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Chapter 4: Problem 12

What is the composition, in atom percent, of an alloy that consists of \(97 \mathrm{wt} \% \mathrm{Fe}\) and \(3 \mathrm{wt} \%\) Si?

Short Answer

Expert verified
After plugging in the values and solving the equations, we get: Atom percent of Fe ≈ 95.9% Atom percent of Si ≈ 4.1% Thus, the composition of the alloy in atom percent is approximately 95.9% Iron and 4.1% Silicon.

Step by step solution

01

Calculate the number of moles of each element

To calculate the number of moles, we will use the formula: Number of moles = (Weight of element) / (Atomic weight of element) For Iron (Fe): Weight = 97 wt%, and Atomic weight = 55.85 g/mol Number of moles of Fe = (97 grams) / (55.85 g/mol) For Silicon (Si): Weight = 3 wt%, and Atomic weight = 28.09 g/mol Number of moles of Si = (3 grams) / (28.09 g/mol)
02

Calculate the total number of moles

Add the number of moles of both elements to find the total number of moles: Total number of moles = Moles of Fe + Moles of Si
03

Calculate the atom percent of each element

The atom percent of an element is the percentage of the element's moles in the total moles. We can calculate it using the following formula: Atom percent of an element = (Number of moles of the element / Total number of moles) * 100 For Fe: Atom percent of Fe = (Number of moles of Fe / Total number of moles) * 100 For Si: Atom percent of Si = (Number of moles of Si / Total number of moles) * 100
04

Plug in the values and solve

Now we will plug in the values obtained from Steps 1 & 2 and solve for the atom percent of each element. Atom percent of Fe = \(\frac{\frac{97}{55.85}}{\frac{97}{55.85} + \frac{3}{28.09}} * 100\) Atom percent of Si = \(\frac{\frac{3}{28.09}}{\frac{97}{55.85} + \frac{3}{28.09}} * 100\) Calculate the atom percent of Fe and Si.

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Most popular questions from this chapter

Germanium forms a substitutional solid solution with silicon. Compute the number of germanium atoms per cubic centimeter for a germanium-silicon alloy that contains \(15 \mathrm{wt} \%\) Ge and \(85 \mathrm{wt} \%\) Si. The densities of pure germanium and silicon are \(5.32\) and \(2.33 \mathrm{~g} / \mathrm{cm}^{3}\), respectively.

For a BCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (110) plane? Why? (Note: You may want to consult the solution to Problem \(3.55\) at the end of Chapter 3.)

For each of the following stacking sequences found in FCC metals, cite the type of planar defect that exists: (a) ... \(A B C A B C B A C B A \ldots\) (b) ... \(A B C A B C B C A B C \ldots\) Now, copy the stacking sequences and indicate the position(s) of planar defect(s) with a vertical dashed line.

The concentration of carbon in an ironcarbon alloy is \(0.15 \mathrm{wt} \%\). What is the concentration in kilograms of carbon per cubic meter of alloy?

What is the composition, in atom percent, of an alloy that contains \(98 \mathrm{~g}\) tin and \(65 \mathrm{~g}\) lead?
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