Question

Consider the following generic reaction: $$ \mathrm{Y}_{2}+2 \mathrm{XY} \longrightarrow 2 \mathrm{XY}_{2} $$ In a limiting reactant problem, a certain quantity of each reactant is given and you are usually asked to calculate the mass of product formed. If \(10.0 \mathrm{~g}\) of \(\mathrm{Y}_{2}\) is reacted with \(10.0 \mathrm{~g}\) of \(\mathrm{XY}\), outline two methods you could use to determine which reactant is limiting (runs out first) and thus determines the mass of product formed. A method sometimes used to solve limiting reactant problems is to assume each reactant is limiting and then calculate the mass of product formed from each given quantity of reactant. How does this method work in determining which reactant is limiting?

Short answer

There are two methods to determine the limiting reactant: Method 1: Determine the moles of each reactant and compare their mole ratios: 1. Moles of Y2 = Mass of Y2 / MY2 2. Moles of XY = Mass of XY / MXY 3. Compare the ratios (Y2 moles)/1 : (XY moles)/2. The reactant with the smaller amount in the comparison is the limiting reactant. Method 2: Calculate the theoretical product mass from each reactant: 1. Assume each reactant is limiting separately and calculate the mass of XY2 formed for each. 2. Compare the masses of XY2 formed in both scenarios: XY2 mass from Y2 : XY2 mass from XY. The scenario with a smaller amount of product is the correct one, and the limiting reactant determines the maximum amount of product that can be formed in a reaction. The method that assumes each reactant is limiting is effective in determining the limiting reactant, as it allows us to identify the limiting reactant based on the outcome of the product formation.

Step-by-step solution

Method 1 - Determine Moles of Reactants and Compare Mole Ratio

First, we have to determine the moles of each reactant using the given masses and their molar masses. Assume the molar mass of Y2 is MY2 and the molar mass of XY is MXY. Moles of Y2 = Mass of Y2 / MY2 Moles of XY = Mass of XY / MXY Next, we have to compare the mole ratios of Y2 and XY with the mole ratios given in the balanced chemical equation. For every mole of Y2, two moles of XY are required for the reaction. So, we can divide the moles of Y2 by one and the moles of XY by two and compare: (Y2 moles)/1 : (XY moles)/2 The reactant with the smaller amount in the mole ratio comparison is the limiting reactant.

Method 2 - Calculate Theoretical Product Mass From Each Reactant

In this method, we assume each reactant is limiting separately and calculate the mass of the product XY2 formed when each reactant runs out: a) Assuming Y2 is limiting, we calculate the mass of XY2 formed using stoichiometry: Moles of Y2 = Mass of Y2 / MY2 XY2 mass from Y2 = Moles of Y2 * (2 * MXY2) b) Assuming XY is limiting, we calculate the mass of XY2 formed: Moles of XY = Mass of XY / MXY XY2 mass from XY = Moles of XY * (MXY2) Compare the mass of the product formed in both scenarios: XY2 mass from Y2 : XY2 mass from XY The scenario that gives a smaller amount of product is the correct one, because the limiting reactant determines the maximum amount of product that can be formed in a reaction.

Effectiveness of the Assumed Limiting Reactant Method

The method discussed in Method 2 where each reactant is assumed to be limiting separately is effective in determining the limiting reactant because by calculating the mass of the product formed in each scenario, it compares which reactant produces a lower amount of the product. Since the limiting reactant determines the maximum amount of product that can be formed, this approach allows us to identify the limiting reactant based on the outcome of the product formation.

Key concepts

Mole Ratio

The mole ratio is a key concept in the realm of chemistry, particularly in reactions. A balanced chemical equation showcases the exact proportion of reactants to products in a reaction. These proportions are expressed through coefficients in the equation, known as the 'mole ratio'.
For example, in the reaction \(\mathrm{Y}_{2} + 2 \mathrm{XY} \longrightarrow 2 \mathrm{XY}_{2}\), the coefficients tell us that:

• One mole of \(\mathrm{Y}_{2}\) reacts with two moles of \(\mathrm{XY}\)
• This produces two moles of \(\mathrm{XY}_{2}\)

Understanding the mole ratio allows a chemist to predict how much reactant is needed, or how much product can be made from given reactants. It is essential to compare the actual moles you have, to the moles required as shown by the mole ratio, to find which reactant might be limiting.

Stoichiometry

Stoichiometry is the methodical approach used in chemistry to calculate the quantities of reactants and products involved in a chemical reaction. It relies heavily on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction.
By using stoichiometry, you can determine the amount of product that will form from given amounts of reactants. This involves using the balanced chemical equation to set up a dimensional analysis using the mole ratio.
For example, if we need to find out how much \(\mathrm{XY}_{2}\) is produced from \(10 \mathrm{~g}\) of \(\mathrm{Y}_{2}\) and \(10 \mathrm{~g}\) of \(\mathrm{XY}\), stoichiometry guides us by showing how to convert these masses to moles, compare to the balanced equation, and calculate the resulting mass of the product.

Theoretical Yield

The theoretical yield is the amount of product expected to form when the limiting reactant is completely used up, assuming perfect reactions without any losses. It establishes a benchmark of the maximum amount of product possible from given quantities of reactants.
Using the mole ratio from the balanced equation, theoretical yield calculations allow you to predict how much product can form. The calculations involve converting all reactants' masses to moles and then using the stoichiometry of the reaction to determine the number of moles of product that can form if the reaction were 100% efficient.
This concept is crucial in assessing the efficiency and feasibility of chemical reactions in both laboratory and industrial processes.

Moles Calculation

Calculating moles is a fundamental task in chemistry, required often in stoichiometric calculations, as it helps relate the mass of a substance to the number of particles or entities it contains. The conversion formula used is:

• Moles of a substance = Mass of the substance / Molar mass of the substance

For instance, to find the moles of \(\mathrm{Y}_{2}\) in our example, you'd divide \(10.0 \mathrm{~g}\) by its theoretical molar mass \(M_{\mathrm{Y}_{2}}\). This conversion is crucial because reactions at the molecular level occur in fixed ratios of molecules or moles, not necessarily in terms of mass.
Understanding how to convert mass to moles allows for accurate predictions and comparisons in chemical reactions, facilitating the identification of limiting reactants and enabling the calculation of theoretical yields.