Question

$25.3 \, g$ of sodium carbonate, $Na_2CO_3$ is dissolved in enough water to make $250 \, mL$ of solution. If sodium carbonate dissociates completely, molar concentration of sodium ion, $Na^+$ and carbonate ions,$CO^{2-}_3$ are respectively (Molar mass of $Na_2CO_3 = 106 \, g \, mol^{-1}$)

• A. 0.477 M and 0.477 M
• B. 0.955 M and 1.910 M
• C. 1.910 M and 0.955 M
• D. 1.90 M and 1.910 M

Answer 1

The Correct Option is C

To determine the molar concentrations of sodium ions Na^+ and carbonate ions CO_3^{2-}, we must first find the concentration of the sodium carbonate Na_2CO_3 in the solution.

1. Calculate the number of moles of Na_2CO_3:
   • Molar mass of Na_2CO_3 = 106 \, g \, mol^{-1}.
   • The mass of Na_2CO_3 given is 25.3\, g.
   • Number of moles of Na_2CO_3 = \frac{25.3}{106} \approx 0.2387 \, mol.
2. Calculate the concentration of Na_2CO_3 in the solution:
   • Volume of the solution is 250 \, mL = 0.250 \, L.
   • Concentration of Na_2CO_3 = \frac{0.2387}{0.250} \approx 0.955 \, M.
3. Dissociation of Na_2CO_3:
   • Sodium carbonate dissociates completely in water as follows:
   Na_2CO_3 \rightarrow 2 \, Na^+ + CO_3^{2-}
   • From the equation, 1 mole of Na_2CO_3 gives 2 moles of Na^+ and 1 mole of CO_3^{2-}.
4. Calculate the molar concentration of ions:
   • For Na^+: The concentration is twice that of Na_2CO_3, therefore, 2 \times 0.955 \, M = 1.910 \, M.
   • For CO_3^{2-}: The concentration is the same as that of Na_2CO_3, which is 0.955 \, M.

Thus, the molar concentrations of sodium ions Na^+ and carbonate ions CO_3^{2-} are 1.910 M and 0.955 M respectively. Therefore, the correct answer is 1.910 M and 0.955 M.