Problem 67 - Chemistry Matter and Change

Question

According to lab procedure, you stir 25.0 \(\mathrm{g}\) of MgCl \(_{2}\) into 550 \(\mathrm{mL}\) of water. What is the percent by mass of \(\mathrm{MgCl}_{2}\) in the solution?

Step-by-Step Solution

Answer

The percent by mass of MgCl₂ is approximately 4.35%.

Step 1: Calculate Total Mass of Solution

Begin by calculating the total mass of the solution. You have 25.0 g of MgCl₇ and 550 mL of water. To get the total mass, you need to consider the mass of water, assuming it has a density of 1 g/mL, so the mass of 550 mL of water is 550 g. Therefore, the total mass of the solution is the sum of the mass of MgCl₂ and water: 25.0 g + 550 g = 575.0 g.

Step 2: Calculate Percent by Mass

Now, calculate the percent by mass of MgCl₂ in the solution using the formula: \(\text{Percent by mass} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100\%\). The mass of the solute (MgCl₂) is 25.0 g, and the total mass of the solution is 575.0 g. Therefore, \((25.0 / 575.0) \times 100\% \approx 4.35\%\).

Key Concepts

Percent by Mass

Percent by mass is a way of expressing the concentration of a particular component in a mixture. It essentially tells us how much, in terms of mass, a solute contributes to the total mass of the solution. To calculate it, we use the following formula: \[ \text{Percent by mass} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100\% \]Think of it like slicing a pie. If the solute is a slice, the percent by mass tells you how much of the pie that slice represents. In chemical solutions, it helps to understand the concentration in simple terms, without needing sophisticated equipment or measurements beyond a simple mass scale. This is a very handy way in chemistry to easily communicate the amount of a component present.

Solution Concentration

Solution concentration refers to the amount of a substance present in a certain volume of solution. Although there are various methods to describe concentration, *percent by mass* provides insights into how much solute is actually in the solution compared to the whole. Concentration can be expressed in different forms:

• Molarity - moles of solute per liter of solution.
• Molality - moles of solute per kilogram of solvent.
• Percent by mass - as in our current example, shows the mass ratio of solute to solution.

By understanding the concentration, chemists can determine how a solution will interact with other substances or how it will behave under certain conditions. In the exercise above, we found a 4.35% concentration, meaning a small portion of the entire solution weight is due to the solute, which is MgCl₂.

Mass of Solute

The mass of the solute is the amount, in grams, of a substance that gets dissolved in a solvent to form a solution. In the exercise, MgCl₂ is the solute, and it has a starting mass of 25.0 grams. The solute's mass is crucial in determining the concentration of a solution. Knowing this helps to predict how strong or dilute a solution will be. If you increase the mass of the solute while keeping the solvent constant, the solution becomes more concentrated. On the other hand, decreasing solute mass or increasing solvent quantity dilutes the solution. In our example, even though the solute is just 25 grams compared to the total 575 grams of solution, this significantly impacts the concentration calculation.

Total Mass of Solution

Total mass of the solution is the sum of the mass of the solute and the mass of the solvent. It's a key value needed for calculating the percent by mass. In the example given, we find the total mass by adding the 25.0 grams of MgCl₂ (our solute) and 550 grams of water (our solvent). This gives us a total mass of 575.0 grams. Understanding this concept allows you to place context around how much of a substance is present in a given solution. It is also an essential step in computing concentration, providing a real-world understanding of how solutions are formulated, how they behave in the physical world, and ensures accurate chemical properties are maintained during experimentation.