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Chapter 9: Problem 186

The semiconductor \(\mathrm{NiO}\), which consists of \(\mathrm{Ni}^{2+}\) and \(\mathrm{O}^{2-}\) ions, can be reacted with lithium to prepare "lithium-doped" \(\mathrm{Ni}_{1-x} \mathrm{Li}_{x} \mathrm{O}\). Suppose \(x=0.050\). (a) How many lithium atoms would be present in one mole of the doped material? (Give your answer in moles and as an absolute number of atoms.)

Short Answer

Expert verified
In one mole of the lithium-doped material \(\mathrm{Ni}_{1-x} \mathrm{Li}_{x} \mathrm{O}\) with \(x = 0.050\), there would be 0.050 moles or \(3.011 \times 10^{22}\) lithium atoms.

Step by step solution

01

Identify the formula for the lithium-doped material

We are given the formula for lithium-doped NiO as \(\mathrm{Ni}_{1-x} \mathrm{Li}_{x} \mathrm{O}\), where x represents the mole fraction of lithium in the material, with \(x = 0.050\)
02

Calculate the number of moles of lithium atoms in one mole of the doped material

To find the moles of lithium atoms, we can multiply x by the number of moles of the doped material. Number of moles of lithium atoms = Number of moles of the doped material × x = 1 mole × 0.050 = 0.050 moles
03

Convert moles of lithium atoms to an absolute number of atoms

To convert the moles of lithium atoms to an absolute number of atoms, we simply multiply the moles of lithium atoms by Avogadro's number. Number of lithium atoms = Number of moles of lithium atoms × Avogadro's number = 0.050 moles × \(6.022 \times 10^{23}\) atoms/mol = \(3.011 \times 10^{22}\) lithium atoms So, there are 0.050 moles or \(3.011 \times 10^{22}\) lithium atoms present in one mole of the lithium-doped \(\mathrm{Ni}_{1-x} \mathrm{Li}_{x} \mathrm{O}\).

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Most popular questions from this chapter

Consider the unbalanced chemical equation \(\mathrm{KCl}+\mathrm{O}_{2} \rightarrow \mathrm{KClO}_{3}\) If you react \(42.6 \mathrm{~g}\) of \(\mathrm{KCl}\) and \(36.5 \mathrm{~g}\) of \(\mathrm{O}_{2}\) and the reaction has a percent yield of \(56.0 \%\), how many grams of \(\mathrm{KClO}_{3}\) are produced?

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