Calculate the molality of each of the following aqueous solutions: (a) \(2.50 M \mathrm{NaCl}\) solution (density of solution \(=1.08 \mathrm{~g} / \mathrm{mL}),\) (b) 48.2 percent by

When it comes to the study of solutions in chemistry, understanding how to convert between different units of concentration such as molarity and molality is a must-have skill. Molarity, denoted by the symbol 'M,' is a measure of the number of moles of solute per liter of solution. Molality, indicated by 'm,' refers to the moles of solute per kilogram of solvent.

Molarity can be converted to molality by using the density of the solution. Here's the general approach: First, you need the mass of the solution – this can often be found if the density and volume of the solution are known. Then subtract the mass contributed by the solute to obtain the mass of the solvent alone. Remember, density is mass per unit volume, so by multiplying the density by the volume, you get the total mass. With the mass of the solute and the mass of the solution, you can easily calculate the mass of the solvent. Divide the moles of solute by this mass (in kilograms) to find the molality. This straightforward conversion is crucial for many laboratory and industrial applications where temperature changes might affect the solution's volume.

Solution concentration refers to the amount of solute present in a given amount of solution or solvent. There are several ways to express concentration, including molarity, molality, percent composition, and parts per million (ppm).

Why is knowing the concentration important? Accurate knowledge of concentration allows chemists to predict how substances will react together and is essential for creating desired reaction outcomes in both research and industry settings. For instance, in a chemical reaction, using a solution with the incorrect concentration can lead to incomplete reactions, side-reactions, or even hazardous conditions. Additionally, understanding different concentration terms is critical when transitioning from theoretical chemistry to practical laboratory work.

The moles of solute in a solution is a measure of the amount of a substance present. One mole is defined as the amount of substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of pure carbon-12, which is approximately 6.022 x 10^23 entities (Avogadro's number).

To calculate the moles of solute, you can use the molarity of the solution and the volume of the solution. The formula is: \[ \text{moles of solute} = \text{molarity of solution} \times \text{volume of solution (in liters)} \]
The concept of moles bridges the gap between the microscopic world of atoms and the macroscopic world that we live in, allowing chemists to carry out calculations that relate to visible amounts of materials.

The mass of solvent in a solution is the weight of the liquid or solid that is used to dissolve the solute. When calculating molality, it is important to measure the mass of the solvent rather than the total mass of the solution because molality is defined as moles of solute per kilogram of solvent.

When given the solution's total mass and the mass of the solute, as in our example, the mass of the solvent can be found by subtraction. It's important to note that the solvent mass must be expressed in kilograms (kg) when calculating molality. This is because molality is a ratio of moles to kilograms, reflecting how concentrated a solution is without being affected by temperature changes, unlike molarity, which is volume-based.