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Chapter 4: Problem 14

What is the composition, in atom percent, of an alloy that consists of \(5.5 \mathrm{wt} \% \mathrm{~Pb}\) and \(94.5 \mathrm{wt} \% \mathrm{Sn} ?\)

Short Answer

Expert verified
Answer: The atom percent composition of the alloy is 3.22% Pb and 96.78% Sn.

Step by step solution

01

Understand and write down the given information

We have the following information: - \(5.5\ \text{wt}\% \ \text{Pb}\) - \(94.5\ \text{wt}\% \ \text{Sn}\) Let's assume we have \(100\ \text{grams}\) of the alloy. So, - \(5.5\ \text{grams} \ \text{Pb}\) - \(94.5\ \text{grams} \ \text{Sn}\)
02

Calculate moles of Pb and Sn

Using their respective molar masses, we'll calculate the moles of Pb and Sn. - Molar mass of Pb: \(207.2\ \text{g/mol}\) - Molar mass of Sn: \(118.7\ \text{g/mol}\) Moles of Pb: $$ \text{moles}_\text{Pb} = \frac{5.5\ \text{grams} \ \text{Pb}}{207.2\ \text{g/mol} \ \text{Pb}} = 0.02654\ \text{mol} \ \text{Pb} $$ Moles of Sn: $$ \text{moles}_\text{Sn} = \frac{94.5\ \text{grams} \ \text{Sn}}{118.7\ \text{g/mol} \ \text{Sn}} = 0.7964\ \text{mol} \ \text{Sn} $$
03

Calculate the total moles in the alloy

Now, sum up the moles of Pb and Sn to find the total moles in the alloy. $$ \text{Total moles} = \text{moles}_\text{Pb} + \text{moles}_\text{Sn} = 0.02654\ \text{mol} \ \text{Pb} + 0.7964\ \text{mol} \ \text{Sn} = 0.82294\ \text{mol} $$
04

Calculate atom percent composition

We can calculate the atom percent composition of Pb and Sn in the alloy using the formula: $$ \text{Atom percent composition} = \frac{\text{moles of the respective element}}{\text{Total moles}} \times 100 $$ Atom percent of Pb: $$ \text{Atom percent Pb} = \frac{0.02654\ \text{mol} \ \text{Pb}}{0.82294\ \text{mol}} \times 100 = 3.22\ \% $$ Atom percent of Sn: $$ \text{Atom percent Sn} = \frac{0.7964\ \text{mol} \ \text{Sn}}{0.82294\ \text{mol}} \times 100 = 96.78\ \% $$ So, the alloy consists of \(3.22 \%\) Pb and \(96.78 \%\) Sn in atom percent.

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