Calculate the percentage composition in terms of mass of a solution obtained by mixing \(300 \mathrm{~g}\) of a \(25 \%\) and \(400 \mathrm{~g}\) of a \(40 \%\) solution by mass.

Understanding the nature of solutions and mixtures is a foundational concept in chemistry and daily life scenarios. A solution is a homogeneous mixture, a kind of mixture in which the composition is uniform throughout. It's made up of two components: a solute and a solvent. The solute is the substance that gets dissolved, while the solvent is the substance that does the dissolving. In the case of liquid solutions, water is often the solvent.

There is no visible separation of the components in a solution, and the particles are so small that they cannot be seen by the naked eye. Mixtures, on the other hand, can be either homogeneous or heterogeneous, where the components may or may not be uniformly distributed, respectively.

When solutions are formed, interactions between molecules of the solute and solvent occur which keeps the solute particles dispersed uniformly. This is vital for the calculations related to mass percentage, as uniform distribution ensures consistency in concentration throughout the solution.

The concentration of a solution refers to the amount of solute present in a given amount of solvent or solution. It is a measure of how 'concentrated' the solution is. There are multiple ways to express concentration, some of the most common include molarity, molality, and mass percentage.

Mass Percentage

Mass percentage is one way to express the concentration of a solution in terms of mass, represented as a percentage. It indicates what proportion of the total mass of the solution comes from the solute. To calculate it, you divide the mass of the solute by the total mass of the solution and then multiply by 100 to get the percentage.

This concept is particularly important since it allows for a straightforward understanding of how much solute is within a given solution without the complications of unit conversions that can accompany other concentration measures, and is readily applicable in many practical scenarios including cooking, pharmaceuticals, and chemical manufacturing.

The mass percentage calculation is crucial in determining the composition of mixtures and solutions alike. It aids in various fields, for instance in pharmacology for preparing the correct dosage of medication or in chemistry for reactant mixtures.

To calculate the mass percentage, follow these steps:

• First, express the percentage concentration as a decimal. This is done by dividing the given percentage by 100.
• Next, calculate the mass of the solute in each solution by multiplying the percentage in decimal form by the total mass of that solution.
• Add the masses of the solute from each solution to find the total mass of solute in the final mixture.
• Sum up the total masses of the original solutions to determine the total mass of the mixture.
• Finally, divide the total mass of solute by the total mass of the mixture and multiply the result by 100 to obtain the mass percentage of the solute in the mixture.

Applying this formula to real-life situations ensures accurate quantification of components, whether for scientific experimentation or everyday use.