Question

The combination reaction of magnesium metal and bromine to form magnesium bromide is represented by the following balanced equation: $$ \mathrm{Mg}(s)+\mathrm{Br}_{2}(l) \longrightarrow \mathrm{MgBr}_{2}(l) $$ If \(1.0 \mathrm{~mol}\) of \(\mathrm{Mg}\) is mixed with \(2.0 \mathrm{~mol}\) of \(\mathrm{Br}_{2}\), and \(0.84 \mathrm{~mol}\) of \(\mathrm{MgBr}_{2}\) is obtained, what is the percent yield for the reaction?

Short answer

The percent yield of the reaction is 84%.

Step-by-step solution

Determine the theoretical yield

According to the balanced chemical equation, 1 mole of Mg reacts with 1 mole of Br2 to form 1 mole of MgBr2. So, if you start with 1.0 mole of Mg, the maximum amount of MgBr2 you can theoretically produce is also 1.0 mole.

Calculate the percent yield

The percent yield is the ratio of the actual yield to the theoretical yield, expressed as a percentage. It can be calculated using the formula: Percent yield = (Actual yield / Theoretical yield) x 100%. In this case, the actual yield is 0.84 mol of MgBr2, and the theoretical yield is 1.0 mol of MgBr2. So, the percent yield = (0.84 mol / 1.0 mol ) x 100%.

Key concepts

Chemical Reaction

Understanding chemical reactions is fundamental to grasping concepts in chemistry. A chemical reaction involves the transformation of one or more substances into new products. The reactants, in this case magnesium (\texttt{Mg}) and bromine (\texttt{Br\(_2\)}), interact during the reaction to create a new compound, magnesium bromide (\texttt{MgBr\(_2\)}).

Each reaction can be depicted by a chemical equation that not only represents the substances involved but also their quantities. For a chemical reaction to occur, reactants must be in the right proportions as dictated by stoichiometry – the calculation of reactants and products in a chemical reaction. In our example, the balanced equation \texttt{Mg(s) + Br\(_2\)(l) \rightarrow MgBr\(_2\)(l)} shows that one mole of magnesium reacts with one mole of bromine to generate one mole of magnesium bromide.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be produced from a given amount of reactants under ideal conditions. This is a crucial concept in chemistry as it sets the benchmark for the actual yield attained in an experiment. The theoretical yield is determined by using the balanced chemical equation and stoichiometry.

As seen in the exercise, the balanced reaction indicates that one mole of \texttt{Mg} would produce one mole of \texttt{MgBr\(_2\)} if you start with a sufficient amount of \texttt{Br\(_2\)}. The calculation has an implicit assumption: that everything reacts and there are no losses or side reactions. In reality, several factors prevent the full conversion of reactants to products, which is why actual yields are often less than theoretical yields. The knowledge of theoretical yield is paramount for calculating the efficiency of chemical reactions, known as the percent yield.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantities of materials consumed and produced in chemical reactions. It is derived from the Greek words 'stoicheion' (element) and 'metron' (measure). Stoichiometry is based on the law of conservation of mass, which states that in a chemical reaction, matter is neither created nor destroyed. Therefore, the total mass of the reactants must be equal to the total mass of the products.

In the context of the given exercise, stoichiometry allows us to calculate the theoretical yield by using the balanced chemical equation as a reference. The balanced equation represents the stoichiometric relationship between the reactants (\texttt{Mg} and \texttt{Br\(_2\)}) and the product (\texttt{MgBr\(_2\)}). These stoichiometric calculations are vital for understanding how much product can theoretically be made and are a significant step in optimizing chemical processes and determining the percent yield.