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 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

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)

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)

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)

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

Key concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution. It is expressed as the number of moles of a solute per liter of solution, which is symbolized by the unit M (molar).
To compute molarity, you need the amount of solute in moles and the volume of solution in liters. The formula is:

• Molarity (M) = Moles of solute / Volume of solution in liters

For example, if you have a solution with 3 moles of sodium carbonate in 1 liter, the molarity is 3 M.
Understanding molarity is crucial to solving problems like calculating the concentration of sodium ions, as it provides a straightforward way to relate quantity to volume.

Sodium Carbonate

Sodium carbonate (Na₂CO₃), often known as soda ash or washing soda, plays a critical role in chemistry. This compound contains two sodium ions per formula unit, making it a major source of sodium ions in solutions.
When we assess the sodium ion concentration, knowing the composition of Na₂CO₃ helps us determine how many sodium ions are produced. For each mole of sodium carbonate, there are two moles of sodium ions, which can be calculated using stoichiometry.
This characteristic of sodium carbonate is pivotal when mixing it with other solutions, like sodium bicarbonate, to calculate the total sodium concentration in a mixture.

Sodium Bicarbonate

Sodium bicarbonate (NaHCO₃), commonly known as baking soda, is another important compound that releases sodium ions when dissolved in water. Unlike sodium carbonate, each mole of sodium bicarbonate contains only one sodium ion.
This difference in composition is crucial when calculating the concentration of sodium ions in a mixture. In problems that involve combining sodium carbonate and sodium bicarbonate, we must account for this difference in their ability to release sodium ions.
For instance, in the exercise, if you mix 30.0 mL of a 1.0 M sodium bicarbonate solution with other compounds, you can calculate the moles of sodium ions by considering this one-to-one ratio.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions.
In the context of the exercise, stoichiometry helps us calculate how many sodium ions can be obtained from a given amount of compounds.
It involves understanding the chemical formulas and ratios of ions to molecules. For example:

• Sodium carbonate provides 2 moles of sodium ions per mole of compound.
• Sodium bicarbonate provides 1 mole of sodium ions per mole of compound.

These ratios allow us to add up the sodium ions from different sources to find the total, leading to important calculations like the one needed for finding the sodium ion concentration in a mixed solution.