Question

What will be the normality of a solution obtained by mixing \(0.45 \mathrm{~N}\) and \(0.60 \mathrm{~N} \mathrm{NaOH}\) in the ratio \(2: 1\) by volume? (a) \(0.4 \mathrm{~N}\) (b) \(0.5 \mathrm{~N}\) (c) \(1.05 \mathrm{~N}\) (d) \(0.15 \mathrm{~N}\)

Short answer

The normality of the solution obtained by mixing is 0.5 N.

Step-by-step solution

Understanding the concept of Normality

Normality (N) is a measure of concentration equivalent to molarity multiplied by the equivalent factor. In the case of NaOH, which has an equivalent factor of 1 (since it provides 1 mole of OH- ions per mole of NaOH), the normality is the same as its molarity. When two solutions are mixed, the total normality can be calculated using the volumes and normalities of the individual solutions.

Calculate the volume of each solution

First, find out how much volume of each solution is being mixed. Since the ratio given is 2:1, let's assume that 2 volumes of 0.45 N solution are mixed with 1 volume of 0.60 N solution. If we take the volume unit as 'v', then the volume of the 0.45 N solution is 2v and the volume of the 0.60 N solution is v.

Calculate the equivalent of each solution

The equivalent of each solution is calculated by multiplying its normality by its volume. For the 0.45 N solution, the equivalents are 0.45 N * 2v = 0.9v. For the 0.60 N solution, the equivalents are 0.60 N * v = 0.60v.

Calculate the total equivalents and total volume

Sum the equivalents of both solutions to find the total equivalents: 0.9v + 0.60v = 1.5v. Also, sum the volumes of both solutions to find the total volume: 2v + v = 3v.

Calculate the normality of the mixed solution

To find the final normality of the solution, divide the total equivalents by the total volume. Final Normality = Total Equivalents / Total Volume = 1.5v / 3v = 0.5 N.

Key concepts

Chemical Concentration

Understanding chemical concentration is essential when working with solutions in chemistry. It helps us to describe how much of a substance, known as the solute, is contained in a certain amount of solvent (usually a liquid). Concentration can be expressed in multiple ways, with the most common units being molarity, molality, and normality.

Understanding these units can seem tricky at first, but it's comparable to learning different measurement systems like metric and imperial. For instance, you might think of molarity as the number of moles of solute per liter of solution—the scientific equivalent of specifying cups of sugar per gallon of water in a recipe. Just as bakers use different measures for different recipes, chemists choose the most appropriate unit of concentration for their work.

Normality specifically refers to the molarity of reactive units in a solution. This could include ions like H+ in an acid or OH- in a base. In practice, it's crucial to recognize not all solutes contribute equally to a chemical reaction, and that's where normality becomes an indispensable unit for chemists, adding an extra layer of precision to solution preparation and titration calculations.

Molarity and Normality

Molarity (M) and normality (N) are both measures of chemical concentration, but they have distinct meanings. Molarity is expressed as moles of solute per liter of solution (\( \text{M} = \frac{\text{moles of solute}}{\text{liters of solution}} \)). It provides insight into the strength of a solution with respect to volume, without regarding the role the solute plays in a reaction.

Normality extends the idea by considering how a substance behaves in a reaction, specifically its equivalence. Normality is defined as the number of equivalents of solute per liter of solution (\( \text{N} = \frac{\text{equivalents of solute}}{\text{liters of solution}} \)). One equivalent equals the amount of a substance that reacts with or supplies one mole of hydrogen ions (H+) in an acid-base reaction, or electrons in a redox reaction.

In the context of our exercise, sodium hydroxide (NaOH) is a base that provides one mole of OH- ions per mole of NaOH. Since it releases one equivalent per mole, the molarity and normality of NaOH are the same. Understanding this relationship is essential for accurately calculating solution concentrations and for predicting the outcomes of chemical reactions.

Solution Mixing Calculations

Solution mixing calculations involve combining two or more solutions with known concentrations to create a new solution with a desired concentration. These calculations can be performed following a straightforward method, which is relevant for everyday tasks such as diluting concentrated solutions to a usable strength or for more complex laboratory preparations.

When mixing solutions, the total volume of the mixed solution is simply the sum of the individual volumes. However, the concentration of the mixed solution – measured in normality in this context – can be determined by the concept of 'equivalents'. An equivalent is a measure that takes into account the volume and concentration (normality) of each solution being mixed. By calculating the number of equivalents from each solution (by multiplying its normality by its volume) and then adding these up, we can find the combined number of equivalents.

To get the final concentration, the total equivalents are divided by the total volume of the mixture. Implementing these steps carefully ensures accurate formulations, which is particularly important in chemical industries, pharmaceutical preparations, and laboratory experiments where precision is paramount.