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.

Short answer

Two methods can be used to determine the limiting reactant and the mass of the product formed. Method 1: Comparing moles of reactants 1. Calculate molar masses of Y2 and XY. 2. Convert given grams to moles for each reactant. 3. Determine the mole ratio of reactants. 4. Divide moles of each reactant by the stoichiometric coefficients. 5. The reactant with the smallest value is the limiting reactant. 6. Use the limiting reactant's moles to calculate moles of product formed. 7. Calculate the mass of the product formed by multiplying the moles of the product by the molar mass of the product. Method 2: Comparing masses of reactants 1. Calculate molar masses of Y2 and XY. 2. Determine the mass ratio of reactants. 3. Calculate the mass of Y2 required to completely react with the given mass of XY. 4. Compare the actual mass of Y2 with the calculated mass of Y2 required to react. 5. The reactant requiring the smallest amount of the other reactant to completely react is the limiting reactant. 6. Use the mass of the limiting reactant and the mass ratio to determine the mass of the product formed.

Step-by-step solution

Method 1: Comparing Moles of Reactants

The first method uses the concept of the mole. We need to follow these steps to determine the limiting reactant and the mass of the product formed: Step 1: Calculate the molar masses of the reactants Y2 and XY. Step 2: Convert the given grams to moles for each reactant by dividing the mass of the reactant by the molar mass. Step 3: Determine the mole ratio of the reactants (based on the balanced equation). Step 4: Divide the moles of each reactant by their respective stoichiometric coefficients (mole ratio) in the balanced equation. Step 5: The reactant with the smallest value from the previous step is the limiting reactant. Step 6: Use the limiting reactant's moles to calculate the moles of the product formed. Step 7: Calculate the mass of the product formed by multiplying the moles of the product by the molar mass of the product.

Method 2: Comparing Masses of Reactants

The second method uses the mass of the reactants instead of moles. We need to follow these steps to determine the limiting reactant and the mass of the product formed: Step 1: Calculate the molar masses of the reactants Y2 and XY. Step 2: Determine the mass ratio of the reactants, based on the stoichiometry of the balanced equation and molar masses. Step 3: Calculate the mass of Y2 required to completely react with the given mass of XY using the mass ratio. Step 4: Compare the actual mass of Y2 with the calculated mass of Y2 required to react. Step 5: The reactant that requires the smallest amount of the other reactant to completely react is the limiting reactant. Step 6: Use the mass of the limiting reactant and the mass ratio to determine the mass of the product formed.

Key concepts

Stoichiometry

Stoichiometry is the study of the quantities of substances consumed and produced in chemical reactions. When we balance a chemical equation, like the generic reaction given: \( \mathrm{Y}_{2}+2 \mathrm{XY} \longrightarrow 2 \mathrm{XY}_{2} \), we establish a ratio of reactants to products. This ratio is crucial because it guides us in determining how much of each substance we need or will produce.
In the example problem, stoichiometry helps identify how much of the product \( \mathrm{XY}_{2} \) will be formed from given amounts of \( \mathrm{Y}_{2} \) and \( \mathrm{XY} \). By understanding the stoichiometric coefficients (the numbers in front of molecules in the equation), we can establish a relationship between moles of reactants and products. Stoichiometry, therefore, provides a bridge between the world of atoms and the laboratory scale, where measurable amounts of chemicals are used.

Molar Mass

Molar mass is the mass of one mole of a substance and is usually expressed in grams per mole (g/mol). It is crucial in converting between the mass of a substance and the number of moles, which helps us understand quantities in chemical reactions.
To calculate molar mass, you sum the atomic masses of all the atoms in a molecule. For example, if Y atom has an atomic mass of \(X\) g/mol, the molar mass of \( \mathrm{Y}_{2} \) would be \(2 \times X\) g/mol. Similarly, for \( \mathrm{XY} \), you would add the atomic masses of X and Y. By converting grams to moles using molar mass, you can then proceed to use stoichiometric relationships to analyze reactions.

• Molar mass allows for easy conversion between measurements of mass and the number of atoms or molecules.
• It simplifies complex calculations, making it easier to predict how much product can be made or how much reactant is needed.

Mole Ratio

Mole ratio is derived from the coefficients of substances in a balanced chemical equation. These coefficients tell us the proportionate number of moles of each reactant and product involved in the reaction.
For the given reaction, the mole ratio is \(1:2:2\), meaning 1 mole of \( \mathrm{Y}_{2} \) reacts with 2 moles of \( \mathrm{XY} \) to produce 2 moles of \( \mathrm{XY}_{2} \).
Using mole ratios, we can determine which reactant is the limiting reactant in a given chemical reaction. For example, if you have less than the stoichiometric ratio of \( \mathrm{Y}_{2} \) relative to \( \mathrm{XY} \), then \( \mathrm{Y}_{2} \) would be the limiting reactant. Therefore, mole ratios are essential in:

• Predicting the amounts of products formed.
• Identifying the limiting reactant.
• Balancing chemical equations correctly.

Chemical Reactions

Chemical reactions involve the reorganization of atoms to convert reactants into products. The balanced equation \( \mathrm{Y}_{2}+2 \mathrm{XY} \longrightarrow 2 \mathrm{XY}_{2} \) exemplifies a chemical reaction, showing how reactants are transformed into products.
In a chemical reaction, the conservation of mass dictates that the number of atoms of each element must remain the same before and after the reaction. This is why balancing equations is necessary. Not only does it help maintain mass balance, but it also helps chemists and students predict the amounts of reactants needed and products formed.
Understanding chemical reactions includes:

• Recognizing types of reactions such as synthesis, decomposition, and exchange reactions.
• Comprehending that energy change often accompanies reactions, either being absorbed or released.
• Interpreting reaction progress and identifying limiting and excess reactants.

By mastering these concepts, you can efficiently analyze and predict the outcomes of complex chemical transformations.