Nitrogen and fluorine react to form nitrogen trifluoride according to the balanced chemical equation \(\mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \rightarrow 2 \mathrm{NF}_{3}(g)\) For each of the following reaction mixtures, choose the limiting reactant: (a) \(0.50 \mathrm{~mol} \mathrm{~N}_{2}(g)\) and \(0.50 \mathrm{~mol} \mathrm{~F}_{2}(g)\) (b) \(12.0 \mathrm{~mol} \mathrm{~N}_{2}(g)\) and \(20.0 \mathrm{~mol} \mathrm{~F}_{2}(g)\) (c) \(2.5 \mathrm{~mol} \mathrm{~N}_{2}(g)\) and \(7.5 \mathrm{~mol} \mathrm{~F}_{2}(g)\) (d) 100 molecules \(\mathrm{N}_{2}(g)\) and 500 molecules \(\mathrm{F}_{2}(g)\) (e) \(5.00 \mathrm{~g} \mathrm{~N}_{2}(g)\) and \(15.0 \mathrm{~g} \mathrm{~F}_{2}(g)\) (f) \(20.0 \mathrm{mg} \mathrm{N}_{2}(g)\) and \(70.0 \mathrm{mg} \mathrm{F}_{2}(g)\)

Stoichiometry is the mathematical relationship between reactants and products in a chemical reaction. Imagine it as a recipe in cooking: to make a specific dish, you need certain proportions of ingredients. Similarly, to produce a certain amount of a chemical product, precise amounts of reactants must be combined in defined ratios.

For instance, the simple act of baking can teach us stoichiometry. Consider baking cookies that require 2 cups of sugar for every 3 cups of flour. If you have 4 cups of sugar and 3 cups of flour, sugar is in excess, and flour limits how many cookies you can make. This is exactly how stoichiometry works in chemistry, but instead of cups, we use moles, a unit measuring the number of particles in a substance.

Chemical reactions are processes that transform one or more substances into different substances. It's essential to understand that these transformations are governed by specific laws, the most fundamental being the conservation of mass. This means that in a chemical reaction, atoms are neither created nor destroyed; they are merely rearranged.

The balanced chemical equation \(\mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \rightarrow 2 \mathrm{NF}_{3}(g)\) provides a clear picture of this principle. For every one molecule of nitrogen gas \(\mathrm{N}_{2}(g)\), it requires three molecules of fluorine gas \(\mathrm{F}_{2}(g)\) to produce two molecules of nitrogen trifluoride \(\mathrm{NF}_{3}(g)\). The equation is balanced; it respects the law of conservation of mass by ensuring that the number of atoms of each element remains unchanged from reactants to products.

The mole-to-mole ratio is a crucial concept in stoichiometry. It defines how many moles of one substance will react with or produce a certain number of moles of another substance.

To visualize this, imagine placing marbles (representing moles of a substance) on a scale to balance against marbles of another substance according to the ratio given by a chemical equation. In the reaction between nitrogen and fluorine, the mole-to-mole ratio is 1:3, meaning one mole of nitrogen reacts with three moles of fluorine to produce a predictable amount of the product.

Revisiting the Cookie Analogy

Returning to the cookie analogy, if the recipe (chemical equation) specifies 2 cups of sugar for 3 cups of flour (mole-to-mole ratio), and you only have 3 cups of sugar and 2 cups of flour, you won't have the right ratio to make a full batch of cookies. Similarly, when you have 0.50 mol of \(\mathrm{N}_{2}(g)\) and 0.50 mol of \(\mathrm{F}_{2}(g)\), you cannot produce the maximum amount of \(\mathrm{NF}_{3}(g)\) because you are limited by the amount of fluorine available, just as you would be limited by the amount of flour in your cookies.