Question

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

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

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 \(NaHCO_3\).

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 \(= Molarity \times Volume \times Number\,of\,sodium\,ions\,in\,a\,formula\,unit = 1.0 M \times 30.0 mL \times 1\)

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 \(= (3.0 M \times 70.0 mL \times 2) + (1.0 M \times 30.0 mL \times 1)\)

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 \(= Volume\,of\,sodium\,carbonate\,solution + Volume\,of\,sodium\,bicarbonate\,solution = 70.0 mL + 30.0 mL\)

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.

Key concepts

Molarity

Molarity is a measure used to describe the concentration of a solute in a solution. It tells us how many moles of a substance are present in one liter of solution. Think of it like this: if a solution has a molarity of 1 M, it means there is 1 mole of solute in every liter of the solution.

In our exercise, two different molarities are used. Sodium carbonate (\(Na_2CO_3\)) has a molarity of 3.0 M, meaning each liter of this solution holds 3 moles of sodium carbonate. Sodium bicarbonate (\(NaHCO_3\)) has a molarity of 1.0 M, indicating 1 mole of sodium bicarbonate in every liter. When calculating sodium ion concentration, it's crucial to include these molarities, as they affect the total moles present in the given volume of solutions.

To work with molarity effectively, convert the solutions' volumes from milliliters to liters. Remember, 1 liter is 1000 milliliters, so use this conversion when tackling problems involving molarity.

Sodium Carbonate

Sodium carbonate, known chemically as \(Na_2CO_3\), is a compound that contains two sodium ions per formula unit. When it dissolves in water, it disassociates completely, releasing these sodium ions into the solution. This property is important for chemical calculations involving sodium ion concentrations.

In the exercise, we begin with a 70.0 mL volume of sodium carbonate solution at a molarity of 3.0 M. To calculate the number of moles of sodium ions, you:

• First, convert the volume to liters by dividing 70.0 by 1000.
• Multiply the molarity by the volume in liters.
• Account for the fact that each formula unit of sodium carbonate yields two sodium ions by multiplying by 2.

This step gives us the moles of sodium ions contributed by the sodium carbonate solution, crucial for finding the total in the mixture.

Sodium Bicarbonate

Sodium bicarbonate, or \(NaHCO_3\), is slightly different compared to sodium carbonate. It contributes just one sodium ion per formula unit upon dissolution in water. This affects how we calculate its impact on sodium ion concentration in solutions.

With the given 30.0 mL of 1.0 M sodium bicarbonate, the steps to determine the moles of sodium ions are straightforward:

• Convert 30.0 mL to liters by dividing by 1000.
• Multiply the molarity by the volume in liters for the total moles of sodium bicarbonate.
• Since only one sodium ion comes from each formula unit, there's no need to multiply by more than 1.

This calculation yields the moles of sodium ions from the sodium bicarbonate portion, which you'll later add to the sodium ions from sodium carbonate to find the total sodium ion contribution.

Chemical Calculations

Chemical calculations are essential in determining concentrations, amounts, and compositions in solutions. This exercise efficiently combines several fundamental steps to achieve the sodium ion concentration using chemical principles.

Here's a breakdown of the necessary steps:

• Identify the moles of sodium ions from both sodium carbonate and sodium bicarbonate solutions by accounting for their respective molarities, volumes, and number of sodium ions per formula unit.


• Add these mole values to find the total moles of sodium ions present in the mixed solution.


• Sum the initial solution volumes to determine the total volume of the mixture in liters.


• Calculate the sodium ion concentration by dividing the total moles of sodium ions by the total volume in liters.

These steps show how mathematical principles underpin chemical reality. Such techniques are vital for understanding real-world chemical systems beyond the textbook context.