Question

Solution Concentration If \(6.73 \mathrm{g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) is dissolved in enough water to make \(250 .\) mL of solution, what is the molar concentration of the sodium carbonate? What are the molar concentrations of the \(\mathrm{Na}^{+}\) and \(\mathrm{CO}_{3}^{2-}\) ions?

Short answer

The molar concentration of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is 0.254 M; \(\mathrm{Na}^{+}\) is 0.508 M; \(\mathrm{CO}_{3}^{2-}\) is 0.254 M.

Step-by-step solution

Calculate Moles of Na2CO3

First, we need to calculate how many moles of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) are present in \(6.73 \text{ g}\). We use the formula: \(\text{moles} = \text{mass (g)} / \text{molar mass (g/mol)}\). The molar mass of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is \(2 \times 22.99 + 12.01 + 3 \times 16.00 = 105.99 \text{ g/mol}\). The moles of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) are calculated as follows: \(6.73 \text{ g} / 105.99 \text{ g/mol} \approx 0.0635 \text{ moles}\).

Determine Molar Concentration of Na2CO3

The molar concentration of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is calculated using the formula: \(\text{Concentration (M)} = \text{moles} / \text{volume (L)}\). The volume of the solution is \(250 \text{ mL} = 0.25 \text{ L}\). Thus, the concentration of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is \(0.0635 \text{ moles} / 0.25 \text{ L} = 0.254 \text{ M}\).

Calculate Molar Concentration of Na+ Ions

Since \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) dissociates into 2 \(\mathrm{Na}^{+}\) ions for every molecule, the concentration of \(\mathrm{Na}^{+}\) ions is twice that of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\). Therefore, the concentration of \(\mathrm{Na}^{+}\) is \(2 \times 0.254 \text{ M} = 0.508 \text{ M}\).

Calculate Molar Concentration of CO3^2- Ions

Each molecule of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) produces only one \(\mathrm{CO}_{3}^{2-}\) ion upon dissociation. Therefore, the concentration of \(\mathrm{CO}_{3}^{2-}\) ions is the same as the concentration of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\), which is \(0.254 \text{ M}\).

Key concepts

Molarity

Molarity is a way of expressing the concentration of a solution. It tells us how many moles of a solute are present in one liter of solution. This unit of measurement is very handy in chemistry as it helps us quantify how much solute has been dissolved. The formula for calculating molarity is \\[\text{Molarity} (M) = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}}\]. \In the context of the exercise, we calculated the molarity of sodium carbonate (\(\text{Na}_2\text{CO}_3\)) by first finding out how many moles of the compound we had, and then considering the volume of the solution. Molarity not only helps in finding out the concentration of the primary solution but it's foundational for further calculations.

Concentration Calculations

Concentration calculations are essential for understanding how much solute is present in a given volume of solution. Once we know the molarity, it's possible to conduct several chemistry-related calculations. To calculate the concentration of our sodium carbonate solution: \

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• We first determined the moles of \(\text{Na}_2\text{CO}_3\) using its molar mass.
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• Then, using the formula for molarity, we found the concentration of the solution in moles per liter (\(M\)).
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\This process highlights the steps needed to find concentrations, an important concept in solution chemistry, which forms the basis for titrations, dilutions, and more.

Chemical Solutions

Chemical solutions are mixtures of solutes dissolved in solvents, like our sodium carbonate in water example. Understanding solutions is crucial because it allows scientists to predict behavior in various chemical reactions and environments. In this exercise, \(\text{Na}_2\text{CO}_3\) was dissolved in water, creating a homogeneous solution. \Here are some key points about chemical solutions: \

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• The solute is the substance being dissolved (\(\text{Na}_2\text{CO}_3\) in our case).
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• The solvent is the substance doing the dissolving, generally in greater amount (water, here).
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• Temperature, pressure, and nature of solute/solvent affect solubility.
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\Understanding the nature of chemical solutions helps in performing reactions and predicting the properties of the resultant mixtures.

Ion Dissociation

Ion dissociation is a process where ionic compounds split into ions when they dissolve in water. This behavior is crucial for reactions in solutions. For \(\text{Na}_2\text{CO}_3\): \

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• It dissociates into two \(\text{Na}^+\) ions and one \(\text{CO}_3^{2-}\) ion for each molecule.
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• This dissociation allows us to calculate the individual ion concentrations in the solution.
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\In this exercise, understanding dissociation was essential for determining the molar concentrations of \(\text{Na}^+\) and \(\text{CO}_3^{2-}\) ions separately. \Knowing how compounds dissociate helps in analyzing electrolytes, predicting the formation of acids or bases, and assessing conductivity in solutions.