Calculate Water Needed For Saturated NaCl Solution At 20°C

Introduction

Understanding solubility is crucial in chemistry, especially when preparing solutions. Solubility, defined as the maximum amount of a solute that can dissolve in a specific amount of solvent at a given temperature, is a fundamental concept. In this article, we will explore how to calculate the amount of water needed to create a saturated solution of sodium chloride (NaCl) at a specific temperature. Specifically, we will address the question: If NaCl has a solubility of 36.0 g in 100.0 g of H2O at 20°C, how many grams of water are needed to prepare a saturated solution containing 80.0 g of NaCl? This involves understanding the concept of saturated solutions and using proportional relationships to find the required amount of solvent.

Understanding Saturated Solutions

A saturated solution is one in which the solvent has dissolved the maximum possible amount of solute at a given temperature. In other words, no more solute can be dissolved in the solution under the same conditions. The solubility of a substance is the concentration of the solute in a saturated solution. For NaCl, the solubility of 36.0 g in 100.0 g of H2O at 20°C means that for every 100.0 grams of water, a maximum of 36.0 grams of NaCl can be dissolved at this temperature. Any additional NaCl added beyond this limit will not dissolve and will remain as a solid at the bottom of the solution. It's important to note that solubility is temperature-dependent; higher temperatures generally allow more solute to dissolve, while lower temperatures may decrease the solubility.

Factors Affecting Solubility

Several factors can influence the solubility of a solute in a solvent. The nature of the solute and solvent plays a significant role; polar solutes tend to dissolve in polar solvents, and nonpolar solutes dissolve in nonpolar solvents – a principle often summarized as "like dissolves like." Temperature is another crucial factor, as discussed earlier, with most solids showing increased solubility at higher temperatures. However, the solubility of gases in liquids usually decreases with increasing temperature. Pressure also affects the solubility of gases; higher pressure increases gas solubility in liquids, a concept utilized in carbonated beverages where carbon dioxide is dissolved under pressure.

Applications of Solubility in Chemistry

Solubility principles are applied in various chemical processes and applications. In analytical chemistry, understanding solubility helps in techniques like precipitation, where a substance is selectively precipitated out of a solution based on its solubility. In pharmaceuticals, solubility is critical for drug formulation and delivery, as the drug must dissolve in bodily fluids to be effective. Industrial processes, such as crystallization and extraction, also rely heavily on solubility differences to separate and purify substances. Additionally, environmental chemistry uses solubility data to predict the fate and transport of pollutants in water systems, assessing potential risks to water quality and aquatic life.

Calculating Water Needed

To determine the amount of water needed for a saturated solution with 80.0 g of NaCl, we use the given solubility ratio: 36.0 g NaCl per 100.0 g H2O. The key here is to set up a proportion that relates the known solubility to the desired amount of NaCl. This is a straightforward application of proportional reasoning, a fundamental skill in chemistry and other quantitative fields. By correctly setting up and solving the proportion, we can accurately calculate the amount of water required to dissolve 80.0 g of NaCl at 20°C, ensuring the solution is saturated without excess water.

Setting Up the Proportion

The first step in solving this problem is to set up the correct proportion. We know that the solubility of NaCl is 36.0 g in 100.0 g of H2O at 20°C. This gives us a ratio that we can use as a conversion factor. We want to find out how many grams of water (x) are needed to dissolve 80.0 g of NaCl. The proportion can be set up as follows:

(36.0 g NaCl) / (100.0 g H2O) = (80.0 g NaCl) / (x g H2O)

Here, we are equating the ratio of NaCl to water in the saturated solution with the desired ratio for 80.0 g of NaCl. This proportion states that the ratio of NaCl to water must remain constant for the solution to be saturated. The left side of the equation represents the known solubility, while the right side represents the scenario we want to solve. Ensuring the units align correctly (grams of NaCl over grams of H2O) is crucial for accurate calculations. This setup allows us to solve for the unknown, which is the amount of water needed.

Solving for the Unknown

To solve for x, we cross-multiply and isolate the variable. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and vice versa. Applying this to our proportion gives us:

36. 0 g NaCl * x g H2O = 80.0 g NaCl * 100.0 g H2O

This step transforms the proportion into a linear equation that is easier to solve. The equation now shows the product of NaCl and water on both sides, allowing us to proceed with algebraic manipulation. Next, we simplify the equation:

37. 0x = 8000

Now, we isolate x by dividing both sides of the equation by 36.0:

x = 8000 / 36.0

Performing this division will give us the value of x, which is the amount of water needed to dissolve 80.0 g of NaCl at 20°C. This algebraic manipulation is a standard technique in solving proportional problems and is essential for accurately determining the required quantity of solvent.

Calculating the Result and Expressing the Answer

Performing the division, we get:

x ≈ 222.2 g H2O

Thus, approximately 222.2 grams of water are needed to prepare a saturated solution containing 80.0 g of NaCl at 20°C. It is crucial to express the answer with the appropriate units, which in this case are grams of H2O. The unit ensures that the answer is correctly interpreted and understood in the context of the problem. Additionally, in scientific contexts, paying attention to significant figures is important. The initial values (36.0 g, 100.0 g, and 80.0 g) each have three significant figures, so our final answer should also be expressed with three significant figures. Therefore, we round our answer to 222 g H2O, acknowledging the precision of our measurements and calculations. This accurate calculation and expression of the result are vital for both academic and practical applications in chemistry.

Conclusion

In summary, to prepare a saturated solution containing 80.0 g of NaCl at 20°C, approximately 222 grams of water are needed. This calculation was performed using the given solubility of NaCl (36.0 g in 100.0 g of H2O) and setting up a proportion to find the unknown amount of water. Understanding solubility and how to calculate it is essential in various fields, from chemistry labs to industrial applications. The key takeaways from this article include the importance of recognizing what a saturated solution is, knowing how to set up and solve proportions, and expressing results with appropriate units and significant figures. By mastering these skills, one can confidently tackle similar problems involving solutions and concentrations. Ultimately, this exercise highlights the practical application of basic chemistry principles in real-world scenarios.

Importance of Accurate Calculations in Chemistry

Accurate calculations are paramount in chemistry, as even small errors can lead to significant discrepancies in experimental results and outcomes. In fields such as pharmaceuticals, where precise dosages are crucial for patient safety, incorrect calculations can have severe consequences. Similarly, in industrial chemical processes, maintaining accurate proportions of reactants and products is essential for efficiency and safety. The process of calculating the amount of water needed for a saturated NaCl solution exemplifies the importance of attention to detail and the proper use of mathematical tools. This skill is not just academic; it is a fundamental requirement for any practical application of chemistry. Accurate measurements, correct unit conversions, and appropriate use of significant figures all contribute to the reliability and validity of chemical experiments and applications.

Real-World Applications of Solution Chemistry

The principles of solution chemistry, including solubility, molarity, and concentration, have a wide range of real-world applications. In environmental science, understanding the solubility of pollutants in water is critical for assessing and mitigating environmental risks. In medicine, intravenous solutions are carefully prepared to match the osmotic pressure of blood, ensuring that cells neither swell nor shrink. The food and beverage industry relies on solution chemistry for quality control, from ensuring the correct salt concentration in processed foods to maintaining the appropriate sugar levels in beverages. In agriculture, fertilizers are often applied as solutions to ensure efficient nutrient uptake by plants. Even in everyday household activities, such as cooking and cleaning, we encounter solutions and their properties. This ubiquitous presence of solution chemistry underscores its significance in various aspects of our lives.

Further Exploration of Solubility and Solutions

To deepen understanding of solubility and solutions, further exploration of related topics is beneficial. The concept of molarity, which expresses the concentration of a solution in terms of moles of solute per liter of solution, is a crucial extension of solubility. Understanding colligative properties, such as boiling point elevation and freezing point depression, provides insights into how solutes affect the physical properties of solutions. The effect of temperature and pressure on solubility, as well as the kinetics of dissolution, are also important areas to investigate. Additionally, exploring different types of solutions, including electrolytes and nonelectrolytes, can provide a more comprehensive understanding of solution behavior. Through continued learning and experimentation, one can develop a strong foundation in the principles of solution chemistry, enabling more advanced study and application in related fields.