Problem 9 - General Chemistry: Principles and Modern Applications

Question

A saturated aqueous solution of \(\mathrm{NaBr}\) at \(20^{\circ} \mathrm{C}\) contains \(116 \mathrm{g} \mathrm{NaBr} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\). Express this composition in the more conventional percent by mass, that is, as grams of NaBr per 100 grams of solution.

Step-by-Step Solution

Answer

The composition of saturated aqueous solution of NaBr at 20°C is 53.70 % by mass, which means there are 53.70 grams of NaBr in every 100 grams of the total solution.

Step 1: Calculate total mass of the solution

According to the problem, we have 116 g of NaBr (solute) in every 100 g of water (solvent). To find out total mass of solution, we should add the mass of the solute to the mass of the solvent: 116 g (NaBr) + 100 g (H2O) = 216 g

Step 2: Calculate percent by mass

Now, expressing the composition as grams of solute per 100 grams of solution (percent by mass), we find the percentage that the solute represents of the total. This can be found by using the formula: \[ ( \frac{mass \ of \ the \ solute}{mass \ of \ the \ solution} ) \times 100 \] Substituting in the values which we have: \( \frac{116 \ g}{216 \ g} \) x 100 = 53.70 %

Key Concepts

Percent Mass Calculation

When tackling problems involving percent mass calculation, the goal is to determine the composition of a solution in terms of mass percentage. This is done by expressing how much of the solute contributes to the overall mass of the solution. Let’s break it down:

To begin, you need to find the total mass of the solution. This simply means adding together the mass of the solute and the solvent.
For example:

• Solute (e.g., NaBr): 116 g
• Solvent (e.g., water): 100 g
• Total Solution Mass: 116 g + 100 g = 216 g

Once we know the total mass, the percent by mass is calculated using:\[percent \, mass = \left( \frac{mass \, of \, solute}{total \, mass \, of \, solution} \right) \times 100\]Applying this formula helps you convert the solute's contribution into a percentage of the total solution, giving a clear and practical representation of concentration in the form of percent mass.

Solution Concentration

Understanding solution concentration is crucial in chemistry as it indicates how much solute is dissolved in a given amount of solvent or solution. There are several ways to express concentration, such as molarity, molality, and percent mass. Here, we focus on percent by mass, which tells us the mass of the solute in every 100 parts by mass of the solution.

In our example, knowing that we have 116 grams of NaBr in a solution makes it easy to recognize the amount of solute present. Percent by mass allows chemists to easily compare and prepare solutions with precision. It’s particularly useful when preparing solutions for reactions that require exact amounts of reagents to control reaction rates and equilibria.

Saturated Solution

A saturated solution is a chemical solution containing the maximum concentration of a solute dissolved in the solvent at a given temperature. Once a solution is saturated, adding more solute will not dissolve; instead, it may start to precipitate. Understanding this concept is important for predicting how solutions will behave under different conditions.

In our particular problem, a saturated solution of NaBr at 20°C contains 116 g of NaBr per 100 g of water. This means that at this temperature, the solution cannot dissolve any additional NaBr unless conditions change, such as an increase in temperature which often allows saturation limits to increase.

The idea behind working with saturated solutions is to ensure that you operate within known limits of solubility to avoid undissolved solids, which can affect reactions and experimental accuracy. Thus, when a solution is saturated, further solute additions must consider solubility factors to ensure desired outcomes.