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Chapter 9: Problem 49

An intermetallic compound is found in the goldtitanium system that has a composition of \(58.0\) wt \(\%\) Au-42.0 wt \(\%\) Ti. Specify the formula for this compound.

Short Answer

Expert verified
Answer: The empirical formula for the given intermetallic compound is AuTi3.

Step by step solution

01

Calculate the moles of each element

First, we need to calculate the moles of both Au and Ti in the compound using their atomic weights (Au = 197 g/mol, Ti = 47.867 g/mol). We can use the following formula to calculate the moles (n) of each element, given the mass (m) and atomic weight (M): n = m / M For example, if we have 100 g of the compound: - Mass of Au = 58.0 g (58.0 wt.% of 100 g) - Mass of Ti = 42.0 g (42.0 wt.% of 100 g) We can now calculate the moles of each element: - Moles of Au = 58.0 g / 197 g/mol = 0.294 moles (approximately) - Moles of Ti = 42.0 g / 47.867 g/mol = 0.877 moles (approximately)
02

Find the ratio of moles of each element

Now, we need to find the ratio between the moles of Au and Ti. We can do this by dividing the moles of each element by the smallest number of moles. In our case, the smallest number of moles is for Au (0.294 moles). - Ratio of moles of Au = 0.294 / 0.294 = 1 - Ratio of moles of Ti = 0.877 / 0.294 = 2.98 (approximately) The ratio of moles of Ti to Au is almost 3:1, so we can round this ratio to the nearest whole number to obtain the empirical formula.
03

Determine the formula of the compound

Based on the ratio obtained in the previous step, we can write the formula of the intermetallic compound. Since the mole ratio is approximately 1:3 for Au to Ti, the formula for this compound can be represented as AuTi3.

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Most popular questions from this chapter

An intermetallic compound is found in the aluminum-zirconium system that has a composition of \(22.8 \mathrm{wt} \%\) Al-77.2 wt \(\% \mathrm{Zr}\). Specify the formula for this compound.

Two intermetallic compounds, \(\mathrm{A}_{3} \mathrm{~B}\) and \(\mathrm{AB}_{3}\), exist for elements \(A\) and \(B\). If the compositions for \(\mathrm{A}_{3} \mathrm{~B}\) and \(\mathrm{AB}_{3}\) are \(91.0 \mathrm{wt} \% \mathrm{~A}-9.0 \mathrm{wt} \% \mathrm{~B}\) and \(53.0\) \(\mathrm{wt} \% \mathrm{~A}-47.0 \mathrm{wt} \% \mathrm{~B}\), respectively, and element \(\mathrm{A}\) is zirconium, identify element \(\mathrm{B}\).

For a lead-tin alloy of composition \(80 \mathrm{wt} \% \mathrm{Sn}-\) \(20 \mathrm{wt} \% \mathrm{~Pb}\) and at \(180^{\circ} \mathrm{C}\left(355^{\circ} \mathrm{F}\right)\), do the following: (a) Determine the mass fractions of the \(\alpha\) and \(\beta\) phases. (b) Determine the mass fractions of primary \(\beta\) and eutectic microconstituents. (c) Determine the mass fraction of eutectic \(\beta\).

For alloys of two hypothetical metals \(\mathrm{A}\) and \(\mathrm{B}\), there exist an \(\alpha\), A-rich phase and a \(\beta\), B-rich phase. From the mass fractions of both phases for two different alloys provided in the following table (which are at the same temperature), determine the composition of the phase boundary (or solubility limit) for both \(\alpha\) and \(\beta\) phases at this temperature. $$ \begin{array}{lcc} \hline \begin{array}{c} \text { Alloy } \\ \text { Composition } \end{array} & \begin{array}{c} \text { Fraction } \\ \boldsymbol{\alpha} \text { Phase } \end{array} & \text { Fraction } \\ \hline 70 \mathrm{wt} \% \mathrm{~A}-30 \mathrm{wt} \% \mathrm{~B} & 0.78 & 0.22 \\ \hline 35 \mathrm{wt} \% \mathrm{~A}-65 \mathrm{wt} \% \mathrm{~B} & 0.36 & 0.64 \\ \hline \end{array} $$

(a) Briefly describe the phenomenon of coring and why it occurs. (b) Cite one undesirable consequence of coring.
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