Question

Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing number of atoms: \(0.50 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}, 23 \mathrm{~g} \mathrm{Na}, 6.0 \times 10^{23} \mathrm{~N}_{2}\) molecules.

Short answer

The samples can be ranked in order of increasing number of atoms as follows: 1. \(\mathrm{Na}\): \(6.022 \times 10^{23}\ \mathrm{atoms}\) 2. \(\mathrm{H_{2}O}\): \(9.033 \times 10^{23}\ \mathrm{atoms}\) 3. \(\mathrm{N_{2}}\): \(1.2 \times 10^{24}\ \mathrm{atoms}\)

Step-by-step solution

Convert \(\mathrm{H_2O}\) moles to molecules and determine the total number of atoms

Use Avogadro's number (\(6.022 \times 10^{23}\)) to convert moles to molecules: Molecules of \(\mathrm{H_2O} = 0.50\ \mathrm{mol} \times 6.022 \times 10^{23}\ \mathrm{molecules/mol} = 3.011 \times 10^{23}\ \mathrm{molecules}\) Now, we can find the total number of atoms in this sample by multiplying the number of molecules by the number of atoms in one \(\mathrm{H_2O}\) molecule (2 hydrogen atoms + 1 oxygen atom = 3 atoms): Total \(\mathrm{atoms} = 3.011 \times 10^{23}\ \mathrm{molecules} \times 3\ \mathrm{atoms/molecule} = 9.033 \times 10^{23}\ \mathrm{atoms}\) Next, let's find the number of atoms in the \(\mathrm{Na}\) sample:

Convert mass of \(\mathrm{Na}\) to moles and determine the total number of atoms

Use the atomic weight of \(\mathrm{Na}\) from the periodic table (22.99 g/mol) to convert mass to moles: Moles of \(\mathrm{Na} = \frac{23\ \mathrm{g}}{22.99\ \mathrm{g/mol}} = 1.000\ \mathrm{mol}\) Now, use Avogadro's number to convert moles to atoms: Total \(\mathrm{atoms} = 1.000\ \mathrm{mol} \times 6.022 \times 10^{23}\ \mathrm{atoms/mol} = 6.022 \times 10^{23}\ \mathrm{atoms}\) Finally, let's find the total number of atoms in the \(\mathrm{N_2}\) molecules sample:

Determine the total number of atoms in \(6.0 \times 10^{23} \ \mathrm{N_2}\) molecules

Since each \(\mathrm{N_{2}}\) molecule consists of 2 nitrogen atoms, we can find the total number of atoms by multiplying the number of molecules by the number of atoms in one \(\mathrm{N_{2}}\) molecule: Total \(\mathrm{atoms} = 6.0 \times 10^{23}\ \mathrm{molecules} \times 2\ \mathrm{atoms/molecule} = 1.2 \times 10^{24}\ \mathrm{atoms}\) Now, we can rank the samples in order of increasing number of atoms: 1. \(\mathrm{Na}\): \(6.022 \times 10^{23}\ \mathrm{atoms}\) 2. \(\mathrm{H_{2}O}\): \(9.033 \times 10^{23}\ \mathrm{atoms}\) 3. \(\mathrm{N_{2}}\): \(1.2 \times 10^{24}\ \mathrm{atoms}\)