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Chapter 11: Problem 17

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\(M\) sodium bicarbonate.

Short Answer

Expert verified
The sodium ion concentration in the solution is 4.5 M.

Step by step solution

01

Convert volumes to liters

Since the volumes of solutions are given in milliliters, we need to convert them to liters for easier calculations. To convert from milliliters to liters, divide by 1000. - 70.0 mL = 0.070 L for sodium carbonate solution - 30.0 mL = 0.030 L for sodium bicarbonate solution
02

Calculate moles of sodium ions in sodium carbonate solution

To calculate the moles of sodium ions present in sodium carbonate solution, we use the formula: moles = molarity × volume. In sodium carbonate (Na2CO3), there are 2 sodium ions per molecule. Therefore, the moles of sodium ion can be calculated as: Moles in Na2CO3 = Molarity of sodium carbonate × Volume of sodium carbonate × Number of sodium ions per molecule Moles of Na in Na2CO3 = 3.0 mol/L × 0.070 L × 2 = 0.42 mol
03

Calculate moles of sodium ions in sodium bicarbonate solution

Similarly for sodium bicarbonate (NaHCO3), there is 1 sodium ion per molecule. Calculate the moles of sodium ions by using the formula: moles = molarity × volume. Moles of Na in NaHCO3 = Molarity of sodium bicarbonate × Volume of sodium bicarbonate × Number of sodium ions per molecule Moles of Na in NaHCO3 = 1.0 mol/L × 0.030 L × 1 = 0.03 mol
04

Calculate the total moles of sodium ions

Add the moles of sodium ions from both sodium carbonate and sodium bicarbonate solutions to find the total moles of sodium ions in the mixture. Total moles of Na = Moles of Na in Na2CO3 + Moles of Na in NaHCO3 Total moles of Na = 0.42 mol + 0.03 mol = 0.45 mol
05

Calculate the total volume of the mixture

To find the total volume of the mixture, add the volumes of sodium carbonate and sodium bicarbonate solutions together. Total volume = Volume of sodium carbonate solution + Volume of sodium bicarbonate solution Total volume = 0.070 L + 0.030 L = 0.100 L
06

Calculate the concentration of sodium ions

Finally, divide the total moles of sodium ions by the total volume of the mixture to find the concentration of sodium ions in the mixture. Concentration of Na = Total moles of Na / Total volume Concentration of Na = 0.45 mol / 0.100 L = 4.5 M The sodium ion concentration in the solution is 4.5 M.

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