Surgical grade titanium has the mass percent composition of 64.39% titanium, 11.42% vanadium, and 24.19% aluminum. What is the empirical formula of this compound?

Question

BlackTom AI · Accepted Answer

We are given the mass percent composition of a surgical grade titanium alloy: 64.39% Ti, 11.42% V, and 24.19% Al. The goal is to find the empirical formula by converting these masses to moles and then simplifying to the smallest whole-number ratio.

First, convert each element’s mass to moles using their approximate atomic masses: Ti ≈ 47.867 g/mol, V ≈ 50.9415 g/mol, Al ≈ 26.9815 g/mol.
- Moles of Ti: 64.39 g Ti ÷ 47.867 g/mol ≈ 1.343 mol
- Moles of V: 11.42 g V ÷ 50.9415 g/mol ≈ 0.2245 mol
- Moles of Al: 24.19 g Al ÷ 26.9815 g/mol ≈ 0.896 mol

Next, find the simplest whole-number ratio by dividing all mole results by the smallest value among them (0.2245):
- Ti: 1.343 ÷ 0.2245 ≈ 5.98 ≈ 6
- V: 0.2245 ÷ 0.2245 = 1
- Al: 0.896 ÷ 0.2245 ≈ 3.99 ≈ 4

Thus, the empirical formula corresponds to Ti6VAl4, which reflects a near-6:1:4 ratio of Ti to V to Al.

Now, evaluate the given answer options against these derived ratios:
- Ti3V2Al: This would imply Ti:V:Al ratios of 3:2:1, which does not match the computed 6:1:4 ratio. The proportions are not close to the calculated mole ratios and would misrepresent the relative amounts.
- Ti4V2Al3: This corresponds to 4:2:3 or simplified to 2:1:1.5, which is not an integer-consistent ratio with the data; the Ti fraction would be too low and Al too high relative to Ti and V.
- TiVAl: A 1:1:1 ratio, far from the calculated Ti-rich composition (Ti should be about six times V and two-thirds more than Al).
- Ti6VAl4: This gives a 6:1:4 ratio, exactly matching the rounded mole ratio discovered above. It aligns with the mass percents when converted to moles and normalized.
- Ti2VAl3: This yields 2:1:1.5, which again does not fit the derived Ti-dominant composition and misrepresents the relative abundances of V and Al.

In summary, only the Ti6VAl4 option reproduces the smallest whole-number ratio corresponding to the computed mole amounts from the given mass percentages, while the other options fail to reflect the correct proportional relationships among Ti, V, and Al.

Surgical grade titanium has the mass percent composition of 64.39% titanium, 11.42% vanadium, and 24.19% aluminum. What is the empirical formula of this compound?

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