Question

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

Short answer

The percent by mass of MgCl2 in the solution is approximately 4.35%.

Step-by-step solution

Calculate the mass of the total solution

First, we need to find the mass of 550 mL of water. Since the density of water is 1g/mL, the mass of 550 mL of water can be found by multiplying the volume of water by its density. \(mass\_water = volume\_water * density\_water\) \(mass\_water = 550 \, mL * 1 \, g/mL = 550 \, g \) Now, we can find the total mass of the solution by adding the mass of water and the mass of MgCl2. \(mass\_solution = mass\_water + mass_{MgCl2}\) \(mass\_solution = 550 \, g + 25.0 \, g = 575 \, g \)

Calculate the percent by mass of MgCl2

Percent by mass can be found using the formula: \[\% \, by \, mass = \frac{mass \, of \, solute}{mass \, of \, solution} * 100\] where solute is the MgCl2 and solution is the mixture of water and MgCl2. We have already found the mass of solution in the previous step. Now, we can simply plug the values into the equation and solve for the percent by mass of MgCl2. \[\% \, by \, mass = \frac{25.0 \, g}{575 \, g} * 100\] \[\% \, by \, mass \approx 4.35 \%\]

Answer

The percent by mass of MgCl2 in the solution is approximately 4.35%.

Key concepts

Solute and Solvent

When creating a solution in chemistry, two main components are involved: the solute and the solvent. The solute is the substance that is being dissolved, while the solvent is the substance that dissolves the solute. In our exercise example, \(\mathrm{MgCl}_2\) is the solute, and water is the solvent. Understanding the nature of solutes and solvents is crucial for many chemical processes, including the creation of solutions in a lab setting.

When combining a solute with a solvent, the physical state can change, and it's essential to recognize that the resulting mixture, known as a solution, is homogeneous. This means that the solute particles are evenly distributed throughout the solvent, creating a system where the concentration is uniform. When referring to aqueous solutions, water, due to its ability to dissolve a wide range of substances, is commonly the solvent of choice.

Concentration of Solution

The concentration of a solution is a measure of how much solute is dissolved in a given quantity of solvent. Concentration can be expressed in various ways, including molarity, molality, and percent by mass, among others. For our exercise, we are concerned with percent by mass, which is a popular way to convey concentration, especially when dealing with non-aqueous solutions or when precise molar concentrations aren't necessary.

To comprehend percent by mass, think of it as the portion of the total mass that the solute constitutes. It is calculated by dividing the mass of the solute by the total mass of the solution and then multiplying by 100 to get a percentage. This provides a straightforward method for identifying how 'concentrated' a solution is, with higher percentages indicating more solute per unit of solution.

Mass Calculations in Chemistry

Performing mass calculations is an integral part of chemistry that helps in determining various quantitative aspects of substances involved in a reaction or a solution. In our exercise, finding the percent by mass began with calculating the mass of the water, followed by the mass of the solute (\(\mathrm{MgCl}_2\)), and then determining the total mass of the solution. These calculations are foundational for any quantitative analysis in chemistry.

Mass is a basic property of matter and provides a means for stoichiometric calculations, which is essential in predicting the outcomes of chemical reactions and processes. Whether you're mixing solutions, reacting chemicals, or analyzing compounds, mass calculations allow you to quantify components and describe chemical phenomena with precision. Accurate mass measurement ensures that solutions are prepared correctly, which is vital for both experimental success and safety in a laboratory environment.