Question

What is the percent-by-mass concentration of \(\mathrm{NaCl}\) in a solution that is prepared by adding \(15.0 \mathrm{~g}\) of \(\mathrm{NaCl}\) to \(90.0 \mathrm{~g}\) of water?

Short answer

The percent-by-mass concentration of NaCl in the solution is 14.29%

Step-by-step solution

step 1: Identify the given values

Here, the mass of NaCl is given as 15.0 g and mass of water is given as 90.0 g.

step 2: Calculate the total mass of the solution

Add the mass of NaCl and water to get the total mass. Total mass = mass of NaCl + mass of water = 15.0 g + 90.0 g = 105.0 g

step 3: Calculate the percent-by-mass concentration of NaCl

Use the formula for percent-by-mass which is (mass of solute / total mass of solution) * 100. Here, the mass of solute is mass of NaCl and the total mass of solution is calculated in step 2. So, percent-by-mass = (15.0 g / 105.0 g) * 100

step 4: Compute the Final Percentage

Upon calculating the above expression we get percent-by-mass = 14.29%

Key concepts

Solution Chemistry

Solution chemistry is the study of solutions, which are homogeneous mixtures of two or more substances. In solutions, the solute is the substance that is dissolved, while the solvent is the substance in which the solute is dissolved. Take table salt (NaCl) dissolving in water, for example. NaCl is the solute, and water is the solvent. These solutions have specific properties and concentrations, such as percent-by-mass concentration, which measures how much of the solute is present per 100 grams of the solution.
This concentration is important in various applications, such as when preparing a saline solution for medical uses or in cooking. Understanding solution chemistry helps in estimating how these processes affect the characteristics of the solution and the efficiency of chemical reactions within the solution.

Mass of Solute

The mass of the solute refers to the quantity of the substance being dissolved in the solvent. In our example, NaCl is the solute with a mass of 15.0 g. To determine concentrations, the amount of solute is crucial because it dictates the resulting strength or dilution of the solution.

• Measurement: Typically measured in grams, the mass must be accurate for precise concentration calculations.
• Role in Percent Concentration: The mass of the solute directly influences its percentage in the total solution. For example, increasing the mass of NaCl will increase its presence percentage-wise in the solution.

It's a straightforward concept: more solute means more intense concentration, while less solute means a diluted solution. This fundamental understanding is essential for fields like pharmacology, where precise dosages are critical.

Total Mass of Solution

The total mass of the solution is the sum of the mass of the solute and the solvent. It's an essential value when calculating concentrations. In this case, adding 15.0 g of NaCl to 90.0 g of water yields a solution with a total mass of 105.0 g.
Knowing the total mass lets you determine what portion of that mass comes from a particular solute, giving you the percent-by-mass concentration.

• Calculation Formula: Total Mass = Mass of Solute + Mass of Solvent. This foundational formula helps understand the solution’s makeup.
• Application in Concentration: Once the total mass is known, it’s used to compute not only percent-by-mass but also other measures like molarity or molality, based on needs.

Recognizing the total mass's role in solution concentration builds a complete picture of how solutes interact within a given solvent, useful in chemistry fields ranging from industrial formulations to research-level investigations.