Question

You have two beakers, one filled to the \(100-\mathrm{mL}\) mark with sugar (the sugar has a mass of \(180.0 \mathrm{~g}\) ) and the other filled to the \(100-\mathrm{mL}\) mark with water (the water has a mass of \(100.0 \mathrm{~g}\) ). You pour all the sugar and all the water together in a bigger beaker and stir until the sugar is completely dissolved. a. Which of the following is true about the mass of the solution? Explain. i. It is much greater than \(280.0 \mathrm{~g}\). ii. It is somewhat greater than \(280.0 \mathrm{~g}\). iii. It is exactly \(280.0 \mathrm{~g}\). iv. It is somewhat less than \(280.0 \mathrm{~g}\). v. It is much less than \(280.0 \mathrm{~g}\). b. Which of the following is true about the volume of the solution? Explain. i. It is much greater than \(200.0 \mathrm{~mL}\). ii. It is somewhat greater than \(200.0 \mathrm{~mL}\). iii. It is exactly \(200.0 \mathrm{~mL}\). iv. It is somewhat less than \(200.0 \mathrm{~mL}\). v. It is much less than \(200.0 \mathrm{~mL}\).

Short answer

The short answer to the given question is: a. The true statement about the mass of the solution is (iii) "It is exactly \(280.0 \mathrm{~g}\)." because the mass of the solution is the sum of the masses of sugar and water. b. The true statement about the volume of the solution is (iv) "It is somewhat less than \(200.0 \mathrm{~mL}\)." because there can be a slight change in volume when sugar is dissolved in water, but the change is generally small.

Step-by-step solution

To find the mass of the solution, we need to add the masses of sugar and water. The mass of sugar is \(180.0 \mathrm{~g}\) and the mass of water is \(100.0 \mathrm{~g}\). So, the total mass of the solution will be \(180.0 \mathrm{~g} + 100.0 \mathrm{~g} = 280.0 \mathrm{~g}\). #step 2#: Determine the truthfulness of statements about the mass of the solution

Since the total mass of the solution is calculated as \(280.0 \mathrm{~g}\), we can conclude that statement (iii) "It is exactly \(280.0 \mathrm{~g}\)." is true. All other statements are not true. #step 3#: Analyze the change in volume after dissolving sugar into water

When sugar is dissolved in water, there might be some changes in the volume due to the interaction between sugar and water molecules. However, the change is usually quite small and generally, the volume change could be somewhat less than the total initial volumes of sugar and water. #step 4#: Determine the truthfulness of statements about the volume of the solution

Based on the analysis in step 3, we can conclude that statement (iv) "It is somewhat less than \(200.0 \mathrm{~mL}\)." reflects the likely change in the volume of the solution after dissolving sugar into water. All other statements are not accurate.

Key concepts

Mass Conservation in Chemistry

In the context of chemistry, the principle of mass conservation, also known as the law of conservation of mass, states that mass is neither created nor destroyed in a chemical reaction. When you mix substances, like sugar and water, the total mass remains constant throughout the process.

For example, when dissolving sugar in water, the mass before and after dissolving should be the same, assuming no mass is lost to the environment. This is exemplified in the exercise where the sugar has a mass of 180.0 g, and the water has a mass of 100.0 g. After dissolution, the total mass of the solution remains exactly 280.0 g. Understanding this principle is fundamental in solution preparation chemistry, as it ensures accuracy in experiments and chemical formulations.

However, a common misconception is that the same conservation applies to the volume, which is not true as volumes can change depending on the substances' properties and how they interact with one another.

Properties of Solutions

A solution is a homogeneous mixture consisting of a solute dissolved in a solvent. The properties of solutions, such as boiling point, freezing point, and vapor pressure, depend on the nature of the solute and solvent as well as their concentrations. In the context of the exercise, we are primarily concerned with volume and concentration after dissolving a solid in a liquid.

A peculiar property of solutions is that when a solute like sugar dissolves in a solvent like water, the volume may not be additive; the final volume can be less than the sum of the individual volumes. This is due to the 'solute-solvent interactions,' where molecules of solute fit in between solvent molecules, leading to a reduction in the overall volume. This observation helps explain why the volume of the solution in the exercise might be 'somewhat less than 200.0 mL' after the sugar is completely dissolved.

Solubility and Dissolution

Solubility is a chemical property referring to the maximum amount of a solute that can dissolve in a solvent at a given temperature and pressure to form a stable solution. Dissolution is the process by which this occurs. Solubility can be affected by temperature, pressure, and the nature of the solute and solvent.

In the exercise, sugar's solubility in water is high, which allows the 180.0 g of sugar to dissolve completely in 100.0 mL of water. The dissolution process is facilitated by stirring, which allows sugar molecules to interact with water molecules, breaking down the sugar into its component molecules and distributing them throughout the water.

The complete dissolution of sugar represents the solution's homogeneity, meaning the sugar molecules are uniformly distributed in water, forming a consistent solution without any concentration gradients. This fact is crucial for understanding the behavior of solutions in various chemical processes and industrial applications.