Find the milli-cquivalent of : (a) \(\mathrm{Ca}(\mathrm{OH})_{2}\) in \(111 \mathrm{~g}\). (b) \(\mathrm{NaOH}\) in \(30 \mathrm{~g}\), (c) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in \(4.9 \mathrm{~g}\).

Understanding the concept of equivalent weight is essential when dealing with chemical reactions, especially in the context of stoichiometry and analytical chemistry. Simply put, equivalent weight is a measure of the reactive capacity of a molecule, atom, or ion. It is calculated based on the molar mass of a substance and reflects the mass that will combine with or replace one mole of hydrogen atoms.

The formula to determine the equivalent weight is: \[\text{Equivalent weight} = \frac{\text{Molar Mass}}{\text{Valence}} \]
In this formula, the molar mass is the mass of one mole of a substance, and valence represents the combining capacity of an element, often determined by the number of electrons it can lose, gain, or share. It's key to note that equivalent weight varies with the type of reaction the substance is involved in, as it depends on the valence, which can change in different scenarios.

For instance, in the provided exercise, to calculate the equivalent weight of \(\mathrm{Ca}(\mathrm{OH})_{2}\), we consider the valence of calcium, which is 2. This is because in a reaction, one mole of \(\mathrm{Ca}^{2+}\) would neutralize two moles of \(\mathrm{H}^{+}\) ions.

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of any substance. It is expressed in units of grams per mole (g/mol) and can be obtained by adding the atomic masses of the constituent atoms in a molecular formula. The atomic masses are sourced from the periodic table, which provides the average mass of atoms considering all isotopes.

The importance of molar mass lies in its role in converting moles to grams and vice versa, a crucial step in quantitative chemical calculations. Calculating the molar mass allows us to accurately measure substances for reactions and to convert between the mass of a substance and the number of moles, given that:
\[\text{Number of moles} = \frac{\text{Mass in grams}}{\text{Molar Mass}} \]
Using the example of \(\mathrm{NaOH}\), its molar mass is calculated by adding the atomic mass of sodium (Na), oxygen (O), and hydrogen (H). This total gives us the mass of one mole of \(\mathrm{NaOH}\), which is crucial for many laboratory calculations.

The valence of ions is a concept that reveals an ion's ability to combine with other ions or atoms. It is typically the charge of the ion, which indicates how many electrons the atom has lost or gained to form the ion. For monovalent ions, they have a valence of 1, indicating they can combine with one hydrogen atom or its equivalent. Divalent ions, with a valence of 2, can combine with two hydrogen atoms or their equivalent.

This knowledge is crucial when determining the equivalent weight of a substance and, subsequently, when calculating milliequivalents. As the valence tells us the combining power of an ion, it is a guiding factor in the stoichiometry of reactions and in balancing chemical equations. For example, the sulfate ion in \(\mathrm{H}_{2} \mathrm{SO}_{4}\) has a valence of 2 because it can donate two protons (H+ ions) in an acid-base reaction.

The term 'gram equivalents' is a stoichiometric measure used in chemistry to express how much of a substance reacts with a fixed amount (usually one mole) of another substance. It is derived from the equivalent weight and the mass of the substance in grams:
\[\text{Gram Equivalents} = \frac{\text{Mass in grams}}{\text{Equivalent Weight}} \]

Understanding gram equivalents is vital for tasks such as normalizing concentrations for titrations, where reactions depend on the number of moles that are available to react. For practical application, to find gram equivalents for a given mass, divide the mass of the substance by its equivalent weight. This value can then be easily converted to milliequivalents by multiplying by 1000, catering to finer measurements, which is precisely what is required in the steps provided for the exercise.