Calculating Mass Of NH4Cl For Saturated Solution At 50°C

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This article delves into the chemistry question of determining the mass of ammonium chloride (NH4Cl) needed to dissolve in a specific amount of water at a given temperature to create a saturated solution. This is a classic solubility problem that combines fundamental concepts of chemistry, including molar mass, solubility, and the factors affecting the dissolution process. Understanding these concepts is crucial not only for academic purposes but also for various practical applications in fields such as pharmaceuticals, environmental science, and chemical engineering.

Understanding Saturated Solutions and Solubility

To begin, it's essential to define what a saturated solution actually is. A saturated solution is a chemical solution containing the maximum concentration of a solute dissolved in the solvent. In simpler terms, it's the point where no more solute can dissolve in the solvent at a specific temperature. Think of it like adding sugar to a glass of water: initially, the sugar dissolves easily, but eventually, you reach a point where the sugar starts settling at the bottom, no matter how much you stir. This undissolved sugar indicates that the solution is saturated.

Solubility, on the other hand, is a measure of how much solute can dissolve in a solvent at a particular temperature. It is typically expressed as grams of solute per 100 grams of solvent (g/100g H2O). Solubility is influenced by various factors, including temperature, pressure (for gases), and the nature of the solute and solvent. For many solid solutes, like ammonium chloride, solubility increases with temperature, meaning more solute can be dissolved in a hot solvent than a cold one. This temperature dependence is a crucial aspect when calculating the mass of solute required for saturation at a specific temperature.

The concept of solubility is crucial in various fields. In pharmaceuticals, it determines how effectively a drug can be absorbed into the bloodstream. In environmental science, it affects the transport and fate of pollutants in water systems. In chemical engineering, it plays a pivotal role in designing separation and purification processes. Therefore, mastering the principles of solubility is not just an academic exercise but a practical necessity for many professionals.

Factors Affecting Solubility: Temperature's Crucial Role

As mentioned earlier, temperature plays a significant role in the solubility of solids in liquids. For most ionic compounds like ammonium chloride (NH4Cl), solubility increases with temperature. This phenomenon occurs because the process of dissolving an ionic compound is endothermic, meaning it requires energy. When the temperature rises, more energy is available to break the ionic bonds in the solute crystal lattice and the intermolecular forces in the solvent, allowing more solute to dissolve.

Consider ammonium chloride (NH4Cl) dissolving in water. The dissolution process can be represented as follows:

NH4Cl (s) + Heat → NH4+ (aq) + Cl- (aq)

The "+ Heat" in the equation indicates that energy is required for the reaction to occur. Therefore, increasing the temperature provides the necessary energy, shifting the equilibrium to the right and favoring the dissolution of NH4Cl. This is why a hot solution can hold more NH4Cl than a cold one.

In contrast, the solubility of gases in liquids generally decreases with increasing temperature. This is because gases have a tendency to escape from the solution as their kinetic energy increases at higher temperatures. Think about a carbonated beverage: it fizzes more when warm because the carbon dioxide gas is less soluble and escapes more readily. This difference in temperature dependence between solids and gases highlights the complex interplay of factors governing solubility.

Understanding the effect of temperature on solubility is crucial for a variety of applications. For instance, in the crystallization of chemical compounds, controlling the temperature allows for precise control over the purity and yield of the crystals. In environmental chemistry, temperature influences the concentration of dissolved oxygen in water, which is vital for aquatic life. Therefore, a thorough understanding of this principle is essential for professionals in diverse fields.

Calculating the Mass of NH4Cl for a Saturated Solution at 50°C

Now, let's tackle the original question: What is the mass of NH4Cl that must dissolve in 200 grams of water at 50°C to make a saturated solution?

To solve this, we need to know the solubility of NH4Cl in water at 50°C. This information is typically found in solubility tables or graphs in chemistry textbooks or online resources. Let's assume, for the sake of this example, that the solubility of NH4Cl at 50°C is 42 grams per 100 grams of water (42 g NH4Cl / 100 g H2O). This is a plausible value based on typical solubility data for NH4Cl, although the exact figure may vary slightly depending on the source.

The solubility value gives us the ratio of NH4Cl to water in a saturated solution at the given temperature. We can use this ratio to calculate the mass of NH4Cl needed for 200 grams of water. Here's the calculation:

  1. Set up a proportion:

    (42 g NH4Cl) / (100 g H2O) = (x g NH4Cl) / (200 g H2O)

    Where 'x' is the mass of NH4Cl we need to find.

  2. Solve for x:

    x = (42 g NH4Cl * 200 g H2O) / (100 g H2O)

    x = 84 g NH4Cl

Therefore, 84 grams of NH4Cl must dissolve in 200 grams of water at 50°C to make a saturated solution. This result corresponds to answer choice C in the options provided.

This calculation demonstrates the practical application of solubility data. By knowing the solubility of a substance at a particular temperature, we can predict the mass of solute needed to create a saturated solution in a given amount of solvent. This type of calculation is frequently used in laboratory settings, industrial processes, and even in everyday tasks like making solutions for cleaning or cooking.

Step-by-Step Solution and Explanation

To solidify your understanding, let's break down the solution process step-by-step, highlighting the key concepts involved:

  1. Identify the Problem:

    The problem asks us to determine the mass of NH4Cl needed to create a saturated solution in 200 grams of water at 50°C.

  2. Gather Necessary Information:

    • The amount of water (solvent): 200 grams
    • The temperature: 50°C
    • The solubility of NH4Cl in water at 50°C (we assumed 42 g NH4Cl / 100 g H2O for this example – in a real problem, this value would be provided or need to be looked up).

  3. Understand Solubility:

    Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature. A saturated solution contains this maximum amount.

  4. Set up a Proportion:

    We use the solubility as a ratio to set up a proportion:

    (Solubility of NH4Cl) = (Mass of NH4Cl) / (Mass of Water)

    (42 g NH4Cl) / (100 g H2O) = (x g NH4Cl) / (200 g H2O)

  5. Solve for the Unknown (x):

    Cross-multiply and solve for x:

    x = (42 g NH4Cl * 200 g H2O) / (100 g H2O)

    x = 84 g NH4Cl

  6. State the Answer:

    Therefore, 84 grams of NH4Cl must dissolve in 200 grams of water at 50°C to make a saturated solution.

This step-by-step approach can be applied to similar solubility problems involving different solutes, solvents, and temperatures. The key is to understand the concept of solubility, find the appropriate solubility data, and use proportions to calculate the required mass of solute.

Common Mistakes and How to Avoid Them

When solving solubility problems, several common mistakes can lead to incorrect answers. Here's a rundown of these mistakes and how to avoid them:

  1. Using the Wrong Solubility Value:

    • Mistake: Using solubility data for a different temperature or a different solute-solvent pair.
    • Solution: Always ensure you are using the solubility value that corresponds to the specific temperature and substances in the problem. Look up the data in a reliable source if it's not provided.

  2. Incorrectly Setting up the Proportion:

    • Mistake: Inverting the ratio or mixing up the units.

    • Solution: Double-check that the proportion is set up correctly, with the same units on both sides. The ratio should be:

      (Grams of Solute) / (Grams of Solvent) = (Grams of Solute) / (Grams of Solvent)

  3. Forgetting Units:

    • Mistake: Omitting units during calculations, which can lead to confusion and errors.
    • Solution: Always include units in your calculations and make sure they cancel out correctly. This helps verify that you are using the correct relationships.

  4. Assuming Solubility is Constant:

    • Mistake: Assuming that the solubility of a substance is the same at all temperatures.
    • Solution: Remember that solubility is temperature-dependent, especially for solids and gases in liquids. Use the solubility value specific to the given temperature.

  5. Not Understanding Saturated Solutions:

    • Mistake: Not grasping the concept of a saturated solution and what it represents.
    • Solution: Recall that a saturated solution contains the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature. No more solute will dissolve under these conditions.

By being mindful of these common pitfalls, you can improve your accuracy and confidence in solving solubility problems. Practice and careful attention to detail are key.

Real-World Applications of Solubility

Solubility is not just a theoretical concept confined to chemistry textbooks; it has numerous practical applications in various real-world scenarios. Understanding solubility principles is crucial in diverse fields, from medicine to environmental science to industrial chemistry. Here are a few examples:

  1. Pharmaceuticals:

    • Drug Formulation: Solubility is a critical factor in drug formulation. The solubility of a drug determines how easily it dissolves in bodily fluids, which affects its absorption and bioavailability. Poorly soluble drugs may have limited therapeutic effects.
    • Drug Delivery: Solubility considerations are essential in designing drug delivery systems, such as intravenous solutions, tablets, and capsules. Formulations are often designed to enhance drug solubility and ensure effective delivery to the target site.

  2. Environmental Science:

    • Water Pollution: The solubility of pollutants in water affects their transport, distribution, and persistence in the environment. Highly soluble pollutants can spread rapidly and contaminate large areas, while insoluble pollutants may accumulate in sediments.
    • Water Treatment: Solubility principles are applied in water treatment processes to remove contaminants. For example, precipitation reactions are used to remove dissolved metals from water by converting them into insoluble solids.

  3. Industrial Chemistry:

    • Crystallization: Solubility differences are exploited in crystallization processes to purify chemical compounds. By carefully controlling temperature and solvent conditions, desired compounds can be selectively crystallized out of a solution.
    • Extraction: Solubility is the basis for many extraction techniques used in the chemical industry. For instance, liquid-liquid extraction separates compounds based on their relative solubilities in two immiscible solvents.

  4. Food Science:

    • Food Processing: Solubility affects various aspects of food processing, such as the dissolution of sugars, salts, and other ingredients. It also influences the texture and stability of food products.
    • Beverage Production: The solubility of gases, such as carbon dioxide in carbonated beverages, is crucial for their taste and effervescence. Temperature and pressure are carefully controlled to maintain the desired gas solubility.

These examples highlight the broad significance of solubility in various fields. A solid grasp of solubility principles is essential for professionals working in these areas to make informed decisions and solve practical problems.

Conclusion: Mastering Solubility for Success

In conclusion, understanding solubility and its applications is crucial in various scientific and practical contexts. The question of determining the mass of NH4Cl needed to create a saturated solution in water at a specific temperature serves as an excellent example of how fundamental chemistry concepts can be applied to solve real-world problems.

We've explored the definition of saturated solutions, the factors affecting solubility (particularly temperature), the step-by-step process of calculating the mass of solute needed for saturation, common mistakes to avoid, and the diverse applications of solubility in fields like pharmaceuticals, environmental science, industrial chemistry, and food science.

By mastering these principles, you'll be well-equipped to tackle a wide range of solubility-related challenges, whether in the laboratory, in industrial settings, or in everyday situations. So, keep practicing, keep exploring, and keep applying your knowledge of solubility to make a difference in the world around you.