Question

For the reaction below, determine the limiting reactant for each of the initial amounts of reactants. $$2 \mathrm{Na}(s)+\mathrm{Br}_{2}(g) \longrightarrow 2 \mathrm{NaBr}(s)$$ a. \(2 \mathrm{mol} \mathrm{Na}, 2 \mathrm{mol} \mathrm{Br}_{2}\) b. \(1.8 \mathrm{mol} \mathrm{Na}, 1.4 \mathrm{mol} \mathrm{Br}_{2}\) c. \(2.5 \mathrm{mol} \mathrm{Na}, 1 \mathrm{mol} \mathrm{Br}_{2}\) d. \(12.6 \mathrm{mol} \mathrm{Na}, 6.9 \mathrm{mol} \mathrm{Br}_{2}\)

Short answer

The limiting reactants are: a. Na, b. Na, c. Br2, d. Na.

Step-by-step solution

- Understanding the Reaction

Analyze the balanced equation to determine the stoichiometric ratio of reactants, which is 2 moles of Na to 1 mole of Br2.

- Calculating Maximum Product Moles

Use the stoichiometric ratio to calculate how many moles of product (NaBr) can be produced from each given amount of reactant.

- Determining the Limiting Reactant for Set a

For 2 moles of Na, the maximum moles of NaBr is 2 moles. For 2 moles of Br2, the maximum moles of NaBr is 2*2 = 4 moles. Since Na can only produce 2 moles, it is the limiting reactant.

- Determining the Limiting Reactant for Set b

For 1.8 moles of Na, the maximum moles of NaBr is 1.8 moles. For 1.4 moles of Br2, the maximum moles of NaBr is 1.4*2 = 2.8 moles. Since Na can only produce 1.8 moles, it is the limiting reactant.

- Determining the Limiting Reactant for Set c

For 2.5 moles of Na, the maximum moles of NaBr is 2.5 moles. For 1 mole of Br2, the maximum moles of NaBr is 1*2 = 2 moles. Since Br2 can only produce 2 moles, it is the limiting reactant.

- Determining the Limiting Reactant for Set d

For 12.6 moles of Na, the maximum moles of NaBr is 12.6 moles. For 6.9 moles of Br2, the maximum moles of NaBr is 6.9*2 = 13.8 moles. Since Na can only produce 12.6 moles, it is the limiting reactant.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is derived from the Greek words 'stoiokheion' (element) and 'metron' (measure), essentially meaning the measurement of elements.

When you are baking a cake, the recipe requires specific amounts of each ingredient. Too much or too little of one ingredient can result in a cake that doesn't turn out as expected. Similarly, in chemistry, the 'recipe' for a chemical reaction is provided by a balanced chemical equation. Each reactant and product in the equation is present in a defined molar ratio. Stoichiometry allows chemists to predict the amounts of substances consumed and produced in a given reaction.

A Closer Look at Ratios

Consider the reaction '2 Na(s) + Br₂(g) → 2 NaBr(s)'. The coefficients in the balanced equation tell us that two moles of sodium react with one mole of bromine to produce two moles of sodium bromide. This 2:1:2 ratio is pivotal in determining the exact amounts of reactants needed and the amount of product that can be formed.

Chemical Reaction

A chemical reaction is the process by which substances, known as reactants, transform into different substances, known as products. During this process, reactant molecules undergo a rearrangement of atoms and bond modifications to form product molecules.

In the context of our example, '2 Na(s) + Br₂(g) → 2 NaBr(s)', sodium (Na) and bromine (Br₂) are the reactants undergoing the transformation, and sodium bromide (NaBr) is the product. To fully grasp the concept of a chemical reaction, we must appreciate that matter is conserved throughout the process. This principle is known as the Law of Conservation of Mass. The balanced chemical equation reflects this law, showing that the number of atoms of each element is the same on both sides of the reaction arrow.

Identifying Limiting Reactants

In chemical reactions, the limiting reactant is the substance that is entirely used up first, thus determining the maximum amount of product that can be formed. This concept is central when dealing with real-world applications, such as industrial production, where the efficient use of resources is crucial.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a bridge between the atomic world and the macroscopic world we interact with daily. One mole of any substance contains exactly 6.022 × 10²³ entities (atoms, molecules, ions, etc.), known as Avogadro's number.

Using the mole concept allows chemists to count particles by weighing them. We can relate the mass of a substance to the number of moles and, consequently, to the number of particles.

Connecting Moles to Limiting Reactants

In the reaction '2 Na(s) + Br₂(g) → 2 NaBr(s)', we consider the number of moles of sodium and bromine to determine which is the limiting reactant. By comparing the mole ratio of reactants to the coefficients in the balanced equation, we can identify the reactant that will be exhausted first, controlling the extent of the reaction.

Understanding the mole concept is crucial when performing stoichiometry calculations, as it enables you to convert between mass, the number of moles, and the number of particles, effectively bridging the gap between the laboratory and the theoretical aspects of chemical reactions.