Question

Calculate the sodium ion concentration when \(70.0 \mathrm{~mL}\) of 3.0 \(M\) sodium carbonate is added to \(30.0 \mathrm{~mL}\) of \(1.0 \mathrm{M}\) sodium bicarbonate.

Short answer

The sodium ion concentration in the resulting mixture is \(4.5 M\).

Step-by-step solution

Determine moles of sodium ions in each solution

We can calculate the moles of sodium ions in each solution by using the formula: moles = volume (in L) × concentration (in M). For the sodium carbonate solution: Volume = \(70.0 mL = 0.070 L\) Concentration = 3.0 M Since sodium carbonate (\(Na_2CO_3\)) contains 2 moles of sodium ions per mole of compound: Moles of sodium ions = \(0.070 L \times 3.0 M \times 2 = 0.42\, moles\) For the sodium bicarbonate solution: Volume = \(30.0 mL = 0.030 L\) Concentration = 1.0 M Since sodium bicarbonate (\(NaHCO_3\)) contains 1 mole of sodium ions per mole of compound: Moles of sodium ions = \(0.030 L \times 1.0 M \times 1 = 0.03\, moles\)

Determine total moles of sodium ions and total volume

Now that we have determined the moles of sodium ions from both the sodium carbonate and the sodium bicarbonate solutions, we combine the moles of sodium ions from both solutions to get the total moles. Total moles of sodium ions = \(0.42\, moles + 0.03\, moles = 0.45\, moles\) Next, we need to find the total volume of the mixed solution: Total volume = volume of sodium carbonate solution + volume of sodium bicarbonate solution Total volume = \(0.070 L + 0.030 L = 0.100 L\)

Calculate the concentration of sodium ions

Now that we know the total moles of sodium ions and the total volume of the solution, we can find the concentration of sodium ions in the resulting mixture by dividing the total moles by the total volume. The formula for concentration is: \(concentration = \frac{moles}{volume}\). Concentration of sodium ions = \(\frac{0.45\, moles}{0.100 L} = 4.5 M\) The sodium ion concentration in the resulting mixture is 4.5 M.