Step 1: determine the rate constant and reaction order
Carbonic Acid Decomposition: Rate Law & Analysis Step by step Solution with Explanation
Your question:
In a 1 L batch reactor, 1 mol/L carbonic acid decomposes into carbon dioxide and water at room temperature and atmospheric pressure. An online system of gas chromatography has recorded the concentration of carbonic acid, CAC_ACA, carbon dioxide, CPC_PCP and water, CSC_SCS over a period of time.
Carbonic Acid Decomposition: Rate Law & Analysis Answers and Explanation
Step 1: Determine the Rate Constant and Reaction Order
Calculate the Reaction Rate:
The reaction rate can be approximated using the change in concentration of CAC_ACA over small time intervals.
Assume a general rate law of the form:
r=kCAn
| ttt (s) | CAC_ACA (mol/L) | Rate (mol/L/s) | ln(CA)\ln(C_A)ln(CA) | ln(Rate)\ln(\text{Rate})ln(Rate) |
|---|---|---|---|---|
| 60 | 0.74 | 0.0032 | -0.301 | -5.737 |
| 120 | 0.548 | 0.00423 | -0.601 | -5.466 |
| 180 | 0.406 | 0.0039 | -0.901 | -5.544 |
| 240 | 0.306 | 0.00342 | -1.183 | -5.676 |
| 300 | 0.223 | 0.00328 | -1.499 | -5.726 |
Plotting these values, the slope of the line gives us nnn, and the intercept gives us ln(k)\ln(k)ln(k).
Perform Linear Regression:
Using the determined reaction order and rate constant, the rate law is:
r=kCAn
To express the rate law based on concentration and conversion, consider the stoichiometric relationship for the decomposition reaction:
H2CO3→CO2+H2O\text{H}_2\text{CO}_3 \rightarrow \text{CO}_2 + \text{H}_2\text{O}H2CO3→CO2+H2O
r=−dtdCA=0.004CA=0.004(1−x)
