Reaction: 2 CH3COOH + CaCO3 = Ca(CH3COO)2 + H2O + CO2 Acetic Acid + Calcium Carbonate = Calcium Acetate + Water + Carbon Dioxide The Density Of Egg Shell (for Calculating Concentration): 1.104 G./cm^3 The Density Of Acetic Acid (for Calculating Concentrations): 0.48g/cm^3 3 Tempratures Used: Room Temprature (23 Degrees C) ,28 Degrees C, And 25 Degrees … Reaction: 2 CH 3 COOH + CaCO 3 = Ca(CH 3 COO) 2 + H 2 O + CO 2 Acetic acid + Calcium carbonate = Calcium acetate + Water + Carbon dioxide The density of Egg Shell (for calculating concentration): 1.104 g./cm^3 The density of acetic acid (for calculating concentrations): 0.48g/cm^3 3 tempratures used: Room temprature (23 degrees C) ,28 degrees C, and 25 degrees C.) constant volume in each run: 200mL of Vinegar in each run ACTIVATION ENERGY= 18 kcal. QUESTION BELOW What is the rate law, rate constant, and order of reaction.
The Correct Answer and Explanation is :
To determine the rate law, rate constant, and order of reaction, we need to analyze the reaction and use the provided information to derive the rate law.
Given Reaction:
[ \text{2 CH}_3\text{COOH} + \text{CaCO}_3 \rightarrow \text{Ca(CH}_3\text{COO)}_2 + \text{H}_2\text{O} + \text{CO}_2 ]
- The reaction involves acetic acid (CH₃COOH) and calcium carbonate (CaCO₃), resulting in calcium acetate, water, and carbon dioxide.
- The density of acetic acid is given as 0.48 g/cm³, and the density of egg shell (used as a source of calcium carbonate) is 1.104 g/cm³.
- The reaction is carried out at three temperatures: room temperature (23°C), 28°C, and 25°C.
- A constant volume of 200 mL of vinegar (acetic acid) is used in each run.
- The activation energy (Ea) is given as 18 kcal/mol.
To Find:
- Rate Law: The rate law expresses the relationship between the rate of the reaction and the concentration of reactants. The general form is:
[ \text{Rate} = k[\text{CH}_3\text{COOH}]^m[\text{CaCO}_3]^n ]
where ( k ) is the rate constant, and ( m ) and ( n ) are the orders of reaction with respect to acetic acid and calcium carbonate, respectively. - Rate Constant (k): This is a proportionality constant in the rate law, which is temperature-dependent.
- Order of Reaction: This refers to the sum of the exponents in the rate law, ( m + n ), and indicates the overall dependence of the rate on the concentrations of reactants.
Explanation:
To determine the order of reaction and rate law:
- Initial Rate Method: Using the data from the experiment at different temperatures and concentrations of acetic acid and calcium carbonate, the initial rates of reaction at each condition can be compared.
- From this, you can deduce how the rate changes with respect to the concentration of each reactant.
- For example, if doubling the concentration of acetic acid causes the rate to double, the reaction is first order with respect to acetic acid (m=1).
- Arrhenius Equation: The relationship between the rate constant and temperature can be derived using the Arrhenius equation:
[ k = A e^{-\frac{E_a}{RT}} ]
where:
- ( k ) is the rate constant,
- ( A ) is the frequency factor,
- ( E_a ) is the activation energy,
- ( R ) is the universal gas constant (8.314 J/mol·K),
- ( T ) is the temperature in Kelvin.
- Activation Energy and Temperature: From the temperature dependence, we can calculate the rate constants at different temperatures and use the data to derive the rate constant ( k ) at the given temperatures.
Conclusion:
Once the orders of reaction for acetic acid and calcium carbonate are determined using the initial rate method, you can calculate the rate constant at different temperatures using the Arrhenius equation. The rate law will be in the form of ( \text{Rate} = k[\text{CH}_3\text{COOH}]^m[\text{CaCO}_3]^n ), with the determined values of ( m ) and ( n ) reflecting the order of reaction with respect to each reactant.