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What is the composition, in atom percent, of an alloy that consists of \(92.5 \mathrm{wt} \% \mathrm{Ag}\) and \(7.5\) wt \(\%\) \(\mathrm{Cu} ?\)

Short Answer

Expert verified
Based on the given information and solution, the alloy's composition in atom percent is approximately 87.9% Ag (silver) and 12.1% Cu (copper).

Step by step solution

01

Obtain molar masses of elements

Look up the molar masses of silver (Ag) and copper (Cu) in the periodic table. The molar mass of Ag is \(107.87\,\text{g/mol}\), and the molar mass of Cu is \(63.55\,\text{g/mol}\).
02

Convert weight percentages to grams

Assume we have \(100\,\text{g}\) of the alloy. Then, we have \(92.5\,\text{g}\) of Ag and \(7.5\,\text{g}\) of Cu.
03

Determine moles of each element in the alloy

Divide the amounts of Ag and Cu in grams by their respective molar masses to find the moles of each element in the alloy. For Ag: \(\text{moles of Ag} = \dfrac{92.5\,\text{g}}{107.87\,\text{g/mol}} = 0.857\,\text{mol}\) For Cu: \(\text{moles of Cu} = \dfrac{7.5\,\text{g}}{63.55\,\text{g/mol}} = 0.118\,\text{mol}\)
04

Calculate total moles in the alloy

Add the moles of Ag and Cu to find the total moles in the alloy. \(\text{Total moles} = 0.857\,\text{mol} + 0.118\,\text{mol} = 0.975\,\text{mol}\)
05

Calculate atom percentages

Divide the moles of each element by the total moles in the alloy and multiply by 100 to obtain atom percentages. For Ag: \(\text{Atom \%} = \dfrac{0.857\,\text{mol}}{0.975\,\text{mol}} \times 100 = 87.9\,\%\) For Cu: \(\text{Atom \%} = \dfrac{0.118\,\text{mol}}{0.975\,\text{mol}} \times 100 = 12.1\,\%\) The composition of the alloy, in atom percent, is approximately \(87.9\,\%\) Ag and \(12.1\,\%\) Cu.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atom Percent
Atom percent, often referred to as "atomic percentage," is a way to express the concentration of an element in an alloy or compound, based on the number of atoms. Unlike weight percent—which is based on mass—atom percent focuses on the relative amounts of constituent atoms.
This concept is particularly useful in materials science and chemistry, where understanding the distribution of atoms in a mixture can affect the properties of a material. To calculate the atom percent:
  • First, determine the number of moles of each element present in the sample, using its molar mass.
  • Then, add up these moles to get the total number of moles in the mixture.
  • Finally, divide the moles of each element by the total moles and multiply by 100 to convert the fraction into a percentage.
This calculation provides insight into the atomic makeup of a material, offering a different perspective than mass-based measures alone.
Molar Mass
Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. It's expressed in grams per mole (g/mol) and is calculated based on the relative atomic masses of the elements present.
To determine molar mass:
  • Look up the atomic masses of each element on the periodic table.
  • Multiply the atomic mass of each element by the number of atoms of that element in the formula if it’s a compound.
  • Sum these values to obtain the molar mass of the substance.
For example, when calculating the molar mass of silver ( Ag ) in an alloy, we simply use its atomic mass, which is approximately 107.87 g/mol. Knowing the molar mass is crucial for converting between grams and moles, a common step in many chemical calculations.
Weight Percentage
Weight percentage (wt.%) is a way to express the concentration of a component in a mixture, based on its mass relative to the total mass of the mixture. It's an especially useful quantitative measure in formulations where the focus is on the proportion of different components by their mass. The calculation for weight percentage involves:
  • Taking the mass of the specific component and dividing it by the total mass of the mixture.
  • Multiplying the result by 100 to express it as a percentage.
In practice, if the total mass of an alloy is assumed to be 100 grams, then 92.5 grams of silver ( Ag ) means it makes up 92.5 wt.% of the alloy, and similarly, 7.5 grams of copper ( Cu ) makes 7.5 wt.%. Understanding weight percentage helps in interpreting the mass-based distribution of components within a sample, which is key in processes like alloy design and quality control.

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Most popular questions from this chapter

(a) For a given material, would you expect the surface energy to be greater than, the same as, or less than the grain boundary energy? Why? (b) The grain boundary energy of a small-angle grain boundary is less than for a high-angle one. Why is this so?

(a) Calculate the fraction of atom sites that are vacant for copper \((\mathrm{Cu})\) at its melting temperature of \(1084^{\circ} \mathrm{C}(1357 \mathrm{~K})\). Assume an energy for vacancy formation of \(0.90 \mathrm{eV} /\) atom. (b) Repeat this calculation at room temperature \((298 \mathrm{~K})\) (c) What is the ratio of \(N_{v} / N(1357 \mathrm{~K})\) and \(N_{v} / N\) \((298 \mathrm{~K}) ?\)

What is the composition, in atom percent, of an alloy that contains \(44.5 \mathrm{lb}_{\mathrm{m}}\) of \(\mathrm{Ag}, 83.7 \mathrm{lb}_{\mathrm{m}}\) of Au, and \(5.3 \mathrm{lb}_{\mathrm{m}}\) of \(\mathrm{Cu}\) ?

Which of the following systems (i.e., pair of metals) would you expect to exhibit complete solid solubility? Explain your answers. (a) \(\mathrm{Cr}-\mathrm{V}\) (b) \(\mathrm{Mg}-\mathrm{Zn}\) (c) \(\mathrm{Al}-\mathrm{Zr}\) (d) \(\mathrm{Ag}-\mathrm{Au}\) (e) \(\mathrm{Pb}-\mathrm{Pt}\)

(a) For BCC iron, compute the radius of a tetrahedral interstitial site. (See the result of Problem 4.9.) (b) Lattice strains are imposed on iron atoms surrounding this site when carbon atoms occupy it. Compute the approximate magnitude of this strain by taking the difference between the carbon atom radius and the site radius and then dividing this difference by the site radius.

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