Concentration of Barium Ion

Oct 13, 2025 by leolavanderia.com.br 117 views

Introduction

When two solutions of different concentrations are mixed, the resulting solution can exhibit various properties, including changes in pH, temperature, and the formation of precipitates. In this scenario, a 20.0-milliliter sample of $0.200$ -molar $K_2CO_3$ solution is added to 30.0 milliliters of $0.400$ -molar $Ba(NO_3)_2$ solution, resulting in the formation of barium carbonate precipitate. The concentration of barium ion, $Ba^{2+}$ , in the resulting solution is the primary focus of this discussion.

Chemical Reaction

The chemical reaction between $K_2CO_3$ and $Ba(NO_3)_2$ can be represented as follows:

Ba(NO_3)_2 + K_2CO_3 \rightarrow BaCO_3 \downarrow + 2KNO_3

In this reaction, barium carbonate ( $BaCO_3$ ) precipitates out of the solution, leaving behind a solution containing potassium nitrate ( $KNO_3$ ) and barium ions ( $Ba^{2+}$ ).

Stoichiometry

To determine the concentration of barium ion in the resulting solution, we need to consider the stoichiometry of the reaction. From the balanced equation, we can see that 1 mole of $Ba(NO_3)_2$ reacts with 1 mole of $K_2CO_3$ to produce 1 mole of $BaCO_3$ and 2 moles of $KNO_3$ . Since the initial concentration of $Ba(NO_3)_2$ is 0.400 molar and the initial concentration of $K_2CO_3$ is 0.200 molar, the limiting reactant can be determined.

Limiting Reactant

To determine the limiting reactant, we need to calculate the number of moles of each reactant present in the initial solutions. The number of moles of $Ba(NO_3)_2$ can be calculated as follows:

n_{Ba(NO_3)_2} = C_{Ba(NO_3)_2} \times V_{Ba(NO_3)_2} = 0.400 \, M \times 30.0 \, mL = 0.012 \, mol

Similarly, the number of moles of $K_2CO_3$ can be calculated as follows:

n_{K_2CO_3} = C_{K_2CO_3} \times V_{K_2CO_3} = 0.200 \, M \times 20.0 \, mL = 0.004 \, mol

Since the number of moles of $Ba(NO_3)_2$ (0.012 mol) is greater than the number of moles of $K_2CO_3$ (0.004 mol), $K_2CO_3$ is the limiting reactant.

Concentration of Barium Ion

Since $K_2CO_3$ is the limiting reactant, the number of moles of $BaCO_3$ formed will be equal to the number of moles of $K_2CO_3$ present in the initial solution. The number of moles of $BaCO_3$ formed can be calculated as follows:

n_{BaCO_3} = n_{K_2CO_3} = 0.004 \, mol

Since 1 mole of $BaCO_3$ is formed from 1 mole of $Ba(NO_3)_2$ , the number of moles of $Ba^{2+}$ remaining in the solution can be calculated as follows:

n_{Ba^{2+}} = n_{Ba(NO_3)_2} - n_{BaCO_3} = 0.012 \, mol - 0.004 \, mol = 0.008 \, mol

The total volume of the resulting solution is the sum of the initial volumes of the two solutions:

V_{total} = V_{Ba(NO_3)_2} + V_{K_2CO_3} = 30.0 \, mL + 20.0 \, mL = 50.0 \, mL

The concentration of barium ion in the resulting solution can be calculated as follows:

C_{Ba^{2+}} = \frac{n_{Ba^{2+}}}{V_{total}} = \frac{0.008 \, mol}{50.0 \, mL} = 0.160 \, M

Conclusion

In conclusion, when a 20.0-milliliter sample of $0.200$ -molar $K_2CO_3$ solution is added to 30.0 milliliters of $0.400$ -molar $Ba(NO_3)_2$ solution, the resulting solution contains a concentration of barium ion, $Ba^{2+}$ , of 0.160 molar. This calculation is based on the stoichiometry of the reaction between $K_2CO_3$ and $Ba(NO_3)_2$ and the determination of the limiting reactant.

References

[1] Chemistry: An Atoms First Approach. (2017). Cengage Learning.
[2] Chemistry: The Central Science. (2018). Pearson Education.
[3] Stoichiometry: The Mole Concept. (2020). Chemistry LibreTexts.

Additional Resources

[1] Stoichiometry Tutorial. (2020). Khan Academy.
[2] Stoichiometry Practice Problems. (2020). Chemistry LibreTexts.
[3] Stoichiometry Calculator. (2020). Wolfram Alpha.

Q&A: Concentration of Barium Ion in the Resulting Solution

Q: What is the concentration of barium ion in the resulting solution?

A: The concentration of barium ion in the resulting solution is 0.160 molar.

Q: Why is $K_2CO_3$ the limiting reactant in this reaction?

A: $K_2CO_3$ is the limiting reactant because it has the lowest number of moles present in the initial solutions. In this case, the number of moles of $K_2CO_3$ (0.004 mol) is less than the number of moles of $Ba(NO_3)_2$ (0.012 mol).

Q: How is the concentration of barium ion calculated?

A: The concentration of barium ion is calculated by dividing the number of moles of barium ion remaining in the solution by the total volume of the resulting solution.

Q: What is the total volume of the resulting solution?

A: The total volume of the resulting solution is the sum of the initial volumes of the two solutions, which is 50.0 milliliters.

Q: What is the significance of the concentration of barium ion in the resulting solution?

A: The concentration of barium ion in the resulting solution is significant because it determines the amount of barium ion available for further reactions.

Q: How does the concentration of barium ion affect the properties of the resulting solution?

A: The concentration of barium ion affects the properties of the resulting solution, such as its pH, conductivity, and solubility.

Q: What are some common applications of barium ion in chemistry?

A: Barium ion has several common applications in chemistry, including the production of barium carbonate, barium sulfate, and other barium compounds.

Q: How can the concentration of barium ion be measured?

A: The concentration of barium ion can be measured using various techniques, including titration, spectroscopy, and chromatography.

Q: What are some common sources of barium ion in chemistry?

A: Barium ion can be obtained from various sources, including barium carbonate, barium sulfate, and other barium compounds.

Q: How can the concentration of barium ion be controlled in a chemical reaction?

A: The concentration of barium ion can be controlled by adjusting the amount of barium ion added to the reaction mixture, as well as the concentration of other reactants.

Q: What are some common safety precautions when handling barium ion?

A: When handling barium ion, it is essential to wear protective gear, including gloves, goggles, and a lab coat. Barium ion can be toxic and should be handled with care.

Additional Resources

[1] Barium Ion: Properties and Applications. (2020). Chemistry LibreTexts.
[2] Barium Ion: Safety Precautions. (2020). American Chemical Society.
[3] Barium Ion: Measurement Techniques. (2020). Analytical Chemistry.

References

[1] Chemistry: An Atoms First Approach. (2017). Cengage Learning.
[2] Chemistry: The Central Science. (2018). Pearson Education.
[3] Stoichiometry: The Mole Concept. (2020). Chemistry LibreTexts.