Problem 74 - Chemistry and Chemical Reactivity

Question

The elements silver, molybdenum, and sulfur combine to form \(\mathrm{Ag}_{2} \mathrm{MoS}_{4} .\) What is the maximum mass of \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\) that can be obtained if \(8.63 \mathrm{g}\) of silver, \(3.36 \mathrm{g}\) of molybdenum, and \(4.81 \mathrm{g}\) of sulfur are combined?

Step-by-Step Solution

Answer

15.40 g of \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\) can be obtained.

Step 1: Write the Chemical Equation

The chemical formula for the compound formed is \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\). This indicates that the reaction involves these elements in these proportions.

Step 2: Determine the Molar Masses

Calculate the molar mass of each element. Silver (Ag) has a molar mass of approximately 107.87 g/mol, molybdenum (Mo) has 95.95 g/mol, and sulfur (S) has 32.07 g/mol.

Step 3: Calculate the Molar Mass of \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\)

Using the molar masses determined: - Silver: \(107.87 \times 2 = 215.74 \) g/mol- Molybdenum: \(95.95 \) g/mol- Sulfur: \(32.07 \times 4 = 128.28 \) g/mol Add them to get the molar mass of \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\):\[ 215.74 + 95.95 + 128.28 = 439.97 \, \text{g/mol} \]

Step 4: Determine Moles of Each Reactant

Calculate moles of each element based on given masses:- Moles of Ag: \( \frac{8.63}{107.87} \approx 0.080 \) mol- Moles of Mo: \( \frac{3.36}{95.95} \approx 0.035 \) mol- Moles of S: \( \frac{4.81}{32.07} \approx 0.150 \) mol

Step 5: Identify Limiting Reactant

From the stoichiometry of \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\), the ratio is 2:1:4 (Ag:Mo:S). Calculate based on smallest moles per required ratio:- Theoretical moles of Ag needed by Mo: \(2 \times 0.035 = 0.070\) mol- Theoretical moles of S needed by Mo: \(4 \times 0.035 = 0.140\) molMo is the limiting reactant since it runs out first using reaction stoichiometry.

Step 6: Calculate Maximum Mass of Product

Since Mo is the limiting reactant, use its moles to determine the mass of the product:- Moles of \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\) = 0.035 mol- Calculate mass: \(0.035 \times 439.97 = 15.399\, \text{g} \)

Step 7: Confirm and State the Result

Since molybdenum determines the yield, the maximum mass of \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\) that can be obtained is approximately 15.40 g.

Key Concepts

Stoichiometry

Stoichiometry is like the recipe for a chemical reaction. It tells you how much of each ingredient, or reactant, you need to make a specific amount of product.
In our exercise, we're combining silver, molybdenum, and sulfur to form the compound Ag2MoS4. Stoichiometry describes the ratio of these elements in the chemical reaction. This ratio is directly derived from the compound's formula:

• 2 atoms of silver (Ag)
• 1 atom of molybdenum (Mo)
• 4 atoms of sulfur (S)

This means, for every 2 moles of silver, you need 1 mole of molybdenum and 4 moles of sulfur. It's important to find out how these ratios apply to our given amount of each element to determine how much of the product we can make.
When you find a limiting reactant, you use stoichiometry to see which reactant runs out first and stops more product from forming. In this example, the stoichiometry reveals that molybdenum is the limiting reactant.

Molar Mass Calculation

Understanding molar mass is crucial when you want to know how much of a compound you can make in a chemical reaction. Molar mass is the weight of one mole of a substance. It's calculated by summing up the atomic masses of all atoms in a molecule.
Consider Ag2MoS4, which is the compound in our example:

• Silver (Ag) has a molar mass of 107.87 g/mol, and there are two Ag atoms in the compound. So, for silver: \[ 107.87 imes 2 = 215.74 ext{ g/mol} \]
• Molybdenum (Mo) has only one atom, with a molar mass of 95.95 g/mol.
• Sulfur (S) has four atoms, with a molar mass of 32.07 g/mol each, so for sulfur: \[ 32.07 imes 4 = 128.28 ext{ g/mol} \]

Adding these together, the total molar mass of Ag2MoS4 is \[ 215.74 + 95.95 + 128.28 = 439.97 ext{ g/mol} \]
This calculation helps us understand how many grams of the compound can be produced from a mole of its reactants.

Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction, showing the reactants and the products they form. It's like a map to follow during a reaction, showing not only what goes in and comes out but also in what proportions.
In our example, the chemical formula for the formation of Ag2MoS4 was given. This formula effectively forms the basis of our chemical equation. The reaction can be simplified to ensure understanding:

• Reactants: 2Ag + Mo + 4S
• Product: Ag2MoS4

This equation not only identifies that silver, molybdenum, and sulfur are combining but also shows the exact proportion needed: 2 silvers, 1 molybdenum, and 4 sulfurs make 1 part of Ag2MoS4.
Understanding this equation also means understanding changes in mass as the reaction progresses, and how much product is expected. This is crucial when working through stoichiometry or when identifying limiting reactants in a chemical reaction.