Predicting Temperature Increase In Neutralization Reaction
Hey guys! Let's dive into a cool chemistry problem where we'll predict the temperature change in a neutralization reaction. This is a classic example that combines stoichiometry, thermochemistry, and calorimetry. So, buckle up, and let's get started!
Understanding the Neutralization Reaction
At the heart of our problem is the neutralization reaction between sodium hydroxide (NaOH), a strong base, and hydrochloric acid (HCl), a strong acid. When these two react, they form sodium chloride (NaCl), which is table salt, and water (Hâ‚‚O). The balanced chemical equation for this reaction is:
NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l)
Now, here's the key piece of information: the enthalpy change (ΔH) for this reaction is -57 kJ/mol. What does that tell us? Well, the negative sign indicates that this is an exothermic reaction. In simpler terms, it releases heat into the surroundings. This released heat is what causes the temperature of the mixture to rise, and that's precisely what we're trying to predict.
Enthalpy change, guys, is a fundamental concept in thermochemistry. It quantifies the heat absorbed or released in a chemical reaction at constant pressure. In our case, -57 kJ/mol means that for every mole of NaOH that reacts with HCl, 57 kilojoules of heat are released. This value is crucial for calculating the total heat released in our experiment, which we'll use to determine the temperature change.
Before we jump into the calculations, let's quickly recap the concepts we've touched upon: neutralization reactions, exothermic processes, and enthalpy change. These concepts form the bedrock of our understanding of chemical reactions involving heat transfer. So, armed with this knowledge, let's move on to the next step: figuring out how much heat is actually released when we mix those solutions of NaOH and HCl.
Calculating the Heat Released
Okay, so we know the enthalpy change per mole of reaction, but how much heat is released in our specific experiment? To figure this out, we need to determine the number of moles of reactants involved. We're given that we have 50 mL of 2 M NaOH and 50 mL of 2 M HCl. Remember, molarity (M) is defined as moles per liter (mol/L).
First, let's convert the volumes from milliliters to liters:
50 mL = 50 / 1000 = 0.050 L
Now, we can calculate the moles of NaOH and HCl using the formula:
Moles = Molarity × Volume
Moles of NaOH = 2 M × 0.050 L = 0.1 moles Moles of HCl = 2 M × 0.050 L = 0.1 moles
Great! We have 0.1 moles of both NaOH and HCl. Since they react in a 1:1 stoichiometric ratio (as seen in the balanced equation), the limiting reactant will determine the maximum amount of product formed and, consequently, the maximum heat released. In this case, we have equal moles of both reactants, so neither is limiting. The reaction will proceed until all 0.1 moles of both NaOH and HCl have reacted.
Now, we can calculate the total heat released (q) using the enthalpy change (ΔH) and the moles of reaction:
q = Moles × ΔH
Since ΔH is given in kJ/mol, we'll get the heat released in kJ. Let's plug in the values:
q = 0.1 moles × (-57 kJ/mol) = -5.7 kJ
The negative sign indicates that heat is released (exothermic reaction), which we already knew. To make our calculations consistent later on, let's convert this to Joules:
q = -5.7 kJ × 1000 J/kJ = -5700 J
So, guys, the reaction releases 5700 Joules of heat. Now that we know the amount of heat released, we're ready to connect this heat to the temperature change using the concept of calorimetry.
Applying Calorimetry: Connecting Heat to Temperature Change
Here's where calorimetry comes into play. Calorimetry, guys, is the science of measuring heat flow. In this problem, we're using a calorimeter to determine how much the temperature of the mixture changes when the neutralization reaction occurs. A calorimeter is essentially an insulated container that minimizes heat exchange with the surroundings. This allows us to assume that the heat released by the reaction is primarily absorbed by the solution and the calorimeter itself.
The fundamental equation we'll use in calorimetry is:
q = C × ΔT
Where:
- q is the heat transferred (in Joules)
- C is the heat capacity (in J/°C)
- ΔT is the change in temperature (in °C)
In our problem, we're given the heat capacity of the calorimeter (100 J/°C). This means that it takes 100 Joules of heat to raise the temperature of the calorimeter by 1 degree Celsius. However, the heat released by the reaction is also absorbed by the solution (the mixture of water and NaCl). To accurately calculate the temperature change, we need to consider the heat capacity of the solution as well.
To simplify things, we'll make a common assumption: the density and specific heat capacity of the solution are approximately the same as that of water. This is a reasonable approximation since the solution is mostly water, and the concentration of NaCl is relatively low. The specific heat capacity of water (c) is approximately 4.18 J/g°C.
Now, we need to calculate the mass of the solution. We have 50 mL of NaOH solution and 50 mL of HCl solution, giving us a total volume of 100 mL. Assuming the density of the solution is approximately 1 g/mL (like water), the mass of the solution is 100 g.
We can now calculate the heat capacity of the solution (C_solution) using the formula:
C_solution = mass × specific heat capacity
C_solution = 100 g × 4.18 J/g°C = 418 J/°C
So, the solution has a heat capacity of 418 J/°C. Now we can calculate the total heat capacity (C_total) of the system (calorimeter + solution):
C_total = C_calorimeter + C_solution
C_total = 100 J/°C + 418 J/°C = 518 J/°C
Alright! We've calculated the total heat capacity of our system. Now we're in the home stretch. We can finally use the calorimetry equation to predict the temperature increase.
Predicting the Temperature Increase
We have all the pieces of the puzzle now! We know the heat released by the reaction (q = 5700 J, we'll use the positive value here since we're looking at the temperature increase), the total heat capacity of the system (C_total = 518 J/°C), and the calorimetry equation (q = C × ΔT). Let's rearrange the equation to solve for ΔT:
ΔT = q / C
Now, let's plug in the values:
ΔT = 5700 J / 518 J/°C ≈ 11.0 °C
Boom! We've predicted the temperature increase. The calculation shows that the temperature of the mixture is expected to rise by approximately 11.0 °C. This, guys, is a significant temperature change, and it makes sense given the exothermic nature of the neutralization reaction and the concentrations of the reactants.
Conclusion
So, there you have it! We've successfully predicted the temperature increase in a neutralization reaction using stoichiometry, thermochemistry, and calorimetry. We started by understanding the reaction itself, then calculated the heat released based on the enthalpy change and the moles of reactants. Finally, we used calorimetry principles to connect the heat released to the temperature change, considering the heat capacity of both the calorimeter and the solution.
This problem is a great example of how different areas of chemistry come together to solve real-world problems. It also highlights the importance of careful measurements and assumptions in experimental science. I hope you guys found this breakdown helpful and insightful! Keep exploring the fascinating world of chemistry!