Calculate normality of \(\mathrm{NH}_{4} \mathrm{OH}\) when \(2 \mathrm{~g}\) is present in \(800 \mathrm{~mL}\) solution. Also calculate its molarity.

Understanding molar mass is essential when dealing with various chemical calculations. Molar mass is the weight of one mole (or Avogadro’s number, which is approximately 6.022 \( \times \) 10^23 particles) of a substance expressed in grams per mole (g/mol). To calculate the molar mass, you sum up the atomic masses of each element in a compound, based on its molecular formula.

For example, ammonium hydroxide \( (NH_4OH) \) contains nitrogen (N), hydrogen (H), and oxygen (O). With the atomic masses for these given as 14.01 g/mol for nitrogen, 1.01 g/mol for each hydrogen atom, and 16.00 g/mol for oxygen, the calculation for the molar mass of \( NH_4OH \) is:

\[ M = 14.01 + 4(1.01) + 16.00 = 35.05 \text{ g/mol} \]

This step is fundamental as it sets the stage for most quantitative aspects in stoichiometry.

The mole concept is central to understanding stoichiometry and solution chemistry. A mole represents a specific number of entities, exactly 6.022 \( \times \) 10^23, which is Avogadro's number. This concept allows chemists to count particles by weighing them. Moles link the microscopic world of atoms and molecules to the macroscopic world that we can measure.

When given a certain mass of a substance, you can calculate the number of moles by dividing the mass by the molar mass of the substance, as seen in the following formula:

\[ n = \frac{mass}{molar \ mass} \]

For a 2 g sample of \( NH_4OH \), with a molar mass of 35.05 g/mol, you would have approximately 0.057 moles of \( NH_4OH \). This relates the mass of ammonium hydroxide to a quantity we can use in further calculations involving its concentration.

The concentration of a solution describes how much solute is dissolved in a certain amount of solvent. Molarity (M) is one of the most commonly used measures of concentration, defined as the number of moles of a solute per liter of solution.

The formula for molarity is:

\[ M = \frac{n}{V(\text{in liters})} \]

Turning to our example, we would determine the molarity of a 2 g \( NH_4OH \) solution present in 800 mL of water by firstly converting the volume to liters (0.8 L). Then, dividing the moles of solute (0.057 moles) by the volume yields the molarity:

\[ M = \frac{0.057 \text{ moles}}{0.8 \text{ L}} = 0.07125 \text{ M} \]

Knowing how to calculate solution concentration is key to many applications in chemistry, including titration and chemical reactivity.

Stoichiometry is the heart of the quantitative relationships in chemistry. It involves using balanced chemical equations to determine the proportions of reactants and products in a chemical reaction. Fundamental to stoichiometry is the concept of the mole, as it allows for predicting volumes, masses, and number of entities involved in a chemical reaction.

When we refer to the normality (N) of a substance like \( NH_4OH \), it's often about a specific reaction, based on the equivalent concept. When ammonium hydroxide is in solution, it can donate one hydroxide ion \( (OH^-) \). The normality, in this case, equals the molarity because it is monoprotic (has only one ion to donate). Thus, with a molarity of 0.07125 M, the normality is also 0.07125 N.

Understanding stoichiometry is crucial not just for basic chemical calculations but also for practical laboratory work and industrial chemical processes.