Problem 81 - Chemistry and Chemical Reactivity

Question

Calculate the mass percent of copper in CuS, copper(II) sulfide. If you wish to obtain \(10.0 \mathrm{g}\) of copper metal from copper(II) sulfide, what mass of CuS (in grams) must you use?

Step-by-Step Solution

Answer

Mass percent of copper in CuS is 66.44%; need 15.06 g of CuS.

Step 1: Find the molar mass of CuS

To find the molar mass of \( \text{CuS} \), we need to add the atomic masses of copper (Cu) and sulfur (S). The atomic mass of Cu is approximately \(63.55 \text{ u}\), and for S it is \(32.07 \text{ u}\). Therefore, the molar mass of \( \text{CuS} \) is \(63.55 + 32.07 = 95.62 \text{ g/mol}\).

Step 2: Calculate the mass percent of copper in CuS

The mass percent of copper in \( \text{CuS} \) is given by the ratio of the mass of copper to the molar mass of \( \text{CuS} \) multiplied by 100. Thus, the mass percent is \( \left( \frac{63.55}{95.62} \right) \times 100 = 66.44\%\).

Step 3: Use mass percent to find required CuS mass

Let \( m \) be the mass of \( \text{CuS} \) needed. Since \(66.44\%\) of \( \text{CuS} \) is copper by mass, then \(0.6644 \times m = 10.0 \text{ g} \). Solving for \( m \), we have \( m = \frac{10.0}{0.6644} \approx 15.06 \text{ g} \).

Key Concepts

Copper(II) Sulfide

Copper(II) sulfide, represented by the chemical formula \( \text{CuS} \), is a compound formed by the combination of copper (Cu) and sulfur (S). In this compound, copper exhibits a +2 oxidation state, which is why it is specified as copper(II). In simple terms, one unit of CuS consists of one copper atom and one sulfur atom bonded together.

• Used in various applications, including the production of copper metal.
• Commonly found in nature as the mineral covellite.
• Appears as a dark grey or black solid.

Understanding CuS is crucial as it provides a foundational example of stoichiometry, where the number and type of atoms in a compound are considered to calculate various properties, like mass percent composition.

Molar Mass Calculation

To solve any chemistry problem involving mass, it’s important to understand molar mass. The molar mass of a compound is the mass of one mole of its molecules or formula units and is expressed in grams per mole \( \text{g/mol} \).

Steps to Calculate Molar Mass

To find the molar mass of copper(II) sulfide (CuS), follow these straightforward steps:1. **Identify the Atomic Mass of Each Element**: Look up the atomic masses on the periodic table. Copper has an atomic mass of approximately 63.55 u, and sulfur is around 32.07 u.2. **Add the Atomic Masses**: Since CuS is made up of one atom each of copper and sulfur, add their atomic masses: \[ 63.55 + 32.07 = 95.62 \text{ g/mol} \]Data from the periodic table is essential when calculating molar masses. This value is essential for subsequent calculations, such as determining mass percentages or performing stoichiometric conversions.

Stoichiometry

Stoichiometry is one of the crucial concepts in chemistry. It involves quantitative relationships between reactants and products in chemical reactions. Here, it applies to calculating the mass percent of copper in copper(II) sulfide and determining how much CuS is needed to get a specific amount of copper.

Key Steps in Stoichiometry

• **Perform Calculations Using Molar Mass**: As seen in the exercise, both molar mass and stoichiometry are needed to find the mass percent of an element in a compound.
• **Convert Mass to Mole**: Use the relationship defined by molar mass unless specified otherwise.
• **Use Ratios**: For example, if 66.44% of CuS is copper by mass, use this ratio to separate out or calculate the amount required for reactions.

Understanding stoichiometry allows chemists and students alike to predict the outcomes of reactions and necessary quantities of reactants, ensuring efficient laboratory work and industrial processes.

Chemistry Problem-Solving

In chemistry, problem-solving often involves tackling exercises through a series of logical steps.

Practical Steps for Solving Chemistry Problems

Different problems can often be solved by breaking them down into simpler components. Here's how you do it with the given task:1. **Understand the Problem**: Clearly define what is being asked—like determining the mass of CuS needed for a given amount of copper.2. **Calculate Molar Mass**: Find the molar mass, as shown in the previous steps. 3. **Use Formulas Appropriately**: For instance, use the percentage formula for mass percent— \[ \text{mass percent} = \left( \frac{\text{mass of element in the compound}}{\text{molar mass of the compound}} \right) \times 100 \]4. **Solve for the Unknown**: Rearrange your formed equation to find the unknown variable, like the mass of CuS.Effective chemistry problem-solving blends conceptual understanding with practical tools like formulae and calculations. The mastery over these techniques leads to accurate experimentations and insightful learning experiences.