Calculating Water Needed For Saturated NaCl Solution

In the realm of chemistry, understanding solubility and saturated solutions is crucial. Solubility, the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature, dictates the behavior of solutions. A saturated solution, on the other hand, is a solution where the solvent has dissolved the maximum amount of solute possible at that temperature. Adding more solute to a saturated solution will simply result in the undissolved solute settling at the bottom. This concept is fundamental in various chemical processes, from laboratory experiments to industrial applications. Grasping the principles of solubility allows chemists to accurately predict and control the composition of solutions, which is vital in synthesizing new compounds, analyzing chemical reactions, and developing new technologies. For instance, in pharmaceutical manufacturing, solubility plays a critical role in determining the bioavailability of drugs, ensuring that the medication dissolves properly in the body to exert its therapeutic effects. Similarly, in environmental chemistry, understanding the solubility of pollutants is essential for assessing their transport and fate in aquatic systems. The interplay between solubility, temperature, and the nature of the solute and solvent forms the backbone of solution chemistry, enabling scientists to manipulate and optimize chemical processes across diverse fields. In this article, we will delve into a practical problem involving sodium chloride (NaCl) solubility and saturated solutions. We will explore how to calculate the amount of water needed to prepare a saturated solution with a specific amount of NaCl, building a solid foundation in solution chemistry principles. This exercise provides a practical approach to understanding the concepts and their application in real-world scenarios. Understanding the principles behind solubility also allows for a more intuitive grasp of more complex chemical phenomena. For example, the common-ion effect, which describes the decrease in solubility of a salt when a soluble compound containing a common ion is added to the solution, is a direct consequence of the equilibrium established between the dissolved and undissolved solute. Similarly, the solubility product constant, Ksp, is a quantitative measure of the solubility of a compound and is widely used in analytical chemistry to predict the formation of precipitates. By mastering these foundational concepts, students and professionals can better navigate the intricate world of chemical reactions and processes.

Problem Statement: Determining Water Amount for Saturated NaCl Solution

H2: The Question of NaCl Solubility

Our main task is to determine the amount of water required to prepare a saturated solution containing 80.0 g of NaCl, given that NaCl has a solubility of 36.0 g in 100. g of H2O at 20 °C. This question is rooted in the concept of solubility and its relationship to saturated solutions. The solubility of a substance is the maximum amount of that substance (solute) that can dissolve in a specific amount of solvent at a given temperature. In this case, NaCl (sodium chloride), commonly known as table salt, is our solute, and H2O (water) is the solvent. A saturated solution is one in which the solvent has dissolved the maximum amount of solute possible at the given temperature. Adding more solute to a saturated solution will not result in further dissolution; instead, the excess solute will remain undissolved, typically settling at the bottom of the container. Understanding the factors that affect solubility, such as temperature and the nature of the solute and solvent, is crucial in chemistry. For example, the solubility of most solid compounds in water increases with temperature, while the solubility of gases in water decreases with increasing temperature. The nature of the solute and solvent also plays a significant role; polar solutes tend to dissolve in polar solvents, and nonpolar solutes tend to dissolve in nonpolar solvents, a principle often summarized as "like dissolves like." In the context of this problem, we are given the solubility of NaCl in water at a specific temperature (20 °C). This information provides a benchmark for determining the amount of water needed to dissolve a different quantity of NaCl while maintaining a saturated solution. The problem requires us to apply the given solubility ratio to a different mass of NaCl, effectively scaling up the solution while preserving the saturation condition. This type of calculation is common in laboratory settings, where chemists often need to prepare solutions of specific concentrations. The problem also highlights the importance of proper unit handling in chemistry calculations. Ensuring that units are consistent and correctly converted is essential for obtaining accurate results. This is a fundamental skill in quantitative chemistry and is crucial for success in more advanced chemical calculations and experiments. Moreover, the problem reinforces the idea that solubility is a temperature-dependent property. The solubility value given (36.0 g NaCl in 100. g H2O at 20 °C) is specific to the stated temperature. If the temperature were different, the solubility, and consequently the amount of water needed, would also be different. This emphasizes the need to always consider temperature when dealing with solubility-related problems. By solving this problem, we not only determine the specific amount of water needed but also reinforce our understanding of the fundamental concepts of solubility, saturated solutions, and the factors that influence them.

Solution Approach: How to Calculate the Required Water Amount

H2: Steps to Determine Grams of Water Needed

To solve this problem, we employ a proportional reasoning approach, leveraging the given solubility of NaCl in water. Our approach hinges on the understanding that the ratio of NaCl to water in a saturated solution remains constant at a given temperature. The problem provides us with the solubility of NaCl as 36.0 g in 100. g of H2O at 20 °C. This means that at 20 °C, a maximum of 36.0 grams of NaCl can dissolve in 100. grams of water to form a saturated solution. We are tasked with finding the amount of water needed to dissolve 80.0 g of NaCl while maintaining the solution's saturation. The key is to set up a proportion using the given solubility as a reference. We know the ratio of NaCl to water in the saturated solution (36.0 g NaCl / 100. g H2O) and we know the desired amount of NaCl (80.0 g). What we need to find is the corresponding amount of water. We can represent the unknown amount of water as 'x' grams. The proportion can be set up as follows:

(36.0 g NaCl) / (100. g H2O) = (80.0 g NaCl) / (x g H2O)

This equation expresses the equality of two ratios: the known solubility ratio and the desired solution ratio. To solve for 'x', we cross-multiply and isolate 'x' on one side of the equation. This is a standard algebraic technique for solving proportions. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal to each other:

36.0 g NaCl * x g H2O = 80.0 g NaCl * 100. g H2O

Now, we simplify the equation and solve for 'x':

36. 0x = 8000

To isolate 'x', we divide both sides of the equation by 36.0:

x = 8000 / 36.0

This calculation will give us the amount of water, in grams, needed to dissolve 80.0 g of NaCl to form a saturated solution at 20 °C. It is important to note that this calculation assumes that the temperature remains constant at 20 °C. If the temperature were to change, the solubility of NaCl would also change, and the amount of water needed would be different. This highlights the importance of specifying the temperature when discussing solubility. After performing the calculation, we will obtain a numerical value for 'x'. It is crucial to express this value with the appropriate units, which in this case are grams of water (g H2O). Additionally, it is good practice to consider the significant figures in the problem. The given values (36.0 g NaCl, 100. g H2O, and 80.0 g NaCl) all have three significant figures, so our final answer should also be expressed with three significant figures to maintain consistency in precision. By following this step-by-step approach, we can accurately determine the amount of water needed to prepare a saturated solution of NaCl, demonstrating a solid understanding of solubility principles and proportional reasoning in chemistry.

Detailed Calculation: Finding the Exact Water Quantity

H2: Solving the Proportion for Water Amount

To calculate the exact quantity of water required, we proceed with the equation derived in the previous section: 36.0x = 8000. This equation represents the proportional relationship between the solubility of NaCl and the amount of water needed for our desired solution. The value 'x' represents the unknown quantity of water in grams that we need to determine. To isolate 'x' and find its value, we perform a simple algebraic step: dividing both sides of the equation by 36.0. This operation maintains the equality of the equation while bringing 'x' to one side:

x = 8000 / 36.0

Now, we perform the division. This step is crucial as it translates the abstract proportional relationship into a concrete numerical value for the amount of water. Using a calculator, we divide 8000 by 36.0. The result of this division is approximately 222.222... grams of water. However, in scientific calculations, it is essential to consider significant figures. Significant figures are the digits in a number that are known with certainty plus one uncertain digit. They indicate the precision of a measurement or a calculation. In our problem, the given values (36.0 g NaCl, 100. g H2O, and 80.0 g NaCl) each have three significant figures. Therefore, our final answer should also be expressed with three significant figures to maintain consistency in precision. To round 222.222... to three significant figures, we look at the first four digits: 222. The digit immediately to the right of the third digit (the first 2 after the decimal point) is less than 5, so we round down, keeping the first three digits as they are. Thus, 222.222... rounded to three significant figures is 222. Therefore, the amount of water needed to prepare a saturated solution containing 80.0 g of NaCl at 20 °C is 222 grams. This result is not just a number; it has a unit (grams) and a context (a saturated solution of NaCl at a specific temperature). The unit is crucial for conveying the physical quantity we are measuring, and the context is essential for understanding the meaning and applicability of the result. It is also important to consider the reasonableness of the answer. Does 222 grams of water seem like a plausible amount to dissolve 80.0 grams of NaCl, given that 36.0 grams of NaCl dissolves in 100 grams of water? The answer is yes, it is reasonable. Since we are dissolving more than twice the amount of NaCl (80.0 g compared to 36.0 g), we would expect to need more than twice the amount of water (222 g compared to 100 g). This simple check helps ensure that our calculation is not only mathematically correct but also makes sense in the physical context of the problem. By performing this detailed calculation and considering significant figures and reasonableness, we arrive at a precise and meaningful answer to our problem.

Final Answer: Water Needed for Saturation

H2: Expressing the Final Result with Units

After performing the detailed calculation, we have determined that 222 grams of water are needed to prepare a saturated solution containing 80.0 g of NaCl at 20 °C. Expressing the final answer with appropriate units is a critical step in any scientific calculation. The numerical value alone is insufficient; the unit provides context and clarifies what the number represents. In this case, the unit is grams (g), which is a unit of mass. Therefore, our final answer is 222 g of H2O. This concise statement conveys the exact amount of water required for the saturated solution. The unit "g of H2O" explicitly states that we are referring to grams of water, leaving no room for ambiguity. This level of precision is essential in chemistry, where even small differences in quantities can significantly affect the outcome of experiments or reactions. The inclusion of the unit also serves as a check on our calculation. If, for example, we had inadvertently performed a calculation that resulted in a unit other than grams (such as liters or moles), we would immediately know that we had made an error somewhere in our process. The unit acts as a sort of "dimensional analysis" check, ensuring that we are manipulating the numbers and units correctly. Furthermore, the final answer should be presented in a clear and easily understandable manner. Simply stating "222" without the unit would be incomplete and could lead to confusion. Adding the unit "g H2O" not only makes the answer more precise but also more accessible to anyone reading our work. It allows others to immediately grasp the significance of the number and how it relates to the original problem. In scientific reports, papers, and presentations, it is standard practice to always include units with numerical values. This is a fundamental aspect of scientific communication and is essential for maintaining clarity and accuracy. The unit is an integral part of the measurement, and omitting it is akin to omitting a crucial word from a sentence. In summary, our final answer, expressed with the appropriate units, is: 222 g of H2O. This answer provides a complete and unambiguous solution to the problem, demonstrating our understanding of solubility principles and our ability to perform accurate chemical calculations. It also highlights the importance of attention to detail in scientific work, where even seemingly small aspects like units play a vital role in conveying information effectively.