Problem 85 - Chemistry The Science in Context

Question

Surgical-Grade Titanium Medical implants and high-quality jewelry items for body piercings are frequently made of a material known as G23Ti, or surgical- grade titanium. The percent composition of the material is \(64.39 \%\) titanium,\(24.19 \%\) aluminum, and \(11.42 \%\) vanadium. What is the empirical formula for surgical-grade titanium?

Step-by-Step Solution

Answer

Answer: The empirical formula for surgical-grade titanium (G23Ti) is Ti₆Al₄V.

Step 1: Convert percentages to grams

Assume a 100g sample of G23Ti, we can convert the percentages directly to grams: - Titanium: \(64.39 \% * 100g = 64.39g\) - Aluminum: \(24.19 \% * 100g = 24.19g\) - Vanadium: \(11.42 \% * 100g = 11.42g\)

Step 2: Convert grams to moles

To convert the mass of each element to moles, divide the mass by the molar mass of the element (rounded to one decimal place): - Titanium: \(64.39g \div 47.9g/mol = 1.34 mol\) - Aluminum: \(24.19g \div 27.0g/mol = 0.90 mol\) - Vanadium: \(11.42g \div 50.9g/mol = 0.22 mol\)

Step 3: Find the simplest whole-number ratio

Divide the number of moles of each element by the smallest number of moles to find the ratio: - Titanium: \(1.34 mol \div 0.22 mol = 6.09 \approx 6\) - Aluminum: \(0.90 mol \div 0.22 mol = 4.09 \approx 4\) - Vanadium: \(0.22 mol \div 0.22 mol = 1.00 \approx 1\) The empirical formula for surgical-grade titanium (G23Ti) is \(\boxed{Ti_6Al_4V}\).

Key Concepts

Percent Composition

Percent composition is a concept that tells us the percentage by mass of each element in a compound. For the alloy used in surgical-grade titanium, the percent composition is given as 64.39% titanium, 24.19% aluminum, and 11.42% vanadium. To find these values, the mass of each component element in a sample is divided by the total mass of the compound, and then multiplied by 100. In this exercise, having percent compositions allows us to easily convert them into a more computationally usable form—grams. Assume you have 100 grams of the compound:

• Titanium contributes 64.39 grams
• Aluminum contributes 24.19 grams
• Vanadium contributes 11.42 grams

This simplification is useful because it allows us to move on to the next step, calculating moles.

Moles

The concept of moles is fundamental in chemistry for counting atoms, ions, or molecules. One mole is Avogadro's number, which is approximately \(6.022 \times 10^{23}\) of these particles. In this exercise, converting the mass of each element in surgical-grade titanium to moles requires the use of each element's molar mass:

• The molar mass of Titanium is about 47.9 g/mol
• For Aluminum, it's approximately 27.0 g/mol
• Vanadium has a molar mass of about 50.9 g/mol

Taking Titanium as an example, divide its mass in grams (64.39 g) by its molar mass (47.9 g/mol), yielding 1.34 moles. Converting each element to moles identifies the quantity of elements in terms more familiar to chemists and helps in finding the simplest compound ratios.

Surgical-Grade Titanium

Surgical-grade titanium, often referred to as G23Ti, is a specialized alloy designed for medical and body-related applications. It is known for being biocompatible, meaning it won't cause adverse reactions when used within the human body. This includes applications like medical implants, such as hip replacements, and high-quality jewelry for body piercings. Its composition typically involves a mix of titanium, aluminum, and vanadium, each contributing to durability, corrosion resistance, and strength:

• Titanium contributes primarily to the biocompatibility and light weight of the material
• Aluminum adds strength without excessive weight
• Vanadium provides heat stabilizing properties

This combination creates a material that is particularly suitable for surgical-grade applications due to its unique balance of properties.

Chemical Composition

Chemical composition refers to the identifiers of a material's make-up, essentially which elements and their respective amounts are present in a substance, such as surgical-grade titanium. Knowing the chemical composition is crucial for understanding how a material can be used and what properties it will exhibit. For example, our sample of surgical-grade titanium includes:

• 64.39% Titanium
• 24.19% Aluminum
• 11.42% Vanadium

Such a composition is meticulously calculated to ensure that the material maintains its structural integrity and safety for medical uses. This balance of elements dictates the empirical formula, which in this case is \( Ti_6Al_4V \), representing the simplest integer ratio of the constituent elements. Empirical formulas are crucial for chemists to communicate and understand the makeup of complex materials like alloys.