75.0 mL of a 1.80 M solution is diluted to a volume of 258 mL. A 129-mL portion of that solution is diluted using 187 mL of water. What is the final concentration?

I figured it out thanks to related questions.

To find the final concentration, we need to calculate the number of moles of solute before and after dilution, and then use these values to determine the final concentration.

Let's break down the problem step by step:

Step 1: Calculate the moles of solute before dilution.
To find the moles of solute before dilution, we can use the formula:

moles = concentration (M) x volume (L)

Given:
- Initial volume = 75.0 mL
- Initial concentration = 1.80 M

First, convert the initial volume from milliliters (mL) to liters (L):
75.0 mL ÷ 1000 mL/L = 0.075 L

Now, use the formula to calculate the moles of solute before dilution:
moles before dilution = 1.80 M x 0.075 L

Step 2: Calculate the moles of solute after dilution.
To find the moles of solute after dilution, we need to use the volume and concentration after the first dilution.

Given:
- Portion volume after the first dilution = 129 mL
- Dilution volume after the first dilution = 187 mL

First, convert the portion volume from milliliters to liters:
129 mL ÷ 1000 mL/L = 0.129 L

Next, convert the dilution volume from milliliters to liters:
187 mL ÷ 1000 mL/L = 0.187 L

Now, we'll calculate the moles of solute after dilution using the following formula:
moles after dilution = initial moles x (portion volume / dilution volume)

moles after dilution = moles before dilution x (0.129 L / 0.187 L)

Step 3: Calculate the final concentration.
To find the final concentration, we need to divide the moles of solute after dilution by the final volume.

Given:
- Final volume = 258 mL

First, convert the final volume from milliliters to liters:
258 mL ÷ 1000 mL/L = 0.258 L

Now, we can calculate the final concentration using the following formula:
final concentration = moles after dilution / final volume

final concentration = moles after dilution / 0.258 L

Now, substitute the calculated value of moles after dilution and calculate the final concentration.

Please note that due to rounding errors throughout the calculations, the final answer may have a slight variation.