hr) is the heat of reaction. The reaction rate constant is a function of temperature as given below. k=k0exp(RTEA) - Note: the rate constant is not one of the equations that you are solving. It is a function of the temperature (one of the variables you are determining), so it will change as Solver changes the temperature to find a solution. This system of equations is known to possess three possible solutions. Using Solver with the initial guesses and parameter values given below, determine the three different steady-state reactant concentrations (CA) and reactor temperatures (T). You should use the following reformulated forms of the equations in your solution: 1kCACA,0CA=0,1kCA(Hr)C^p(TT0)=0 You will also have to set up three different Solver models on three separate worksheets to solve each part of the problem. CA,0=4.0LmolT0=325Kk0=2.21015min1REA=13500KC^p=3785LKJ(Hr)=85,000molJVr=2100LV=700minL=VVr a. Use initial guess T=325,CA=4.0 b. Use initial guess T=325,CA=4.0, and constrain T350 c. Use initial guess T=325,CA=4.0, and constrain T400 nework 4 - Solving Nonlinear Equations Monday, March 27, 2023 ructions: Name your file HW4_LastName. Work each homework problem on separate ksheets in the same Excel file. The numbers appearing in your workbook should be neatly nized and clearly labeled. Upload your Excel workbook to the HW4 Dropbox on Moodle n you are finished. (10 pts) The vapor pressure (Pvap) of a substance is the pressure in the vapor phase of a substance that is equilibrium with the liquid phase. For example, the vapor pressure of water at 100C is atmospheric pressure; stated another way, any substance has a vapor pressure of atmospheric pressure at its normal boiling point. The vapor pressure for a substance is often determined from the Antoine equation, which takes the form: log10Pvap=AT+CB where the temperature (T) is in C and the vapor pressure is in torr. The constants A,B, and C are substance specific constants that are typically valid over a range of temperatures. Notice the log10 on the left-hand side (LHS). Create a worksheet where A,B,C, and T all have their own cells, and Pvap (in torr) is calculated from those quantities. In another cell, the vapor pressure will be converted from torr to kPa. Your conversion must use the CONVERT function for full credit. (NOTE: kPa does not show up as an option, but it is built in.) Once your worksheet is setup, use Goal Seek to determine the temperature of water if the vapor pressure is 500kPa. The Antoine constants for water are: A=8.05573B=1723.64C=233.076