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Chapter 11: Problem 15

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

Expert verified
The concentration of sodium ions after mixing the solutions is calculated by first finding the moles of sodium ions in each solution: \(0.070L\times3.0M\times\frac{2}{1}=0.420\;mol\) for sodium carbonate and \(0.030L\times1.0M\times\frac{1}{1}=0.030\;mol\) for sodium bicarbonate. The total moles of sodium ions is \(0.420\;mol+0.030\;mol=0.450\;mol\). With a total volume of \(0.070L+0.030L=0.100L\), the resulting sodium ion concentration is \(\frac{0.450 \mathrm{~mol}}{0.100\mathrm{ ~L}} = 4.50\mathrm{ ~M}\).

Step by step solution

01

Calculate the moles of sodium ions in each solution

To find the moles of sodium ions in each solution, we first determine the moles of each compound. Sodium carbonate (Na2CO3) has 2 sodium ions for every mole of Na2CO3, and sodium bicarbonate (NaHCO3) has 1 sodium ion for every mole of NaHCO3. We will multiply the volume and concentration of each solution by the appropriate ratio of sodium ions to compound moles to find the total moles of sodium ions. For the sodium carbonate solution: Volume = 70.0 mL = 0.070 L (convert to liters) Concentration = 3.0 M Moles of sodium ions = volume × concentration × (2 sodium ions/1 mole Na2CO3) For the sodium bicarbonate solution: Volume = 30.0 mL = 0.030 L (convert to liters) Concentration = 1.0 M Moles of sodium ions = volume × concentration × (1 sodium ion/1 mole NaHCO3)
02

Calculate the total moles of sodium ions

Add the moles of sodium ions from each solution to find the total moles of sodium ions in the mixture. Total moles of sodium ions = moles of sodium ions (sodium carbonate solution) + moles of sodium ions (sodium bicarbonate solution)
03

Determine the total volume of the mixture

Add the volumes of the two solutions together to find the total volume of the mixture. Total volume = volume (sodium carbonate solution) + volume (sodium bicarbonate solution)
04

Calculate the resulting sodium ion concentration

Finally, divide the total moles of sodium ions by the total volume of the mixture to find the resulting concentration of sodium ions. Sodium ion concentration = total moles of sodium ions / total volume

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