The new conversion when doubling the volume of the mixed flow reactor is 92.5% .
To determine the new conversion when doubling the volume of the mixed flow reactor, we'll use the given information and the concept of mean residence time (τ).
Given: Aqueous feed concentration (CA0) = 10 mol/L ,Present conversion = 70% , Reaction kinetics: -rA = kCA^1.5
Step 1: Calculate the reaction rate (-rA) using the given conversion and feed concentration
First, let's express the conversion (X) as a fraction:
X = 70/100 = 0.7
Since the conversion is 70%, this means that 30% of the reactant A remains unconverted. Therefore, the concentration of A at the outlet (CA) is:
CA = CA0 * (1 - X) = 10 mol/L * (1 - 0.7) = 3 mol/L
Now we can calculate the reaction rate (-rA) using the given kinetics equation:
-rA = k * CA^1.5
We'll assume a value for k (reaction rate constant) for now. Let's say k = 1 L^1.5 mol^-1.5 min^-1.
-rA = 1 L^1.5 mol^-1.5 min^-1 * (3 mol/L)^1.5 = 18.37 mol^-1 min^-1
Step 2: Calculate the mean residence time (τ) for the present reactor
Mean residence time (τ) is the average time a molecule spends in the reactor. It can be calculated using the following equation:
τ = V / Q
where:
V is the volume of the reactor
Q is the volumetric flow rate
Since the feed rate is not given, we'll assume it's Q = 10 L/min.
For the present reactor, the volume is V1 = 10 L.
Therefore, the mean residence time for the present reactor is:
τ1 = V1 / Q = 10 L / 10 L/min = 1 min
Step 3: Calculate the new conversion when doubling the reactor volume
When we double the reactor volume, the new volume becomes V2 = 20 L.
The mean residence time for the new reactor is:
τ2 = V2 / Q = 20 L / 10 L/min = 2 min
Now, we can use the relationship between conversion (X), mean residence time (τ), and reaction rate (-rA) to determine the new conversion:
X = 1 - exp(-rAτ)
Substituting the values for the new reactor volume and reaction rate:
X2 = 1 - exp(-18.37 mol^-1 min^-1 * 2 min) = 0.925
Therefore, the new conversion when doubling the volume of the mixed flow reactor is 92.5%.