Question

Explain the difference in meaning between the following two solutions: " \(50 .\) g of \(\mathrm{NaCl}\) dissolved in \(1.0 \mathrm{~L}\) of water" and \(" 50 . \mathrm{g}\) of \(\mathrm{NaCl}\) dissolved in enough water to make \(1.0 \mathrm{~L}\) of solution." For which solution can the molarity be calculated directly (using the molar mass of \(\mathrm{NaCl}) ?\)

Short answer

The first statement ("50 g of NaCl dissolved in 1.0 L of water") means that 50 g of NaCl is added to a fixed volume of water (1.0 L), but the final volume of the solution isn't necessarily 1.0 L. The second statement ("50 g of NaCl dissolved in enough water to make 1.0 L of solution") means that 50 g of NaCl is added to enough water to ensure the final solution volume is exactly 1.0 L. Molarity can be directly calculated from the second statement, as it considers both solute and solvent in the final volume of the solution. In this case, the molarity would be \(0.855~M\).

Step-by-step solution

Understanding the Statements

The first statement, "50 g of NaCl dissolved in 1.0 L of water", means that a specific amount of solute (50 g of NaCl) is dissolved in a fixed volume of solvent (1.0 L of water). The final volume of the solution isn't necessarily 1.0 L, because when the solute is added to the solvent, the volume increases. The second statement, "50 g of NaCl dissolved in enough water to make 1.0 L of solution", means that the solute (50 g of NaCl) is added to enough solvent to ensure that the final volume of the solution (including both solute and solvent) is exactly 1.0 L.

Understand the Molarity Concept

Molarity (M) is a metric commonly used in chemistry to describe the concentration of a solution. It's defined as the number of moles of solute per liter of solution. The most important thing for this exercise is that molarity relates to the volume of solution, not just the solvent.

Identifying Statement for which Molarity Can be Calculated Directly

Molarity can be directly calculated from the second statement. This is because we know the explicit final volume of the solution (1 L), and the amount of solute (50 g). Therefore, using the molar mass of NaCl, the number of moles of NaCl can be found, and then the molarity. In contrast, for the first statement, the molarity can't be directly calculated, since we don't know the final volume of the solution, only the volume of the solvent - water.

Calculating Molarity (Optional)

Although not asked, it may be interesting to calculate the molarity for the second scenario. Knowing that the molar mass of NaCl is approximately 58.44 g/mol, the moles of NaCl in the solution would be 50g / 58.44 g/mol = 0.855 mol. Therefore, the molarity would be 0.855 mol / 1L = 0.855 M.

Key concepts

Solution Concentration

Understanding solution concentration is essential for grasping many concepts in chemistry. It refers to the amount of solute present within a given volume of solvent. Being able to measure and express this concentration is crucial, especially when you're trying to reproduce results in experiments or cooking up a batch of a glimmering chemical solution.

One common unit of concentration is molarity, which is the number of moles of solute per liter of solution. It's handy because it lets chemists know how many particles of a substance are in a standard volume, allowing for comparisons and calculations. To fully understand solutions and their properties, such as reaction rates or ion ranging, you'll have to master the concept of solution concentration.

Moles of Solute

Next to grapple with is the notion of 'moles of solute.' Think of a mole as a very large collection of particles – in this case, solute particles. Specifically, one mole is Avogadro's number of particles, which is about 6.022 x 10^23.

When you dissolve a substance in a solvent, you're dispersing individual particles throughout another material. To figure out how concentrated your solution is, you calculate the number of moles of solute present in a given volume. Understanding moles is like understanding dozens for eggs: it's just a number that represents a lot of an item, making it easier to quantify substances at the atomic and molecular levels.

Chemistry Problem Solving

Chemistry problem solving often involves a step-by-step approach to decipher the clues presented. It's like being a detective but for molecules and reactions. Start with understanding the given information - what you know about the substances involved, such as their masses, volumes, and chemical properties.

Then, apply concepts and formulas appropriately. For example, when you have the molar mass of a compound like NaCl and the mass of the sample, you can calculate the number of moles. Frameworks like the 'stoichiometry roadmap' guide you from known quantities to what needs to be found. To be a proficient chemistry problem solver, you'll want to practice, sharpen your mathematical skills, and, most importantly, understand the theory behind the concepts you apply.

Molar Mass of NaCl

Lastly, let's focus on the molar mass of NaCl, which is a classic example used in many chemistry exercises. NaCl, or sodium chloride, is commonly known as table salt. Its molar mass, the mass of one mole of NaCl, is approximately 58.44 grams per mole.

The molar mass is calculated by adding the atomic masses of sodium (Na) and chlorine (Cl) from the periodic table. For any compound, determining its molar mass is fundamental, as it links the mass of a substance to the number of its particles - a bridge between the macroscopic world we see and the microscopic world of molecules.