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Chapter 23: Problem 73

Nitinol is a nickel-titanium alloy known as memory metal. The name nitinol is derived from the symbols for nickel (Ni), titanium (Ti), and the acronym for the Naval Ordinance Laboratory (NOL), where it was discovered. If an object made out of nitinol is heated to about \(500^{\circ} \mathrm{C}\) for about an hour and then allowed to cool, the original shape of the object is "remembered," even if the object is deformed into a different shape. The original shape can be restored by heating the metal. Because of this property, nitinol has found many uses, especially in medicine and orthodontics (for braces). Nitinol exists in a number of different solid phases. In the so- called austerite phase, the metal is relatively soft and elastic. The crystal structure for the austerite phase can be described as a simple cubic lattice of Ti atoms with Ni atoms occupying cubic holes in the lattice of Ti atoms. What is the empirical formula of nitinol and what is the percent by mass of titanium in the alloy?

Short Answer

Expert verified
The empirical formula of Nitinol is \(NiTi\). The percent by mass of titanium in the alloy is approximately \(44.9 \% \).

Step by step solution

01

Determine the empirical formula

Given that the crystal structure is a simple cubic lattice of Ti atoms with Ni atoms occupying cubic holes in the lattice of Ti atoms, it can be deduced that the number of Ni and Ti atoms are the same for each unit cell of the lattice. Thus, the empirical formula of nitinol is \(NiTi\).
02

Find molar masses

The molar mass of nickel (Ni) and titanium (Ti) are roughly \(58.69 \, g/mol\) and \(47.87 \, g/mol\), respectively. These values can be found from the periodic table.
03

Calculate percent by mass of titanium

To calculate the percent by mass of titanium in the alloy, use this formula: Percent by mass of component = \(\frac{mass \, of \, component}{total \, mass} \times 100\% \). So, the total mass in one empirical formula unit of nitinol \(NiTi\) is the sum of the molar mass of titanium and nickel i.e. \(58.69 \, g/mol + 47.87 \, g/mol = 106.56 \, g/mol\). Next, plug in the values into the percent formula: Percent by mass of titanium = \(\frac{47.87 \, g/mol}{106.56 \, g/mol} \times 100 \% \approx 44.9 \%\).

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