If The Absorbance Of A Solution Of Copper Ion Decreases By $45%$ Upon Dilution, How Much Water Was Added To 15.0 ML Of A 1.00 M Solution Of $Cu^{2+}$?

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Introduction

In chemistry, dilution is a process where a solution is mixed with a solvent, typically water, to decrease its concentration. This process is commonly used in various applications, including analytical chemistry, pharmaceuticals, and environmental science. One of the key factors that affect the outcome of dilution is the absorbance of the solution, which is a measure of the amount of light that is absorbed by the solution. In this article, we will explore the effect of dilution on the absorbance of a solution of copper ion and determine how much water was added to a 15.0 mL of a 1.00 M solution of $Cu^{2+}$.

Theoretical Background

The absorbance of a solution is a measure of the amount of light that is absorbed by the solution. It is typically measured using a spectrophotometer, which measures the amount of light that is transmitted through the solution. The absorbance is related to the concentration of the solution and the path length of the light through the solution. In general, the absorbance of a solution is directly proportional to the concentration of the solution.

When a solution is diluted, the concentration of the solution decreases, which results in a decrease in the absorbance of the solution. The amount of decrease in absorbance depends on the initial concentration of the solution and the amount of dilution. In this case, we are given that the absorbance of a solution of copper ion decreases by $45%$ upon dilution.

Calculating the Amount of Water Added

To calculate the amount of water added to the solution, we need to use the concept of dilution. When a solution is diluted, the amount of solute (in this case, copper ion) remains constant, but the amount of solvent (in this case, water) increases. The amount of water added can be calculated using the following equation:

V1V2=C2C1\frac{V_1}{V_2} = \frac{C_2}{C_1}

where $V_1$ is the initial volume of the solution, $V_2$ is the final volume of the solution, $C_1$ is the initial concentration of the solution, and $C_2$ is the final concentration of the solution.

In this case, we are given that the initial volume of the solution is 15.0 mL, the initial concentration of the solution is 1.00 M, and the final concentration of the solution is unknown. We are also given that the absorbance of the solution decreases by $45%$ upon dilution.

Solving for the Final Concentration

To solve for the final concentration of the solution, we need to use the concept of absorbance. The absorbance of a solution is related to the concentration of the solution and the path length of the light through the solution. In general, the absorbance of a solution is directly proportional to the concentration of the solution.

Let's assume that the initial absorbance of the solution is $A_1$ and the final absorbance of the solution is $A_2$. We are given that the absorbance of the solution decreases by $45%$ upon dilution, which means that the final absorbance of the solution is $A_2 = 0.55A_1$.

Using the Beer-Lambert Law

The Beer-Lambert law is a fundamental principle in chemistry that relates the absorbance of a solution to the concentration of the solution and the path length of the light through the solution. The Beer-Lambert law is given by the following equation:

A=εbcA = \varepsilon bc

where $A$ is the absorbance of the solution, $\varepsilon$ is the molar absorptivity of the solution, $b$ is the path length of the light through the solution, and $c$ is the concentration of the solution.

In this case, we can use the Beer-Lambert law to relate the initial and final absorbance of the solution to the initial and final concentration of the solution.

Solving for the Final Concentration

Using the Beer-Lambert law, we can write the following equation:

A1A2=C1C2\frac{A_1}{A_2} = \frac{C_1}{C_2}

Substituting the values given in the problem, we get:

A10.55A1=1.00 MC2\frac{A_1}{0.55A_1} = \frac{1.00 \text{ M}}{C_2}

Simplifying the equation, we get:

10.55=1.00 MC2\frac{1}{0.55} = \frac{1.00 \text{ M}}{C_2}

Solving for $C_2$, we get:

C2=1.00 M1.82C_2 = \frac{1.00 \text{ M}}{1.82}

C2=0.55 MC_2 = 0.55 \text{ M}

Calculating the Amount of Water Added

Now that we have the final concentration of the solution, we can use the dilution equation to calculate the amount of water added to the solution.

V1V2=C2C1\frac{V_1}{V_2} = \frac{C_2}{C_1}

Substituting the values given in the problem, we get:

15.0 mLV2=0.55 M1.00 M\frac{15.0 \text{ mL}}{V_2} = \frac{0.55 \text{ M}}{1.00 \text{ M}}

Simplifying the equation, we get:

15.0 mLV2=0.55\frac{15.0 \text{ mL}}{V_2} = 0.55

Solving for $V_2$, we get:

V2=15.0 mL0.55V_2 = \frac{15.0 \text{ mL}}{0.55}

V2=27.3 mLV_2 = 27.3 \text{ mL}

Conclusion

In this article, we explored the effect of dilution on the absorbance of a solution of copper ion and determined how much water was added to a 15.0 mL of a 1.00 M solution of $Cu^{2+}$. We used the concept of dilution and the Beer-Lambert law to relate the initial and final absorbance of the solution to the initial and final concentration of the solution. We found that the final concentration of the solution is 0.55 M and the amount of water added to the solution is 12.3 mL.

References

  • Beer, A. (1852). "Bestimmung der Absorption des Lichtes in verschiedenen Substanzen." Annalen der Physik, 86(1), 78-88.
  • Lambert, J. H. (1760). "Photometria sive de mensura et gradibus luminis, colorum et umbrae." Augsburg: Eberhard Klett.
  • Atkins, P. W. (1998). Physical Chemistry. Oxford University Press.
  • Chang, R. (2005). Physical Chemistry for the Biosciences. University Science Books.

Introduction

In our previous article, we explored the effect of dilution on the absorbance of a solution of copper ion and determined how much water was added to a 15.0 mL of a 1.00 M solution of $Cu^{2+}$. In this article, we will answer some of the most frequently asked questions related to the topic.

Q: What is the relationship between absorbance and concentration?

A: The absorbance of a solution is directly proportional to the concentration of the solution. This is known as the Beer-Lambert law, which states that the absorbance of a solution is equal to the product of the molar absorptivity, the path length of the light through the solution, and the concentration of the solution.

Q: How does dilution affect the absorbance of a solution?

A: When a solution is diluted, the concentration of the solution decreases, which results in a decrease in the absorbance of the solution. The amount of decrease in absorbance depends on the initial concentration of the solution and the amount of dilution.

Q: What is the effect of dilution on the molar absorptivity of a solution?

A: The molar absorptivity of a solution is a constant that depends on the properties of the solute and the solvent. When a solution is diluted, the molar absorptivity remains the same, but the concentration of the solution decreases, which results in a decrease in the absorbance of the solution.

Q: How can I calculate the amount of water added to a solution during dilution?

A: To calculate the amount of water added to a solution during dilution, you can use the dilution equation, which is given by:

V1V2=C2C1\frac{V_1}{V_2} = \frac{C_2}{C_1}

where $V_1$ is the initial volume of the solution, $V_2$ is the final volume of the solution, $C_1$ is the initial concentration of the solution, and $C_2$ is the final concentration of the solution.

Q: What is the significance of the Beer-Lambert law in chemistry?

A: The Beer-Lambert law is a fundamental principle in chemistry that relates the absorbance of a solution to the concentration of the solution and the path length of the light through the solution. It is widely used in various applications, including analytical chemistry, pharmaceuticals, and environmental science.

Q: Can I use the Beer-Lambert law to calculate the concentration of a solution?

A: Yes, you can use the Beer-Lambert law to calculate the concentration of a solution. However, you need to know the molar absorptivity of the solution and the path length of the light through the solution.

Q: What are some common applications of the Beer-Lambert law?

A: The Beer-Lambert law has a wide range of applications in various fields, including:

  • Analytical chemistry: The Beer-Lambert law is used to determine the concentration of a solution by measuring its absorbance.
  • Pharmaceutical industry: The Beer-Lambert law is used to determine the concentration of a solution by measuring its absorbance.
  • Environmental science: The Beer-Lambert law is used to determine the concentration of a solution by measuring its absorbance.

Conclusion

In this article, we answered some of the most frequently asked questions related to the effect of dilution on absorbance. We hope that this article has provided you with a better understanding of the topic and has helped you to answer some of the questions that you may have had.

References

  • Beer, A. (1852). "Bestimmung der Absorption des Lichtes in verschiedenen Substanzen." Annalen der Physik, 86(1), 78-88.
  • Lambert, J. H. (1760). "Photometria sive de mensura et gradibus luminis, colorum et umbrae." Augsburg: Eberhard Klett.
  • Atkins, P. W. (1998). Physical Chemistry. Oxford University Press.
  • Chang, R. (2005). Physical Chemistry for the Biosciences. University Science Books.