The formation of nitroanalyine (an important intermediate in dyes, called ‘fast orange’)
is formed from the reaction of ortho-nitrochlorobenzene (ONCB) and aqueous
ammonia. (See Table 3-1 and Example 9-2.)
The liquid-phase reaction is first-order in both ONCB and ammonia with k = 0.0017
m3/kmol.min at 188 °C with E = 11,273 cal/mol. The initial entering concentrations of
ONCB and ammonia are 1.8 kmol/m3 and 6.6 kmol/m3, respectively.
(a) Write the rate expression for the rate of disappearance of ONCB in terms of concentration.
(b) Set up a stoichiometric table for this reaction for a flow system.
(c) Explain how part (a) would be different for a batch system.
(d) Write –rA solely as a function of conversion. –rA = _______
(e) What is the initial rate of reaction (X = 0) at 188 °C? –rA = _______
at 25 °C? –rA = _______
at 288 °C? –rA = _______
(f) What is the rate of reaction when X = 0.90 at 188 °C? –rA = _______
at 25 °C? –rA = _______
at 288 °C? –rA = _______
(g) What would be the corresponding CSTR reactor volume at 25 °C to achieve 90%
conversion at 25 °C and at 288 °C for a molar feed rate of 2 mol/min:
at 25 °C? V = _______
at 288 °C? V = _______
(a) The rate expression for the rate of disappearance of ONCB is given by:
rate = -k[ONCB]^1[ammonia]^1
(b) Stoichiometric table:
Reaction | Stoichiometric Coefficients
---------------------------------------------
ONCB | -1
Ammonia | -1
Nitroanaline | +1
(c) In a batch system, the concentration of reactants changes over time as the reaction progresses. Therefore, the rate expression in terms of concentration would be different and would involve the change in concentration of ONCB with respect to time.
(d) -rA = k[ONCB]^1[ammonia]^1
(e) The initial rate of reaction (X = 0) at 188°C is given by:
-rA = k[ONCB]0^1[ammonia]0^1
At 25°C, -rA = _______ (Depends on the provided temperature-dependent rate constant)
At 288°C, -rA = _______ (Depends on the provided temperature-dependent rate constant)
(f) The rate of reaction when X = 0.90 at 188°C is given by:
-rA = k[ONCB]0.90^1[ammonia]0.90^1
At 25°C, -rA = _______ (Depends on the provided temperature-dependent rate constant)
At 288°C, -rA = _______ (Depends on the provided temperature-dependent rate constant)
(g) The corresponding CSTR reactor volume at 25°C to achieve 90% conversion for a molar feed rate of 2 mol/min is given by:
V = (F[ONCB]0) / (-rA)
Substituting the values, V = _______ (Depends on the provided temperature-dependent rate constant)
The corresponding CSTR reactor volume at 288°C to achieve 90% conversion for a molar feed rate of 2 mol/min is given by:
V = (F[ONCB]0) / (-rA)
Substituting the values, V = _______ (Depends on the provided temperature-dependent rate constant)
(a) The rate expression for the rate of disappearance of ONCB in terms of concentration can be written as:
Rate = -k[ONCB][NH3]
(b) Stoichiometric table for the reaction:
Reaction: ONCB + NH3 -> Nitroanalyine + HCl
| | | |
| | | |
In 1 1 0 0
Out 0 0 1 1
(c) In a batch system, the rate expression for the rate of disappearance of ONCB would be the same as in part (a). However, the initial concentrations of ONCB and ammonia would change with time as the reaction progresses.
(d) -rA can be written solely as a function of conversion (X) using the formula:
-rA = k*CA*(1-X)
(e) To calculate the initial rate of reaction (X = 0) at 188 °C, we use the given initial concentrations of ONCB and ammonia:
-rA = k*[ONCB]*[NH3]
= 0.0017 * 1.8 * 6.6
= 0.0206 kmol/(m^3.min)
To calculate the initial rate of reaction at 25 °C and 288 °C, we need to find the rate constant (k) at those temperatures. The rate constant (k) can be calculated using the Arrhenius equation:
k = k0 * exp(-E/(R*T))
Where:
k0 is the rate constant at a reference temperature (given as 0.0017 m3/kmol.min)
E is the activation energy (given as 11,273 cal/mol)
R is the gas constant (8.314 J/(mol.K) or 1.987 cal/(mol.K))
T is the temperature in Kelvin (converted from °C)
(k at 25 °C) = 0.0017 * exp(-11273/(1.987 * (25 + 273))) = 0.000045 m3/kmol.min
(k at 288 °C) = 0.0017 * exp(-11273/(1.987 * (288 + 273))) = 0.0114 m3/kmol.min
The initial rate of reaction at 25 °C and 288 °C can now be calculated using the same formula as in part (a):
-rA at 25 °C = 0.000045 * 1.8 * 6.6 = 0.000056 kmol/(m^3.min)
-rA at 288 °C = 0.0114 * 1.8 * 6.6 = 0.134 kmol/(m^3.min)
(f) To find the rate of reaction when X = 0.90 at 188 °C, we use:
-rA = k*CA*(1-X)
= 0.0017 * 1.8 * 6.6 * (1-0.90)
= 0.0206 * 0.10
= 0.00206 kmol/(m^3.min)
To calculate the rate of reaction when X = 0.90 at 25 °C and 288 °C, we use the respective rate constants:
-rA at 25 °C = 0.000045 * 1.8 * 6.6 * (1-0.90) = 3.06e-5 kmol/(m^3.min)
-rA at 288 °C = 0.0114 * 1.8 * 6.6 * (1-0.90) = 0.0134 kmol/(m^3.min)
(g) To find the corresponding CSTR reactor volume at 25 °C and 288 °C to achieve 90% conversion, we need to use the formula:
V = (F0/n)*(-rA)*(1/X)
Where:
F0 is the molar feed rate (given as 2 mol/min)
n is the stoichiometric coefficient of ONCB (given as 1)
-rA is the desired rate of reaction when X = 0.90 (found in part (f))
X is the desired conversion (0.90)
At 25 °C:
V at 25 °C = (2/1)*(3.06e-5)*(1/0.90) = 0.068 m^3
At 288 °C:
V at 288 °C = (2/1)*(0.0134)*(1/0.90) = 0.030 m^3
(a) The rate expression for the rate of disappearance of ONCB can be written as:
Rate = k * [ONCB]^1 * [ammonia]^1
(b) A stoichiometric table for this reaction in a flow system can be set up as follows:
Reactant | Stoichiometric Coefficient
__________________________________
ONCB | -1
Ammonia | -1
Nitroanalyine | +1
(c) In a batch system, the rate expression would be different because the concentrations of the reactants change as the reaction progresses. The rate expression would be based on the change in concentration over time rather than the initial concentrations.
(d) To write -rA solely as a function of conversion, we need to relate the rate of disappearance of ONCB (-rA) to the conversion (X). Since nitroanalyine is formed in a 1:1 stoichiometric ratio with ONCB, we can write:
-rA = k * [ONCB] * (1 - X)
(e) To determine the initial rate of reaction at different temperatures, we can use the rate expression and substitute the initial concentrations of ONCB and ammonia. Keep in mind that the rate constant (k) changes with temperature due to the Arrhenius equation.
For 188 °C:
-rA = k * (1.8) * (6.6) = 0.0017 * 1.8 * 6.6 = _______
For 25 °C and 288 °C, we need to use the activation energy (E) to calculate the new rate constant (k) using the following equation:
k2 = k1 * exp((E / R) * (1/T1 - 1/T2))
where T1 and T2 are the temperatures in Kelvin, and R is the gas constant (8.314 J/(mol·K)).
First, convert the temperatures to Kelvin:
25 °C = 25 + 273.15 K = _______ K
288 °C = 288 + 273.15 K = _______ K
Then calculate the new rate constants and substitute into the rate expression to find -rA.
(f) To find the rate of reaction when X = 0.90, we again use the rate expression and substitute the concentrations determined by the given conversion. Calculate -rA using the same method as in part (e).
(g) The corresponding CSTR reactor volume at 25 °C and 288 °C to achieve 90% conversion can be determined by applying the design equation:
V = (F /(-rA)) * (1 / X)
Given a molar feed rate of 2 mol/min and a desired conversion of 90%, substitute the values into the equation to find the reactor volume (V) at both temperatures.