Calculating Mass Of NaCl Released Heat During Phase Change
Hey guys! Today, we're diving into a fascinating chemistry problem involving sodium chloride (NaCl) and its phase transitions. We're going to calculate the mass of NaCl that releases a specific amount of heat as it changes into a liquid. This problem perfectly illustrates the concepts of enthalpy of fusion and the relationship between heat, moles, and enthalpy change. Let's break it down step by step!
Understanding Enthalpy of Fusion and Vaporization
Before we jump into the calculation, let's quickly recap what enthalpy of fusion ($\Delta H_{\text{fus}}$) and enthalpy of vaporization ($\Delta H_{\text{vap}}$) mean. Enthalpy of fusion is the amount of heat required to melt one mole of a solid substance at its melting point. In simpler terms, it's the energy needed to break the crystal lattice structure of a solid and transform it into a liquid. For NaCl, the $\Delta H_{\text{fus}}$ is given as 30.2 kJ/mol. This means it takes 30.2 kilojoules of energy to melt one mole of solid NaCl. On the other hand, enthalpy of vaporization represents the heat needed to convert one mole of a liquid into a gas at its boiling point. For NaCl, the $\Delta H_{\text{vap}}$ is significantly higher at 171 kJ/mol, reflecting the greater energy input required to overcome the intermolecular forces in the liquid phase and transition to the gaseous phase.
It's crucial to understand that phase transitions involve changes in energy. When a substance melts or vaporizes, it absorbs heat from its surroundings (endothermic process), and the enthalpy change is positive. Conversely, when a substance freezes or condenses, it releases heat into its surroundings (exothermic process), and the enthalpy change is negative. Our problem focuses on the heat released as NaCl changes into a liquid, implying we're dealing with the reverse process of fusion – solidification or freezing.
In this scenario, heat released calculation involves understanding the relationship between the amount of heat (q), the number of moles (n), and the enthalpy change (). The formula we'll use is $q = n \Delta H$, which is a cornerstone in thermochemistry. Here, 'q' represents the heat absorbed or released, 'n' is the number of moles of the substance, and '' is the enthalpy change for the process. The sign of 'q' indicates whether heat is absorbed (positive) or released (negative). Similarly, '' will be negative for exothermic processes (heat released) and positive for endothermic processes (heat absorbed).
Now that we have the foundational knowledge, let's tackle the problem at hand. We need to figure out how much NaCl releases 452 kJ of heat when it transitions into a liquid. Remember, since heat is being released, we're looking at the solidification process, which is the reverse of fusion. This means we'll use the enthalpy of fusion, but with a negative sign because the process is exothermic.
Calculation Steps
Now, let's get our hands dirty with the math! The problem states that NaCl releases 452 kJ of heat as it changes into a liquid. This means we are considering the freezing process, which is the reverse of fusion. Therefore, the enthalpy change for this process will be the negative of the enthalpy of fusion, i.e., $\Delta H = -30.2 \text{ kJ/mol}$. The given heat released, $q$, is 452 kJ. Since heat is released, we represent it as $q = -452 \text{ kJ}$.
Our goal is to find the mass of NaCl. To do this, we first need to calculate the number of moles (n) of NaCl involved using the formula $q = n \Delta H$. Rearranging the formula to solve for n, we get:
Plugging in the values, we have:
So, approximately 14.97 moles of NaCl are involved in releasing 452 kJ of heat during solidification. Now that we have the number of moles, we can calculate the mass of NaCl using its molar mass. The molar mass of NaCl is the sum of the atomic masses of sodium (Na) and chlorine (Cl). Sodium has an atomic mass of approximately 22.99 g/mol, and chlorine has an atomic mass of about 35.45 g/mol. Therefore, the molar mass of NaCl is:
To find the mass of NaCl, we multiply the number of moles by the molar mass:
Therefore, the mass of NaCl that releases 452 kJ of heat as it changes into a liquid (freezes) is approximately 874.75 grams. To summarize, we've used the given heat released, the enthalpy of fusion, and the molar mass of NaCl to determine the mass of NaCl involved in the phase transition.
Step-by-Step Solution
Let's break down the step-by-step solution for calculating the mass of NaCl that releases 452 kJ of heat as it changes into a liquid. This will help solidify our understanding and make it easier to tackle similar problems in the future.
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Identify the Process: First, we recognize that the problem describes NaCl changing into a liquid while releasing heat. This tells us we're dealing with the reverse of melting, which is freezing or solidification. Since freezing is an exothermic process (heat is released), the enthalpy change will be negative.
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Determine the Enthalpy Change (): We are given the enthalpy of fusion ($\Delta H_{\text{fus}}$) for NaCl as 30.2 kJ/mol. Since we're dealing with freezing (the reverse process), the enthalpy change for this process is the negative of the enthalpy of fusion:
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Identify the Heat Released (q): The problem states that 452 kJ of heat is released. Because heat is released, we represent this value as negative:
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Calculate the Number of Moles (n): We use the formula $q = n \Delta H$ to find the number of moles of NaCl. Rearranging the formula to solve for n, we get:
Plugging in our values:
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Determine the Molar Mass of NaCl: To convert moles to grams, we need the molar mass of NaCl. We calculate this by adding the atomic masses of sodium (Na) and chlorine (Cl):
- Atomic mass of Na ≈ 22.99 g/mol
- Atomic mass of Cl ≈ 35.45 g/mol
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Calculate the Mass of NaCl: Finally, we multiply the number of moles by the molar mass to find the mass of NaCl:
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State the Answer: Therefore, the mass of NaCl that releases 452 kJ of heat as it changes into a liquid is approximately 874.75 grams.
By following these detailed steps, we've successfully navigated through the problem. Remember, the key is to identify the process, understand the sign conventions for enthalpy changes and heat, and use the appropriate formulas to connect the given information to what we need to find.
Common Mistakes to Avoid
Alright, let's talk about some common pitfalls that students often encounter when tackling problems like this. Avoiding these mistakes can significantly improve your accuracy and understanding.
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Forgetting the Sign of ΔH: One of the most frequent errors is overlooking the sign of the enthalpy change. Remember, enthalpy changes are negative for exothermic processes (heat released) and positive for endothermic processes (heat absorbed). In our case, since NaCl is changing into a liquid and releasing heat, it's undergoing solidification (freezing), which is exothermic. Therefore, we must use the negative of the enthalpy of fusion (-30.2 kJ/mol) in our calculations. Using the positive value would lead to an incorrect result.
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Using the Wrong Enthalpy Value: It's crucial to identify the correct enthalpy change for the process in question. The problem provides both the enthalpy of fusion and the enthalpy of vaporization. Since we are dealing with NaCl changing into a liquid, we need to consider the enthalpy change associated with melting or freezing (fusion) and not vaporization. Using the enthalpy of vaporization would be incorrect in this scenario.
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Incorrectly Rearranging the Formula: The formula $q = n \Delta H$ is fundamental, but it's essential to rearrange it correctly to solve for the desired variable. In our case, we needed to find the number of moles (n), so we rearranged the formula to $n = \frac{q}{\Delta H}$. Make sure you perform the algebraic manipulation accurately to avoid errors.
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Using Incorrect Units: Paying attention to units is vital in any scientific calculation. Ensure that all values are in consistent units before plugging them into the formula. In this problem, the heat released (q) is given in kJ, and the enthalpy change () is in kJ/mol. This consistency allows us to calculate the number of moles directly. However, if the values were in different units (e.g., J and kJ), we would need to convert them to the same unit before proceeding.
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Rounding Errors: Rounding off intermediate values prematurely can lead to inaccuracies in the final answer. It's generally best to carry as many significant figures as possible throughout the calculation and only round the final answer to the appropriate number of significant figures based on the given data. In our example, we rounded the final mass to two decimal places.
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Misunderstanding Molar Mass: Calculating the molar mass correctly is crucial for converting between moles and grams. Double-check the atomic masses of the elements involved (Na and Cl in this case) and ensure you add them accurately to get the molar mass of the compound (NaCl). An incorrect molar mass will directly affect the final mass calculation.
By being mindful of these common errors, you can approach thermochemistry problems with greater confidence and accuracy. Always double-check your work, pay attention to units and signs, and ensure you're using the correct formulas and values.
Real-World Applications
This type of calculation isn't just an academic exercise; it has real-world applications in various fields! Understanding the heat released or absorbed during phase transitions is crucial in many industrial processes and natural phenomena. For instance, let's explore a couple of examples:
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Industrial Processes: In chemical industries, controlling the temperature during reactions and phase transitions is essential for optimizing yields and ensuring safety. Processes like crystallization, distillation, and drying involve phase changes that either release or absorb heat. Engineers use these principles to design efficient cooling and heating systems. For example, in the production of pharmaceuticals or fine chemicals, precise temperature control during crystallization is vital to obtain the desired crystal form and purity of the product. The heat released or absorbed during these processes needs to be carefully calculated and managed.
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Climate and Weather: Phase transitions of water play a significant role in Earth's climate and weather patterns. The evaporation of water from oceans and lakes absorbs a large amount of heat, which is then released when water vapor condenses to form clouds and precipitation. This heat transfer is a major driver of atmospheric circulation and weather systems. The enthalpy changes associated with these phase transitions (evaporation, condensation, freezing, and melting) influence temperature distribution and weather phenomena like hurricanes and monsoons. Understanding these processes helps meteorologists predict weather patterns and climate changes more accurately.
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Food Industry: Phase transitions are also critical in food processing and preservation. Freezing food, for example, involves the phase transition from liquid to solid, releasing heat in the process. The rate of freezing and the temperature at which it occurs can affect the texture and quality of the frozen product. Similarly, melting chocolate involves a phase transition that requires careful temperature control to maintain the desired consistency and appearance. Food scientists use their knowledge of enthalpy changes and phase transitions to optimize food processing techniques.
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Geothermal Energy: Geothermal energy utilizes the heat from the Earth's interior to generate electricity. In some geothermal power plants, water is pumped underground to be heated by hot rocks. This process involves phase transitions as the water turns into steam, which then drives turbines to produce electricity. Understanding the enthalpy changes involved in these phase transitions is crucial for designing efficient geothermal power plants.
These examples illustrate that the principles we've discussed regarding enthalpy changes and phase transitions have practical implications in diverse fields. By understanding these concepts, we can better appreciate and control the world around us.
So, there you have it, guys! We've successfully calculated the mass of NaCl that releases 452 kJ of heat as it changes into a liquid. We've covered the concepts of enthalpy of fusion, the relationship between heat, moles, and enthalpy change, and even explored some real-world applications. Remember to pay attention to the signs, units, and formulas, and you'll be acing these problems in no time! Keep practicing, and chemistry will become a breeze!