Question

How many grams of titanium could be obtained from a 27.00 mole sample of $\text{T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}$?

Answer 1

Hint: There are 6 moles of titanium in 1 mole of $\text{T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}$ and we know that mass of 1 mole of titanium is its atomic mass that is equal to 47.88 grams. From this, we can calculate the mass of titanium in 27 moles of $\text{T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}$.

Complete answer: $\text{T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}$ is an alpha-beta alloy of titanium and its chemical formula suggests that in 1 mole of this compound, there is a total of 6 moles of titanium, 4 moles of aluminium and 1 mole of vanadium present.
So, to find the mass of titanium present in a 27.00 mole sample of $\text{T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}$, first we need to calculate the total number of moles of titanium present in this much amount of sample and then multiply it by the atomic mass of titanium.
\[\begin{align}
  & \because 1\text{ mole T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}\to \text{6 moles Ti} \\
 & \therefore \text{27 mole T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}\to \left( \text{6}\times \text{27} \right)\text{ i}\text{.e}\text{. 162 moles Ti} \\
\end{align}\]
The atomic mass of titanium is 47.88 grams per mole which means that 1 mole titanium weighs 47.88 grams. So, we can write it as:
\[\begin{align}
  & 1\text{ mole Ti}\to \text{47}\text{.88 g} \\
 & \Rightarrow \text{162 mole Ti}\to \left( \text{47}\text{.88}\times \text{162} \right)\text{ i}\text{.e}\text{. 7756}\text{.6 g} \\
\end{align}\]
Hence, 7756.6 grams of titanium could be obtained from a 27.00 mole sample of $\text{T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}$.

Additional information: $\text{T}{{\text{i}}_{\text{6}}}\text{A}{{\text{l}}_{\text{4}}}\text{V}$ is one of the most common titanium alloys which is mainly used as an excellent corrosion resistance material but due to its low thermal conductivity at room temperature, it cannot be used in machining.

Note:
The atomic mass of an element can be written in units of grams per mole or as amu. The term amu refers to the value of the number of protons and neutrons in an atom with respect to carbon-12 atom. However, the unit of grams per mole is used to define that 1 mole of a substance contains a specific mass of that substance in grams.