Practise expressing concentrations in different ways. Express all answers to four decimal places. (a) What is \(4.000 \mathrm{~g} \mathrm{~L}^{-1}\) sodium hydroxide expressed in terms of molarity? (b) What is \(0.1\) mol \(\mathrm{L}^{-1} \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) expressed in \(g L^{-1} ?\) (c) What is \(5 \% \mathrm{v} / \mathrm{v}\) ethanol, expressed in terms of molarity? (Density of ethanol at \(\left.25^{\circ} \mathrm{C}=0.7892 \mathrm{~g} \mathrm{~mL}^{-1}\right)\) (d) What is \(150 \mathrm{mmol} \mathrm{L}^{-1}\) glucose expressed in terms of per cent concentration \((\% \mathrm{w} / \mathrm{v}) ?\)

Molarity is a key concept in chemistry that refers to the concentration of a solute in a solution. It is defined as the number of moles of a solute divided by the volume of the solution in liters. Represented by the symbol 'M', molarity is expressed as moles per liter (mol/L). To calculate molarity when given the mass of a solute and its volume in solution, one must first convert the mass into moles using the molar mass of the solute.

For a quick understanding, the formula to calculate molarity is:
\[\begin{equation} M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \end{equation}\]
In a real-world example, if you have 4 grams of sodium hydroxide in 1 liter of solution, as seen in the exercise, you would first find the moles of sodium hydroxide using its molar mass and then divide by the volume (1L) to find the molarity.

Percent concentration is another way of expressing how much solute is present in a given volume of solution. There are different ways of expressing percent concentration, including percent by weight (\[\begin{equation} \% w/w \end{equation}\]) and percent by volume (\[\begin{equation} \% v/v \end{equation}\]).

Percent by weight (\[\begin{equation} \% w/w \end{equation}\]) indicates the mass of solute in grams per 100 grams of solution. While percent by volume (\[\begin{equation} \% v/v \end{equation}\]) is the volume of solute in milliliters per 100 milliliters of solution. To convert molarity to percent concentration, you would multiply the molarity by the molar mass and the solution volume, as demonstrated in the glucose example.

Molality is another concentration term in chemistry, distinct from molarity. It's defined as the number of moles of solute per kilogram of solvent (not the solution). Represented as 'm', it is expressed in moles per kilogram (mol/kg). Unlike molarity, molality is not affected by temperature changes because it involves mass and not volume, which can expand or contract with temperature.

To calculate molality, you use the formula:
\[\begin{equation} m = \frac{\text{moles of solute}}{\text{mass of solvent in kilograms}} \end{equation}\]
This concept wasn't directly addressed in the exercises provided, but it is important to understand the difference between molarity and molality, especially when working with solutions at varying temperatures.

The concentration of a solution can also be expressed as grams per liter (g/L). This unit straightforwardly measures the amount of solute in grams that is dissolved in one liter of solvent. It's a common and simple way to describe concentration, particularly in medicine and environmental science.

The process of converting from grams per liter to another unit depends on the context. For instance, in the potassium dichromate example from the exercise, converting grams per liter to molarity involves dividing the mass of the solute in grams by its molar mass to calculate moles, and then by the volume of the solution.