Question

Determine the composition of each vanadium alloy. a.One-half of the \(\mathrm{V}\) atoms are replaced by Cr atoms. b.One-fourth of the \(\mathrm{V}\) atoms are replaced by Fe atoms. c.One-fourth of the \(\mathrm{V}\) atoms are replaced by \(\mathrm{Cr}\) atoms, and one-fourth of the \(\mathrm{V}\) atoms are replaced by Fe atoms.

Short answer

a. Alloy composition: 50% V, 50% Cr. b. Alloy composition: 75% V, 25% Fe. c. Alloy composition: 50% V, 25% Cr, 25% Fe.

Step-by-step solution

Understanding the composition for alloy (a)

In alloy (a), one-half of the vanadium (V) atoms are replaced by chromium (Cr) atoms. If we assume there are 100 vanadium atoms to start with for simplicity, then 50 vanadium atoms are replaced by chromium. Therefore, the alloy consists of 50 V atoms and 50 Cr atoms.

Calculating the composition for alloy (b)

In alloy (b), one-fourth of the vanadium (V) atoms are replaced by iron (Fe) atoms. Assuming the starting number of vanadium atoms to be 100 again, 25 vanadium atoms are replaced by iron. The resulting alloy is composed of 75 V atoms and 25 Fe atoms.

Determining the composition for alloy (c)

In alloy (c), there are two substitutions taking place: one-fourth of the V atoms are replaced by Cr, and another one-fourth by Fe. Starting with 100 V atoms, 25 are replaced by Cr and another 25 by Fe. This leaves us with 50 V atoms, 25 Cr atoms, and 25 Fe atoms in the alloy.

Key concepts

Stoichiometry

Stoichiometry plays a critical role in understanding chemical equations and the relationships between reactants and products. It is the branch of chemistry that deals with the quantitative aspects of chemical reactions. In the context of vanadium alloys, stoichiometry allows us to determine the precise amounts of different elements that combine to form the final product.

For instance, in a vanadium alloy where one-half of the vanadium (V) atoms are replaced by chromium (Cr) atoms, stoichiometry helps quantify this transformation. Assuming an initial amount of 100 vanadium atoms, we know through stoichiometric calculations that 50 of those atoms will be replaced with chromium, giving us a 1:1 ratio of vanadium to chromium atoms in the final alloy composition. This straightforward proportion highlights how stoichiometry aids in predicting the composition of alloys and understanding the underlying atomic relationships.

Chemical Substitution

Chemical substitution refers to the process where one type of atom or group of atoms in a compound is replaced by another. This concept is vital in material science and chemistry, especially when designing alloys with specific properties. Substitution can significantly alter the physical and chemical characteristics of the end material.

In our alloy examples, various proportions of vanadium atoms are substituted by other metals. Alloy (a) sees a direct 1:1 substitution, where for every two vanadium atoms, one is replaced by a chromium atom. In contrast, alloy (b) involves a different ratio where only one out of four vanadium atoms is substituted with an iron atom. These substitutions result in altered compositions and potential changes in the alloy's properties such as strength, resistance to corrosion, and ductility. Understanding the principles of chemical substitution thus equips students with the ability to predict how alterations at the atomic level can impact material characteristics.

Alloy Calculations

Alloy calculations are essential for determining the composition of a metal alloy, which is a mixture of two or more metallic elements. In the exercises provided, the alloy calculations are simplified by starting with a base number of atoms, typically 100, to avoid working with complex atomic weights and the Avogadro's number. This approach makes it easier to understand the ratios and proportions in the alloy.

For the given vanadium alloy scenarios, the calculations demonstrate the step-by-step process for each substitution case. Knowing how to perform these alloy calculations is pertinent for students studying material science or chemistry. The ability to compute the exact proportions of elements in an alloy informs decisions regarding the manufacturing and application of the alloy in real-life scenarios, such as in aerospace or medical industries. Adequate knowledge in alloy calculations sets the foundation for creating materials with desirable properties, customized for specific technical requirements.