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Chapter 11: Problem 15

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

Short Answer

Expert verified
The sodium ion concentration in the mixture is \(= \frac{(3.0 M \times 70.0 mL \times 2) + (1.0 M \times 30.0 mL \times 1)}{70.0 mL + 30.0 mL} = \frac{420 + 30}{100} = \frac{450}{100} = 4.5 M\).

Step by step solution

01

Identify the given information

We are given the following information: - The volume and concentration of sodium carbonate solution: \(70.0 mL\) and \(3.0 M\) - The volume and concentration of sodium bicarbonate solution: \(30.0 mL\) and \(1.0 M\) Keep in mind that sodium carbonate is \(Na_2CO_3\) and sodium bicarbonate is \(NaHCO_3\).
02

Calculate the moles of each sodium ion in each solution

Since the molarity is defined as moles per liter, we can calculate the moles of sodium ions from the given concentrations of sodium carbonate and sodium bicarbonate. For sodium carbonate, we have: Moles of sodium ions \(= Molarity \times Volume \times Number\,of\,sodium\,ions\,in\,a\,formula\,unit = 3.0 M \times 70.0 mL \times 2\) For sodium bicarbonate, we have: Moles of sodium ions \(= Molarity \times Volume \times Number\,of\,sodium\,ions\,in\,a\,formula\,unit = 1.0 M \times 30.0 mL \times 1\)
03

Calculate the total moles of sodium ions in the mixture

To find the total moles of sodium ions in the mixture, we simply add the moles obtained in step 2. Total moles of sodium ions \(= (3.0 M \times 70.0 mL \times 2) + (1.0 M \times 30.0 mL \times 1)\)
04

Calculate the total volume of the mixture

The total volume of the mixture is simply the sum of the initial volumes of both solutions: Total volume \(= Volume\,of\,sodium\,carbonate\,solution + Volume\,of\,sodium\,bicarbonate\,solution = 70.0 mL + 30.0 mL\)
05

Calculate the concentration of sodium ions

Now we can find the concentration of sodium ions in the mixture. To do this, we divide the total moles of sodium ions in the mixture by the total volume of the mixture: Sodium ion concentration \(= \frac{Total\,moles\,of\,sodium\,ions}{Total\,volume} = \frac{(3.0 M \times 70.0 mL \times 2) + (1.0 M \times 30.0 mL \times 1)}{70.0 mL + 30.0 mL}\) Now, perform the calculations to get the answer for the sodium ion concentration.

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