Questions: Calculate the concentrations of each ion present in a solution that results from mixing 39.4 mL of a 0.72 M NaClO3(aq) solution with 73.5 mL of a 0.68 M Na2SO4(aq). Assume that the volumes are additive. - M ClO3^- - M SO4^2- - M Na+

Calculate the concentrations of each ion present in a solution that results from mixing 39.4 mL of a 0.72 M NaClO3(aq) solution with 73.5 mL of a 0.68 M Na2SO4(aq). Assume that the volumes are additive.
- M ClO3^-
- M SO4^2-
- M Na+

Transcript text: Calculate the concentrations of each ion present in a solution that results from mixing 39.4 mL of a 0.72 M $\mathrm{NaClO}_{3}(a q)$ solution with $\mathbf{7 3 . 5} \mathrm{mL}$ of a 0.68 M $\mathrm{Na}_{2} \mathrm{SO}_{4}(a q)$. Assume that the volumes are additive. $\square$ $M \mathrm{ClO}_{3}{ }^{-}$ $\square$ $M \mathrm{SO}_{4}{ }^{2-}$ $\square$ $M \mathrm{Na}^{+}$

Solution

Solution Steps

Step 1: Calculate Total Volume of the Solution

To find the concentrations of ions in the mixed solution, we first need to determine the total volume of the solution. The total volume is the sum of the volumes of the two solutions:

\[ V_{\text{total}} = 39.4 \, \text{mL} + 73.5 \, \text{mL} = 112.9 \, \text{mL} \]

Step 2: Calculate Moles of Each Ion

Next, we calculate the moles of each ion present in the individual solutions before mixing.

For $\mathrm{NaClO}_3$:
- Moles of $\mathrm{NaClO}_3$ = $0.72 \, \text{M} \times 0.0394 \, \text{L} = 0.028368 \, \text{mol}$
- Each $\mathrm{NaClO}_3$ dissociates into $\mathrm{Na}^+$ and $\mathrm{ClO}_3^-$, so:
  - Moles of $\mathrm{Na}^+$ = 0.028368 mol
  - Moles of $\mathrm{ClO}_3^-$ = 0.028368 mol
For $\mathrm{Na}_2\mathrm{SO}_4$:
- Moles of $\mathrm{Na}_2\mathrm{SO}_4$ = $0.68 \, \text{M} \times 0.0735 \, \text{L} = 0.04998 \, \text{mol}$
- Each $\mathrm{Na}_2\mathrm{SO}_4$ dissociates into 2 $\mathrm{Na}^+$ and $\mathrm{SO}_4^{2-}$, so:
  - Moles of $\mathrm{Na}^+$ = 2 \times 0.04998 mol = 0.09996 mol
  - Moles of $\mathrm{SO}_4^{2-}$ = 0.04998 mol

Step 3: Calculate Total Moles of Each Ion

Add the moles of each ion from both solutions:

Total moles of $\mathrm{Na}^+$ = 0.028368 mol + 0.09996 mol = 0.128328 mol
Total moles of $\mathrm{ClO}_3^-$ = 0.028368 mol
Total moles of $\mathrm{SO}_4^{2-}$ = 0.04998 mol

Step 4: Calculate Concentration of Each Ion

Finally, calculate the concentration of each ion in the total solution volume:

Concentration of $\mathrm{Na}^+$: \[ [\mathrm{Na}^+] = \frac{0.128328 \, \text{mol}}{0.1129 \, \text{L}} = 1.1367 \, \text{M} \]
Concentration of $\mathrm{ClO}_3^-$: \[ [\mathrm{ClO}_3^-] = \frac{0.028368 \, \text{mol}}{0.1129 \, \text{L}} = 0.2513 \, \text{M} \]
Concentration of $\mathrm{SO}_4^{2-}$: \[ [\mathrm{SO}_4^{2-}] = \frac{0.04998 \, \text{mol}}{0.1129 \, \text{L}} = 0.4426 \, \text{M} \]

Final Answer

\[ \boxed{[\mathrm{ClO}_3^-] = 0.2513 \, \text{M}} \] \[ \boxed{[\mathrm{SO}_4^{2-}] = 0.4426 \, \text{M}} \] \[ \boxed{[\mathrm{Na}^+] = 1.1367 \, \text{M}} \]

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