Questions: Calculate the number of cations and anions in 4.32 g of Na2SO4.

Transcript text: Calculate the number of cations and anions in 4.32 g of $\mathrm{Na}_{2} \mathrm{SO}_{4}$.

Solution

Solution Steps

Step 1: Determine the Molar Mass of $\mathrm{Na}_2\mathrm{SO}_4$

The molar mass of $\mathrm{Na}_2\mathrm{SO}_4$ is calculated by summing the atomic masses of its constituent elements:

Sodium (Na): $2 \times 22.9898 \, \text{g/mol} = 45.9796 \, \text{g/mol}$
Sulfur (S): $1 \times 32.065 \, \text{g/mol} = 32.065 \, \text{g/mol}$
Oxygen (O): $4 \times 15.999 \, \text{g/mol} = 63.996 \, \text{g/mol}$

Adding these together gives the molar mass of $\mathrm{Na}_2\mathrm{SO}_4$:

\[ M = 45.9796 + 32.065 + 63.996 = 142.0406 \, \text{g/mol} \]

Step 2: Calculate the Number of Moles of $\mathrm{Na}_2\mathrm{SO}_4$

Using the given mass of $\mathrm{Na}_2\mathrm{SO}_4$ (4.32 g), we calculate the number of moles:

\[ \text{moles of } \mathrm{Na}_2\mathrm{SO}_4 = \frac{4.32 \, \text{g}}{142.0406 \, \text{g/mol}} = 0.0304 \, \text{mol} \]

Step 3: Determine the Number of Cations and Anions

Each formula unit of $\mathrm{Na}_2\mathrm{SO}_4$ contains:

2 sodium cations ($\mathrm{Na}^+$)
1 sulfate anion ($\mathrm{SO}_4^{2-}$)

Thus, the number of cations is twice the number of moles of $\mathrm{Na}_2\mathrm{SO}_4$, and the number of anions is equal to the number of moles of $\mathrm{Na}_2\mathrm{SO}_4$.

Number of $\mathrm{Na}^+$ cations: $2 \times 0.0304 \, \text{mol} = 0.0608 \, \text{mol}$
Number of $\mathrm{SO}_4^{2-}$ anions: $0.0304 \, \text{mol}$

Step 4: Convert Moles to Number of Ions

Using Avogadro's number ($6.022 \times 10^{23} \, \text{mol}^{-1}$), we convert moles to the number of ions:

Number of $\mathrm{Na}^+$ cations: \[ 0.0608 \, \text{mol} \times 6.022 \times 10^{23} \, \text{mol}^{-1} = 3.664 \times 10^{22} \, \text{cations} \]
Number of $\mathrm{SO}_4^{2-}$ anions: \[ 0.0304 \, \text{mol} \times 6.022 \times 10^{23} \, \text{mol}^{-1} = 1.832 \times 10^{22} \, \text{anions} \]