Question

Calculate each of the following quantities: (a) Amount (mol) of Mn atoms in \(62.0 \mathrm{mg}\) of Mn (b) Amount (mol) for \(1.36 \times 10^{22}\) atoms of \(\mathrm{Cu}\) (c) Mass (g) of \(8.05 \times 10^{24} \mathrm{Li}\) atoms

Short answer

a) 0.00113 mol, b) 0.0226 mol, c) 92.81 g

Step-by-step solution

Convert Mass of Mn to Moles

To find the amount of Mn atoms in 62.0 mg of Mn, first convert the mass from mg to grams. \[ 62.0 \text{ mg} = 0.0620 \text{ g} \]Next, use the molar mass of Mn, which is approximately 54.94 g/mol, to convert grams to moles. \[ \text{moles of Mn} = \frac{0.0620 \text{ g}}{54.94 \text{ g/mol}} \]Calculate the result. \[ \text{moles of Mn} ≈ 0.00113 \text{ mol} \]

Convert Number of Cu Atoms to Moles

To find the amount of moles for 1.36 × 10^{22} atoms of Cu, use Avogadro's number, which is \(6.022 \times 10^{23}\) atoms/mol.\[ \text{moles of Cu} = \frac{1.36 \times 10^{22} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \]Calculate the result. \[ \text{moles of Cu} ≈ 0.0226 \text{ mol} \]

Convert Number of Li Atoms to Mass

To find the mass of 8.05 × 10^{24} Li atoms, first convert the number of atoms to moles using Avogadro's number.\[ \text{moles of Li} = \frac{8.05 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \]Calculate the moles. \[ \text{moles of Li} ≈ 13.37 \text{ mol} \]Next, use the molar mass of Li, which is approximately 6.94 g/mol, to convert moles to grams.\[ \text{mass of Li} = 13.37 \text{ mol} \times 6.94 \text{ g/mol} \]Calculate the result. \[ \text{mass of Li} ≈ 92.81 \text{ g} \]

Key concepts

molar mass

Molar mass is a fundamental concept in chemistry. It allows us to convert between the mass of a substance and the amount (in moles) of that substance. The molar mass of an element is the mass of one mole of its atoms, typically measured in grams per mole (g/mol). It is equivalent to the atomic or molecular weight of the element or compound, scaled up to Avogadro's number of particles.