Question

A student wants to have 3.011 × 102³ atoms each of magnesium and carbon elements. For this purpose, how much magnesium and carbon will he weigh in grams?

Answer 1

12 g of carbon and 24.3 g of magnesium, each contains 6.022$\times$10²³ number of atoms.
Now
Let X g of carbon have 3.011$\times$10²³ number of atoms.
Therefore,
$$\begin{gathered} \mathrm{X}=\frac{\mathrm{molar}\mathrm{mass}\mathrm{of}\mathrm{carbon}\times \mathrm{number}\mathrm{of}\mathrm{atoms}\mathrm{of}\mathrm{carbon}}{\mathrm{Avogadro}\mathrm{number}} \\ \mathrm{X}=\frac{12\times 3.011\times {10}^{23}}{6.022\times {10}^{23}} \\ \mathrm{X}=6\mathrm{g}\mathrm{of}\mathrm{carbon} \end{gathered}$$
So, 6 g of carbon contains 3.011$\times$10²³ number of atoms.

Again,
Let X g of magnesium have 3.011$\times$10²³ number of atoms.
Therefore,
$$\begin{gathered} \mathrm{X}=\frac{\mathrm{molar}\mathrm{mass}\mathrm{of}\mathrm{magnesium}\times \mathrm{number}\mathrm{of}\mathrm{atoms}\mathrm{of}\mathrm{magnesium}}{\mathrm{Avogadro}\mathrm{number}} \\ \mathrm{X}=\frac{24\times 3.011\times {10}^{23}}{6.022\times {10}^{23}} \\ \mathrm{X}=12\mathrm{g}\mathrm{of}\mathrm{magnesium} \end{gathered}$$
So, 12 g of magnesium contains ​3.011$\times$10²³ number of atoms.

Hence, he will weigh 12 g of magnesium and 6 g of carbon.