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Chapter 4: Problem 7

What is the composition, in atom percent, of an alloy that consists of \(30 \mathrm{wt} \% \mathrm{Zn}\) and 70 \(\mathrm{wt} \% \mathrm{Cu}\) ?

Short Answer

Expert verified
Answer: The atom percent composition of the alloy consists of 29.4% Zn and 70.6% Cu.

Step by step solution

01

Determine the atomic masses

We will use the periodic table to look up the atomic masses of Zn and Cu. The atomic mass of Zn (Zinc) is approximately 65.38 amu and the atomic mass of Cu (Copper) is approximately 63.55 amu.
02

Convert weight percent to grams

To find the number of moles, let's first assume we have 100 grams of the alloy. This will make the conversion to grams easy. In 100 grams of the alloy: - 30 wt% Zn represents \(30\% \times 100g = 30g\) of Zn - 70 wt% Cu represents \(70\% \times 100g = 70g\) of Cu
03

Convert grams to moles

To calculate the number of moles of Zn and Cu, we use the atomic masses we found in Step 1: - Moles of Zn: \(\frac{30g}{65.38\;\text{amu}} = 0.459\;\text{moles\;Zn}\) - Moles of Cu: \(\frac{70g}{63.55\;\text{amu}} = 1.102\;\text{moles\;Cu}\)
04

Calculate the mole ratio

Now that we have the number of moles for both Zn and Cu, let's find their mole ratio. Add the moles of Zn and Cu together: - Total moles: \(0.459\;\text{moles\;Zn} + 1.102\;\text{moles\;Cu} = 1.561\;\text{moles}\)
05

Calculate the atom percent

To find the atom percent, we need to divide the moles of each element by the total moles, and multiply by 100: - Atom percent Zn: \(\frac{0.459\;\text{moles\;Zn}}{1.561\;\text{moles}} \times 100 = 29.40\%\) - Atom percent Cu: \(\frac{1.102\;\text{moles\;Cu}}{1.561\;\text{moles}} \times 100 = 70.60\%\) The composition of the alloy in atom percent consists of about 29.4% Zn and 70.6% Cu.

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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.

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

Determine the approximate density of a highleaded brass that has a composition of \(64.5\) \(\mathrm{wt} \% \mathrm{Cu}, 33.5 \mathrm{wt} \% \mathrm{Zn}\), and \(2 \mathrm{wt} \% \mathrm{~Pb}\).

Determine the ASTM grain size number if 20 grains per square inch are measured at a magnification of \(50 \times\).

Calculate the fraction of atom sites that are vacant for lead at its melting temperature of \(327^{\circ} \mathrm{C}(600 \mathrm{~K})\). Assume an energy for vacancy formation of \(0.55 \mathrm{eV} /\) atom.
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