Question

How many electrons are in (a) an ion of \(\mathrm{Sc}^{3+}\) ? (b) a mol of \(\mathrm{Sc}^{3+}\) ? (c) a gram of \(\mathrm{Sc}^{3+}\) ?

Short answer

Answer: There are 18 electrons in a single Sc³⁺ ion, \(1.084 \times 10^{25}\) electrons in one mole of Sc³⁺ ions, and approximately \(2.405 \times 10^{24}\) electrons in one gram of Sc³⁺ ions.

Step-by-step solution

Part (a): Finding electrons in a single Sc³⁺ ion

First, we need to know the atomic number of Scandium (Sc). The atomic number of an element represents the number of protons in its nucleus. Since Scandium is element 21, it has 21 protons. In a neutral atom, the number of electrons is the same as the number of protons, so a neutral Scandium atom would have 21 electrons. The Sc³⁺ ion has lost 3 electrons, so to find the number of electrons in Sc³⁺, we subtract 3 from 21: \[21 - 3 = 18\] Therefore, there are 18 electrons in a single Sc³⁺ ion.

Part (b): Finding electrons in one mole of Sc³⁺

One mole of any substance contains Avogadro's number of particles, which is \(6.022 \times 10^{23}\). To find the number of electrons in one mole of Sc³⁺ ions, we simply multiply the number of electrons in a single Sc³⁺ ion (which we found in part (a)) by Avogadro's number: \[18 \times (6.022 \times 10^{23})\] Therefore, there are \(1.084 \times 10^{25}\) electrons in one mole of Sc³⁺ ions.

Part (c): Finding electrons in a gram of Sc³⁺

To find the number of electrons in a gram of Sc³⁺ ions, we first need to determine how many moles of Sc³⁺ are in one gram. We can find this by using the molar mass of Scandium, which is approximately 44.96 g/mol. Now, we can find the number of moles of Sc³⁺ in one gram by dividing the mass by the molar mass: \[\frac{1\;\text{gram}}{44.96\;\text{g/mol}}\] This gives us approximately 0.0222 moles of Sc³⁺ in one gram. Now, we can simply multiply the number of electrons in one mole of Sc³⁺ (found in part (b)) by the number of moles in one gram: \[1.084 \times 10^{25}\;\text{electrons/mol} \times 0.0222\;\text{mol}\] Therefore, there are approximately \(2.405 \times 10^{24}\) electrons in one gram of Sc³⁺ ions.