The equilibrium constant for the reaction,
SO2(g)+ NO2(g) <----> NO(g)+ SO3(g)
has been experimentally determined as a function of temperature. The results are presented in the table below.
T (°F) KC
285 662
752 156
842 93.4
932 59.6
1022 40.2
If 0.0791 ft3 SO2, 0.158 ft3 NO2, 0.0791 ft3 NO, and 0.119 ft3 SO3 (all at STP) are transferred to a 1.32 gal reaction vessel and heated to 733 K, determine the following:
a)
The initial reactor pressure in atm
b)
The equilibrium molar concentrations (in mol L–1) of each substance
c)
The equilibrium reactor pressure in atm
To answer these questions, we first need to convert the given volumes of gases to moles using the ideal gas law. The ideal gas law equation is given as:
PV = nRT
Where:
P is the pressure in atm
V is the volume in liters
n is the number of moles
R is the ideal gas constant (0.0821 L*atm/mol*K)
T is the temperature in Kelvin
Let's calculate the number of moles for each gas:
a) The initial reactor pressure in atm:
To find the initial reactor pressure, we need to calculate the total number of moles of gases present in the 1.32 gal reaction vessel at STP (standard temperature and pressure).
1 gallon = 3.78541 liters
1.32 gallons = 1.32 * 3.78541 liters = 4.9986232 liters
Using the ideal gas law equation, we can now calculate the pressure:
P * V = n * R * T
Assuming the temperature is at standard temperature (273.15 K), we can rearrange the equation to solve for pressure:
P = (n * R * T) / V
n(SO2) = (0.0791 ft^3) / (22.414 L/mol) = 0.003525511 mol
n(NO2) = (0.158 ft^3) / (22.414 L/mol) = 0.007051021 mol
n(NO) = (0.0791 ft^3) / (22.414 L/mol) = 0.003525511 mol
n(SO3) = (0.119 ft^3) / (22.414 L/mol) = 0.005312266 mol
P = ((0.003525511 + 0.007051021 + 0.003525511 + 0.005312266) * 0.0821 * 273.15 K) / 4.9986232 L
After performing the calculation, you will get the initial reactor pressure in atm.
b) The equilibrium molar concentrations (in mol L–1) of each substance:
To find the equilibrium molar concentrations, we need to use the equilibrium constant (Kc) for the reaction:
SO2(g) + NO2(g) <> NO(g) + SO3(g)
We can use the given temperature (733 K) to find the corresponding Kc value from the table given:
Kc = 156
Let's assume the equilibrium molar concentrations are represented as follows (in mol/L):
[SO2] = x
[NO2] = y
[NO] = z
[SO3] = w
Using the stoichiometric coefficients from the balanced equation, we can write the expression for Kc, which is:
Kc = ([NO][SO3]) / ([SO2][NO2])
We can rearrange the equation and substitute the equilibrium concentrations:
Kc = (z * w) / (x * y)
Since the equilibrium concentrations of all substances are unknown, we'll assume that the equilibrium concentrations are equal to x, y, z, and w, respectively:
Kc = (z * w) / (x * y) = 156
From this equation, we can solve for each equilibrium concentration [x], [y], [z], and [w].
c) The equilibrium reactor pressure in atm:
To find the equilibrium reactor pressure, we need to use the ideal gas law with the new equilibrium concentrations.
We can repeat the previous steps to find the new moles of each substance using the new equilibrium concentrations [x], [y], [z], and [w]. Then we can calculate the new equilibrium pressure using the ideal gas law equation:
P = (n * R * T) / V
Where [n] is the new number of moles for each substance and [V] is the volume of the reaction vessel.
Performing the calculations, you will get the equilibrium reactor pressure in atm.
To determine the initial reactor pressure in atm, we need to calculate the initial number of moles of each substance using the ideal gas law.
a) The initial reactor pressure in atm:
1. Convert the given volumes from ft3 to L:
0.0791 ft3 = 2.235 L
0.158 ft3 = 4.47 L
0.0791 ft3 = 2.235 L
0.119 ft3 = 3.37 L
2. Convert the volume of the reaction vessel from gal to L:
1.32 gal = 4.99 L
3. Calculate the initial number of moles for each substance using the ideal gas law:
PV = nRT
For SO2:
P1V1 = n1RT1
(Pressure in atm) * (Volume in L) = (moles) * (Ideal gas constant) * (Temperature in K)
Since the pressure and volume are unknown, we will use the initial reactor pressure as P1 and the total volume of all gases as V1.
P1 * V1 = nSO2 * R * T = (0.0791 L + 0.158 L) * (0.0821 atm L/mol K) * (273 K + 733 K)
Repeat this calculation for NO2, NO, and SO3.
4. Calculate the initial reactor pressure:
P1 = (nSO2 + nNO2 + nNO + nSO3) * R * T / V1
Substitute the calculated values of nSO2, nNO2, nNO, and nSO3 into the equation and solve for P1.
b) The equilibrium molar concentrations (in mol L–1) of each substance:
To find the equilibrium molar concentrations of each substance, we need to use the information from the equilibrium constant (Kc) and the stoichiometry of the reaction.
The balanced equation for the reaction is:
SO2(g) + NO2(g) <----> NO(g) + SO3(g)
The stoichiometric coefficients are:
1 : 1 : 1 : 1
At equilibrium, the molar concentrations can be expressed in terms of the initial concentrations and the changes in concentration:
[NO] = [SO3] = [SO2] = [NO2] = x (assuming the change in concentration is x)
Using the equilibrium constant expression:
Kc = ([NO] * [SO3]) / ([SO2] * [NO2])
Substitute the equilibrium concentrations into the equation and solve for x.
c) The equilibrium reactor pressure in atm:
The equilibrium reactor pressure can be calculated using the ideal gas law. The total number of moles at equilibrium can be obtained by adding the initial number of moles to the change in moles for each substance.
Total moles at equilibrium = Initial moles + Change in moles
Use the calculated values of the initial moles and the change in moles, along with the total volume of the reaction vessel, to calculate the equilibrium reactor pressure using the ideal gas law equation:
PV = nRT
Substitute the total moles at equilibrium into the equation and solve for the equilibrium reactor pressure.