If you dissolved \(11.5 \mathrm{~g}\) of \(\mathrm{NaCl}\) in \(1.00 \mathrm{~kg}\) of water, \((\mathrm{a})\) what would be its molal concentration? (b) What are the mass percent \(\mathrm{NaCl}\) and the mole percent \(\mathrm{NaCl}\) in the solution? The volume of this solution is virtually identical to the original volume of the \(1.00 \mathrm{~kg}\) of water. (c) What is the molar concentration of \(\mathrm{NaCl}\) in this solution? (d) What would have to be true about any solvent for one of its dilute solutions to have essentially the same molar and molal concentrations?

When it comes to understanding concentrations of solutions in chemistry, molality is a key concept. It tells us how many moles of a solute are present in a kilogram of solvent. Unlike molarity, molality is not affected by changes in temperature because it relies on mass, not volume.

To calculate molality, first determine the number of moles of solute in the solution. To achieve this, divide the mass of the solute by its molar mass. In the case of our exercise, we have 11.5 grams of NaCl, a common table salt. Considering the molar mass of NaCl is roughly 58.44 grams per mole, we calculate our number of moles like this: \
\[ \text{Number of moles} = \frac{11.5\,\text{g}}{58.44\,\text{g/mol}} \].

Once you have the number of moles, just divide this by the mass of the solvent in kilograms. For our example where the solvent is water weighing 1.00 kg, the molality is simply the moles of NaCl per kg of water. This straightforward formula ensures that you can quickly find the molality: \
\[ \text{Molality} (m) = \frac{\text{Number of moles of NaCl}}{\text{Mass of water in kg}} \].

Understanding and calculating molality is essential for scientists, especially when comparing solutions used in various experiments or processes where temperature may vary, as it provides a measure unaffected by external thermal conditions.

Mass percent composition is a way of expressing the concentration of an element in a compound or a component in a mixture. It is the mass of the component divided by the total mass of the mixture multiplied by 100 to get a percentage. This concept is very useful in preparing solutions and assessing their purity.

To calculate the mass percent, use the formula: \
\[ \text{Mass percent} = \left(\frac{\text{mass of the solute (NaCl)}}{\text{total mass of the solution}}\right) \times 100 \% \].

Following this approach for our exercise, where we have 11.5 grams of NaCl dissolved in 1.00 kg of water (which is 1000 grams), we sum up the mass of NaCl and water to get the total mass of the solution. Then we divide the mass of NaCl by this total mass, and multiply by 100 to achieve the mass percent. Knowing the mass percent of a solution can help with understanding the ratio of solute to solvent, which is particularly imperative when dealing with reactions where concentration plays a role in the reaction rate.

Molarity, often signified by the symbol 'M', is another widely used concentration term in chemistry that defines the number of moles of solute per liter of solution. Unlike molality, molarity is temperature dependent as it uses the volume of the solution, which can expand or contract with temperature fluctuations.

To compute molarity, divide the number of moles of the solute by the volume of the solution in liters. For instance, in the exercise we're exploring, we calculate the molarity of NaCl by considering the density of water (1.00 g/mL) to convert the mass of water to volume in liters since 1.00 kg of water is equivalent to 1.00 L of water. Thus, we use the formula: \
\[ \text{Molarity} (M) = \frac{\text{Number of moles of NaCl}}{\text{Volume of water in liters}} \].

If we wanted molar and molal concentrations to match, the solvent density would need to be precisely 1 kg/L, akin to water. This molar calculation is indispensable for chemists when mixing solutions or studying reactions in a laboratory setting where precision in the solute concentration is crucial for ensuring expected outcomes.