Explain what changes and what stays the same when \(1.00 \mathrm{L}\) of a solution of \(\mathrm{NaCl}\) is diluted to \(1.80 \mathrm{L}\).

Understanding concentration changes during dilution is crucial while working with solutions in chemistry. When a solution, like the sodium chloride (\text{NaCl}) example given, is diluted by adding more solvent, the solute becomes more spread out throughout the increased volume. To visualize this, imagine pouring a small amount of colored syrup into a glass of water. The color represents the solute particles and is quite intense initially. When more water is added, the color (analogous to the solute concentration) becomes lighter – less intensive per unit of volume.

Mathematically, the concentration in terms of molarity, which is moles of solute per liter of solution, can be calculated using the formula: \[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\]. However, when we dilute the solution, the number of moles of solute remains constant while the liters of solution increase, hence the molarity decreases.

For our \text{NaCl} example, if we assume the original solution had a molarity of \text{M}, after dilution to 1.80 liters, the new molarity \text{M}' will be less than \text{M}, specifically: \[\text{M}' = \frac{\text{M} \times 1.00 \text{ L}}{1.80 \text{ L}}\]. This shows us that dilution leads to a decrease in the solute's concentration while maintaining the same amount of solute dispersed in a larger volume.

When performing dilutions, one key principle that is always observed is the conservation of solute, meaning that the amount (in moles) of solute remains the same before and after the dilution process. It's just like if you had a bag of sugar, and you poured it into a larger container – the amount of sugar doesn’t change, only the space it occupies does.

In our \text{NaCl} solution example, if the original 1.00 liter contained a certain number of moles of \text{NaCl}, that number would remain constant even when the volume is increased to 1.80 liters through dilution. The actual mass of \text{NaCl} doesn't change, it's only the volume it's dispersed in that changes. This can be particularly important when you're preparing a series of different concentrations for an experiment or when you're diluting a stock solution to create a working solution. The formula tying the initial and final states of a dilution is given by \[ \text{C}_1 \times \text{V}_1 = \text{C}_2 \times \text{V}_2 \], where \text{C}_1 is the initial concentration, \text{V}_1 is the initial volume, \text{C}_2 is the final concentration, and \text{V}_2 is the final volume.

Molarity is one of the most commonly used measures of concentration in chemistry. It is defined as the number of moles of a solute present in one liter of solution and it has units of moles per liter (M or mol/L). To grasp this better, think of one mole as a specific number of particles of solute – that number is Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles.

Molarity allows chemists to work with the number of particles in a solution in a convenient way, enabling calculations regarding reactions and the amount of substance needed. For example, if a solution has a molarity of 1 M, it means that every liter of this solution contains one mole of the solute. When it comes to dilutions, the molarity will change with the volume of the solution, but the total number of moles will stay the same, which is where the concept of conservation of solute connects with molarity. If the volume of the solution changes, the molarity can be recalculated by using the moles of solute and the new volume.