Question

Calculate the relative number of atoms of each element contained in each of the following alloys: (a) coinage cupronickel, which is \(25 \%\) Ni by mass in copper; (b) a type of pewter that is about \(7 \%\) antimony and \(3 \%\) copper by mass in tin.

Short answer

For cupronickel, the relative number of atoms is based on the number of moles calculated from 25% Ni and 75% Cu. For pewter, the relative number of atoms is based on 7% Sb, 3% Cu, and 90% Sn by mass.

Step-by-step solution

Understand the Composition of Cupronickel

Cupronickel is a copper-nickel alloy with 25% nickel by mass, which means that in every 100 grams of cupronickel, there are 25 grams of nickel and 75 grams of copper.

Calculate Moles of Nickel and Copper in Cupronickel

Using the atomic masses of nickel and copper, calculate the number of moles of each metal in 100 grams of the alloy. Number of moles is given by the formula: moles = mass (g) / atomic mass (g/mol). For nickel (Ni), atomic mass = 58.69 g/mol; for copper (Cu), atomic mass = 63.55 g/mol.

Find the Relative Number of Atoms in Cupronickel

The relative number of atoms is calculated by dividing the number of moles of each element by the smallest number of moles obtained for either element. This gives a ratio that shows the relative number of atoms of nickel to copper in the alloy.

Understand the Composition of Pewter

Pewter in this case consists of 7% antimony and 3% copper by mass in tin. In 100 grams of this pewter, there are 7 grams of antimony, 3 grams of copper, and the rest is tin.

Calculate Moles of Antimony, Copper, and Tin in Pewter

Use the atomic masses to calculate the moles for antimony (Sb), copper (Cu), and tin (Sn). Use the same formula: moles = mass (g) / atomic mass (g/mol). Atomic masses are Sb: 121.76 g/mol, Cu: 63.55 g/mol, Sn: 118.71 g/mol.

Find the Relative Number of Atoms in Pewter

Calculate the relative number of atoms for each metal in pewter by dividing the number of moles of each element by the smallest number of moles obtained among Sb, Cu, and Sn, to find the ratio among them.

Key concepts

Mole Calculations

Understanding mole calculations is pivotal in chemistry, particularly when analyzing substances and their components. In essence, a mole represents Avogadro's number (\(6.022 \times 10^{23}\) atoms, molecules, or ions), which is a standard unit of measurement in chemistry. When dealing with mole calculations, the basic formula to remember is moles = mass (g) / atomic mass (g/mol). This formula allows us to convert grams into moles, providing a basis for comparison between different elements or compounds.

For instance, if we take the cupronickel alloy example and have 25 grams of nickel, we would divide that mass by the atomic mass of nickel to find the number of moles. Similar calculations would be performed for copper in the alloy, offering a direct comparison of the quantity in terms of atoms, not mass. This approach simplifies the comparison because each mole of different substances contains the same number of atoms, irrespective of their individual atomic masses.

Practical Application of Mole Calculations

When you've calculated the moles of the individual elements of an alloy, these mole values can be compared directly to understand the substance's composition. They enable us to figure out the relative amount of each element in the alloy, giving a clear picture of the material's properties and potential uses.

Composition of Alloys

Alloys are materials composed of two or more elements, with at least one being a metal. Their composition determines their physical and chemical properties, as well as their suitability for various applications. Composition is often expressed as a percentage by mass of each component element.

In the case of cupronickel, the alloy contains copper and nickel, often used for its resistance to corrosion and ease of minting coins. Meanwhile, pewter, traditionally used for ornaments and utensils, includes tin as its base element with minor additions of other metals like antimony and copper to alter its properties. By expressing the composition as a percentage, alloy production can be standardized, ensuring that each batch of material meets the required specifications for strength, malleability, and other critical attributes.

Significance in Alloy Analysis

Knowing the specific composition of an alloy is crucial when determining its most appropriate use. For example, varying the percentage of nickel in cupronickel can significantly impact its hardness and color. The exercise provided demonstrates how to dissect the composition to calculate the actual number of atoms of each kind and their ratios, which in turn reflects on the material's macro properties.

Atomic Mass

The atomic mass of an element, often listed in the periodic table, is a weighted average of the masses of the isotopes of that element, measured in grams per mole (g/mol). This average takes into account the relative abundance of each isotope in nature. The atomic mass enables chemists to calculate the moles of an element in a compound and, by extension, predict and explain the ratio of atoms within a compound or alloy.

To perform calculations involving atomic mass, one must understand that this value represents how much one mole of an element weighs. When you have a specific mass of an element, dividing it by its atomic mass will yield the number of moles, as shown in the steps for the provided alloy examples.

Utility in Stoichiometry

The concept of atomic mass is central to stoichiometry, which deals with the quantitative aspects of chemical reactions and substances. When calculating the composition of alloys, knowing the atomic masses of their constituent elements allows us to determine the number of atoms present and their respective ratios within the alloy, conveying a detailed understanding of the alloy's makeup and potential reactivity.