Problem 45 - Chemistry and Chemical Reactivity

Question

Calculate the weight 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 the sulfide (in grams) must you use?

Step-by-Step Solution

Answer

You need approximately 15.05 g of CuS to get 10.0 g copper.

Step 1: Calculate Molar Mass of CuS

First, determine the molar mass of copper(II) sulfide, \( \text{CuS} \). The atomic mass of copper (Cu) is approximately \( 63.55 \text{ g/mol} \) and that of sulfur (S) is approximately \( 32.07 \text{ g/mol} \). Adding these gives the molar mass of \( \text{CuS} \): \( 63.55 + 32.07 = 95.62 \text{ g/mol} \).

Step 2: Calculate Weight Percent of Copper in CuS

The weight percent of an element is calculated using the formula: \( \text{Weight percent} = \left(\frac{\text{mass of element in 1 mole of compound}}{\text{molar mass of compound}}\right) \times 100\%. \) For copper in \( \text{CuS} \), this is \( \left(\frac{63.55}{95.62}\right) \times 100\% \approx 66.46\% \).

Step 3: Calculate Mass of CuS Needed for 10.0 g of Copper

To find the mass of \( \text{CuS} \) required to obtain \( 10.0 \text{ g} \) of copper, use the weight percent of copper from Step 2. Set up the equation: \( \, 0.6646 = \frac{10.0}{x} \, \), where \( x \) is the mass of \( \text{CuS} \). Solve for \( x \): \( x = \frac{10.0}{0.6646} \approx 15.05 \text{ g}\).

Key Concepts

Molar Mass

To understand any stoichiometry problem, it is vital to grasp the concept of molar mass. The molar mass gives us the mass of one mole of a substance and is a crucial stepping stone in chemistry. In our example with copper(II) sulfide (CuS), the molar mass is the sum of the atomic masses of its constituent elements.

The atomic mass of copper (Cu) is approximately 63.55 g/mol. Sulfur (S) has an atomic mass of about 32.07 g/mol. By adding these atomic masses together, we get the total molar mass of CuS: 63.55 + 32.07 = 95.62 g/mol.

• Importance: Knowing the molar mass of a compound is essential for converting between grams and moles, a fundamental process in stoichiometry.
• Application: It helps determine how much of a reactant is needed or how much product can be produced.

Understanding how to calculate molar mass allows you to work through many types of chemical problems with ease.

Weight Percent

Weight percent is an essential concept in analyzing chemical compounds. It tells us the percentage of a specific element’s mass in relation to the total mass of the compound. In the case of CuS, we wanted to find the weight percent of copper.

The formula for calculating weight percent is: \[\text{Weight percent} = \left(\frac{\text{mass of element in 1 mole of compound}}{\text{molar mass of compound}}\right) \times 100\%\] Applying this to copper in CuS gives: \(\left(\frac{63.55}{95.62}\right) \times 100\% \approx 66.46\%\).

• Purpose: Weight percent provides insight into how much of an element is present in a compound.
• Benefit: It is particularly useful in converting between mass and moles in chemical calculations.
• Example: In our exercise, the weight percent helped determine how much CuS is required to obtain a desired amount of copper.

Mastering calculations for weight percent can simplify and solve a variety of practical problems in chemistry.

Copper(II) Sulfide

Copper(II) sulfide, written as CuS, is an intriguing compound primarily composed of copper and sulfur. This compound is seen often in chemistry due to its interesting properties and reactions. Understanding its composition and applications can illuminate many stoichiometric principles.

CuS consists of one copper atom and one sulfur atom in each unit. It is a naturally occurring mineral known as covellite.

• Relevance: CuS is an ideal example to illustrate basic stoichiometric calculations including molar mass and weight percent.
• Example Calculation: Using copper's role in CuS, calculating molar masses and weight percents becomes straightforward.
• Importance: Compounds like CuS provide a gateway to understanding how elements interact to form more complex substances.

Delving into compounds like CuS with stoichiometric calculations aids in comprehending broader chemistry concepts.