Question

The combination reaction of sodium metal and nitrogen gas to form sodium nitride is represented by the following balanced equation: $$ 6 \mathrm{Na}(s)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Na}_{3} \mathrm{~N}(s) $$ If \(0.30 \mathrm{~mol} \mathrm{Na}\) is mixed with \(0.60 \mathrm{~mol} \mathrm{~N}_{2}\), and \(0.092 \mathrm{~mol}\) \(\mathrm{Na}, \mathrm{N}\) is obtained, what is the percent yield for the reaction?

Short answer

The percent yield of the reaction is 92%.

Step-by-step solution

Determine the limiting reactant

The balanced chemical equation shows that 6 mol of sodium react with 1 mol of nitrogen to produce 2 mol of sodium nitride, Na3N. Given initial amounts of reactants are \(0.30 \, \mathrm{mol} \, \mathrm{Na}\) and \(0.60 \, \mathrm{mol} \, \mathrm{N}_2\), which correspond exactly to the stoichiometric ratio, neither reactant is in excess.

Calculate the theoretical yield

The stoichiometry of the reaction shows that 2 mol of sodium nitride are formed for every 6 mol of sodium that react. Therefore, for \(0.30 \, \mathrm{mol} \, \mathrm{Na}\), the amount of sodium nitride that should theoretically be formed is: \( \, \mathrm{mol} \, \mathrm{Na3N} = \, \mathrm{mol} \, \mathrm{Na} \times \frac{2 \, \mathrm{mol} \, \mathrm{Na3N}}{6 \, \mathrm{mol} \, \mathrm{Na}} = 0.30 \, \mathrm{mol} \times \frac{1}{3} = 0.10 \, \mathrm{mol}\).

Calculate percent yield

The percent yield is the actual yield divided by the theoretical yield, multiplied by 100%. With the actual yield being \(0.092 \, \mathrm{mol}\) and the theoretical yield \(0.10 \, \mathrm{mol}\), the percent yield is \( = \frac{0.092 \, \mathrm{mol}}{0.10 \, \mathrm{mol}} \times 100% = 92%\).

Key concepts

Limiting Reactant

In any chemical reaction, it's essential to determine which substance will run out first, as it limits the amount of product that can be formed. This substance is called the **limiting reactant**. Identifying the limiting reactant is crucial because it determines the maximum amount of product that can be produced in the reaction. Without knowing the limiting reactant, we cannot accurately predict how much of the product we can get.
When examining the chemical equation for the reaction between sodium (Na) and nitrogen gas (N₂) to form sodium nitride (Na₃N), we observe that 6 mol of sodium react with 1 mol of nitrogen. This gives us a ratio of 6:1. If we start with 0.30 mol of Na and 0.60 mol of N₂, both are exactly in the necessary ratio. In this case, neither is present in excess, thus no need to calculate further because neither reactant will limit the reaction based on the amount given. This is a special scenario where the reaction proceeds without a clear limiting reactant at the quantities given.

Theoretical Yield

Theoretical yield refers to the maximum amount of product that could be generated from a given amount of reactants, assuming perfect conditions with no losses or side reactions. This is calculated using the stoichiometry of the balanced chemical equation.
For the reaction between sodium and nitrogen gas, we see that 6 moles of sodium yield 2 moles of sodium nitride. Thus, if you begin with 0.30 moles of sodium, you would expect the ideal yield (theoretical yield) to be calculated as follows: \[ \text{mol}\, \mathrm{Na3N} = 0.30\, \text{mol}\, \mathrm{Na} \times \frac{2\, \text{mol}\, \mathrm{Na3N}}{6\, \text{mol}\, \mathrm{Na}} = 0.10\, \text{mol}\, \mathrm{Na3N} \]
This represents the maximum amount of sodium nitride that could be obtained under perfect reaction conditions, without any loss or inefficiencies.

Stoichiometry

Stoichiometry involves using balanced chemical equations to calculate the relationships between reactants and products in a reaction. It helps in determining how much of each ingredient is needed or will be produced.
In our example, knowing the stoichiometry of the reaction is crucial. The balanced equation \(6 \mathrm{Na} + \mathrm{N}_2 \rightarrow 2 \mathrm{Na}_3\mathrm{N}\) tells us that:

• 6 moles of Na react with 1 mole of N₂
• This produces 2 moles of Na₃N

Through stoichiometry, we can determine how much product we can create from given quantities of reactants. This includes making sure that the reactants are available in the ratio needed for the complete reaction, and no reactant is wasted when they are in exact proportions.

Chemical Reactions

A chemical reaction involves the transformation of reactants into products. It is the core process being analyzed, where chemical bonds are broken and new ones are formed. Understanding chemical reactions is crucial in predicting the outcomes of mixing substances.
For the reaction of sodium with nitrogen gas, the simple balanced equation illustrates:

• 6 Na atoms combine with 1 N₂ molecule
• This results in the formation of 2 units of Na₃N

Chemical reactions are usually represented by these equations that inform us about the quantities, in moles, of each substance involved.
Sometimes, conditions such as temperature, pressure, or catalysts can influence these reactions. It’s crucial to follow the stoichiometric ratios and the conditions given to predict and achieve efficient reactions.