Outline the steps needed to determine the limiting reactant when 0.50 mol of \(\mathrm{Cr}\) and \(0.75 \mathrm{mol}\) of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) react according to the following chemical equation. \(2 \mathrm{Cr}+2 \mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow 2 \mathrm{CrPO}_{4}+3 \mathrm{H}_{2}\) Determine the limiting reactant.

When dealing with chemical reactions, a balanced chemical equation serves as the recipe that tells us exactly how reactants combine to form products. Achieving a balanced equation means that the number of atoms for each element is conserved from reactants to products, adhering to the law of conservation of mass.

To visualize this, consider a simple cooking analogy: if a cake recipe requires one egg for every cup of flour, then having three cups of flour necessitates three eggs to maintain the ratio. Similarly, the chemical equation from our exercise, \(2 \mathrm{Cr} + 2 \mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow 2 \mathrm{CrPO}_{4} + 3 \mathrm{H}_{2}\),indicates that two moles of chromium (\(\mathrm{Cr}\)) react with two moles of phosphoric acid (\(\mathrm{H}_{3} \mathrm{PO}_{4}\)) to produce the corresponding products. It is vital to ensure the equation is balanced before proceeding with any calculations; otherwise, we may end up with inaccurate interpretations of the reaction.

The mole ratio is derived from the coefficients of a balanced chemical equation and it tells us the proportions in which substances react or are produced. The concept of mole ratio is crucial because it allows us to quantify the amount of reactants used and products formed.

Using the previous cake analogy, if for every 1 egg (representing \(\mathrm{Cr}\)), you need 1 cup of flour (representing \(\mathrm{H}_{3} \mathrm{PO}_{4}\)), the egg to flour mole ratio is 1:1. Similarly, in our exercise, the 1:1 mole ratio between \(\mathrm{Cr}\) and \(\mathrm{H}_{3} \mathrm{PO}_{4}\) means that each mole of chromium will react with exactly one mole of phosphoric acid.

To apply this concept, you would calculate the expected moles of one reactant, given the moles of the other reactant present. If the exercise provides 0.50 mol of \(\mathrm{Cr}\), you'd expect to need an equal amount of \(\mathrm{H}_{3} \mathrm{PO}_{4}\), which is also 0.50 mol, to completely react according to our 1:1 mole ratio.

Stoichiometry is the section of chemistry that deals with the calculation of reactants and products in chemical reactions. The concept is a cornerstone in understanding how reactions proceed and predicting the amounts of products formed.

Within stoichiometry, one must often identify the limiting reactant. This is the substance that will be completely used up first during the chemical reaction and thus determines the amount of product that can be formed. It is similar to running out of eggs when making multiple cakes; you can only produce as many cakes as the number of eggs allows, regardless of how much flour you have left.

In the context of our exercise, chromium (\(\mathrm{Cr}\)) was identified as the limiting reactant because there was not enough of it to fully react with the available phosphoric acid (\(\mathrm{H}_{3} \mathrm{PO}_{4}\)). Consequently, \(\mathrm{Cr}\) dictates the maximum amount of product that can be formed. Through stoichiometry, once the limiting reactant is identified, we're able to calculate the theoretical yield of a reaction, which is essential for planning and optimization in chemical processes.