Calculating the Final Concentration

Oct 13, 2025 by wbrum.org 24 views

Introduction

In chemistry, dilution is a process of adding a solvent to a solution to decrease its concentration. This process is commonly used in various applications, including laboratory experiments, industrial processes, and pharmaceutical manufacturing. In this article, we will discuss how to calculate the final concentration of a diluted solution.

Understanding Molarity

Molarity is a measure of the concentration of a solution, expressed as the number of moles of solute per liter of solution. It is denoted by the symbol 'M' and is calculated using the following formula:

M = moles of solute / liters of solution

For example, if we have 0.50 L of a 6.0 M KOH solution, we can calculate the number of moles of KOH as follows:

moles of KOH = M x L = 6.0 M x 0.50 L = 3.0 moles

Calculating the Final Concentration

Now, let's calculate the final concentration of the diluted solution. We are given that 0.50 L of a 6.0 M KOH solution is added to make 4.0 L of a diluted solution. We need to find the final concentration of the diluted solution.

To do this, we can use the following formula:

Mf = (Mi x Vi) / (Vi + Vd)

where: Mf = final concentration Mi = initial concentration Vi = initial volume Vd = added volume

In this case, we have:

Mi = 6.0 M Vi = 0.50 L Vd = 3.50 L (4.0 L - 0.50 L)

Now, we can plug in the values and calculate the final concentration:

Mf = (6.0 M x 0.50 L) / (0.50 L + 3.50 L) = 3.0 moles / 4.0 L = 0.75 M

Calculating the Final Concentration of NaOH

Now, let's calculate the final concentration of NaOH in the diluted solution. We are given four options: 0.75 M NaOH, 1.33 M NaOH, 0.33 M NaOH, and 0.021 M NaOH. We need to find the correct answer.

To do this, we can use the same formula as before:

Mf = (Mi x Vi) / (Vi + Vd)

In this case, we have:

Mi = 6.0 M (KOH) Vi = 0.50 L Vd = 3.50 L (4.0 L - 0.50 L)

We are not given the initial concentration of NaOH, but we can assume that it is the same as the final concentration of the diluted solution. Therefore, we can use the following formula:

Mf = (Mi x Vi) / (Vi + Vd) = (Mf x Vi) / (Vi + Vd)

where: Mf = final concentration of NaOH Vi = initial volume of NaOH (0.50 L) Vd = added volume of NaOH (3.50 L)

Now, we can plug in the values and calculate the final concentration of NaOH:

Mf = (Mf x 0.50 L) / (0.50 L + 3.50 L) = Mf x 0.50 L / 4.0 L = Mf / 8.0

We can now use this formula to calculate the final concentration of NaOH for each of the four options:

Option A: 0.75 M NaOH

Mf = 0.75 M / 8.0 = 0.09375 M

Option B: 1.33 M NaOH

Mf = 1.33 M / 8.0 = 0.16625 M

Option C: 0.33 M NaOH

Mf = 0.33 M / 8.0 = 0.04125 M

Option D: 0.021 M NaOH

Mf = 0.021 M / 8.0 = 0.002625 M

Conclusion

In conclusion, we have calculated the final concentration of a diluted solution using the formula:

Mf = (Mi x Vi) / (Vi + Vd)

We have also calculated the final concentration of NaOH in the diluted solution for each of the four options. The correct answer is:

0.75 M NaOH

This is because the final concentration of NaOH is equal to the initial concentration of KOH divided by the total volume of the solution.

References

"Dilution" by Wikipedia
"Molarity" by Chemistry LibreTexts
"Calculating the Final Concentration of a Diluted Solution" by Chemistry LibreTexts

Frequently Asked Questions

Q: What is the final concentration of a diluted solution? A: The final concentration of a diluted solution is calculated using the formula: Mf = (Mi x Vi) / (Vi + Vd)
Q: How do I calculate the final concentration of NaOH in a diluted solution? A: To calculate the final concentration of NaOH in a diluted solution, you can use the formula: Mf = (Mi x Vi) / (Vi + Vd)
Q: What is the correct answer for the final concentration of NaOH in the diluted solution? A: The correct answer is 0.75 M NaOH.