Calculate the new molarity if each of the following dilutions is made. Assume the volumes are additive.

(a) 52.3 mL of water is added to 27.1 mL of 0.124 M KOH solution

(b) 110. mL of water is added to 54.2 mL of 0.808 M NaCl solution

((please show work, thank u so much)

The easiest way to work with these type of calculations is to calculate the number of millimoles present, calculate the total volume and then work out the concentration.

So

Number of millimoles of KOH = N =
27.1 x 0.124 mmoles

Total volume after dilution = V =
52.3 ml + 27.1 ml

Thus new concnetration = N/V

The reason for working in mmoles is that if you work in moles a factor of 1000 appears, which cancels at the end.

Sure, let me perform the calculations for you with a touch of humor.

(a) To calculate the new molarity after the dilution, we need to consider that the volumes are additive.

First, let's calculate the number of moles of KOH in the initial solution:
moles of KOH = molarity x volume = 0.124 M x 27.1 mL = 3.3544 mmol

Now, let's calculate the final volume after the dilution:
final volume = initial volume + added volume = 27.1 mL + 52.3 mL = 79.4 mL

Next, let's calculate the new molarity:
new molarity = moles of KOH / final volume

But wait, before we calculate, let's take a moment to appreciate this lovely chemical reaction between KOH and H2O... *inserts a tiny clap emoji*

Alright, let's get back to business. Calculating the new molarity:
new molarity = 3.3544 mmol / 79.4 mL

And the final answer is...

*drumroll please*

The new molarity after dilution is approximately 0.042 M KOH. Ta-da!

(b) Similarly, let's perform the calculation for the second case with a dash of humor.

To begin, let's find the number of moles of NaCl in the initial solution:
moles of NaCl = molarity x volume = 0.808 M x 54.2 mL = 43.8736 mmol

Now, let's determine the final volume after the dilution:
final volume = initial volume + added volume = 54.2 mL + 110 mL = 164.2 mL

It's time to crunch some numbers and calculate the new molarity:
new molarity = moles of NaCl / final volume

But before that, let me share a little joke about salt: Why did the salt go to therapy? Because it had low self "a-salt"!

Now, let's get back to the calculation:
new molarity = 43.8736 mmol / 164.2 mL

And the answer is...

*inserts suspenseful pause*

The new molarity after dilution is approximately 0.267 M NaCl. Huzzah!

I hope you enjoyed the calculations with a touch of humor. If you have any more questions or need further assistance, feel free to ask!

To calculate the new molarity after a dilution, we can use the formula:

M1V1 = M2V2

where M1 is the initial molarity, V1 is the initial volume, M2 is the final molarity, and V2 is the final volume.

(a) Dilution of KOH solution:
Initial molarity (M1) = 0.124 M
Initial volume (V1) = 27.1 mL
Final volume after dilution (V2) = 27.1 mL + 52.3 mL = 79.4 mL

Using the formula:

M1V1 = M2V2

(0.124 M)(27.1 mL) = M2(79.4 mL)

M2 = (0.124 M)(27.1 mL) / 79.4 mL
M2 = 0.0424 M

Therefore, the new molarity after the dilution is 0.0424 M.

(b) Dilution of NaCl solution:
Initial molarity (M1) = 0.808 M
Initial volume (V1) = 54.2 mL
Final volume after dilution (V2) = 54.2 mL + 110 mL = 164.2 mL

Using the formula:

M1V1 = M2V2

(0.808 M)(54.2 mL) = M2(164.2 mL)

M2 = (0.808 M)(54.2 mL) / 164.2 mL
M2 = 0.266 M

Therefore, the new molarity after the dilution is 0.266 M.

To calculate the new molarity after dilution, you need to use the formula:

M1V1 = M2V2

Where:
M1 = initial molarity
V1 = initial volume
M2 = final molarity
V2 = final volume

Let's solve the problems step by step:

(a) 52.3 mL of water is added to 27.1 mL of 0.124 M KOH solution.

Step 1: Calculate the initial moles of solute (KOH):
Initial moles = Initial molarity * Initial volume
Initial moles = 0.124 M * 27.1 mL

Step 2: Calculate the final volume (V2):
Final volume (V2) = Initial volume (V1) + Volume of water added
Final volume (V2) = 27.1 mL + 52.3 mL

Step 3: Plug the values into the formula and solve for M2:
M1 * V1 = M2 * V2
(0.124 M) * (27.1 mL) = M2 * (27.1 mL + 52.3 mL)

Now, you can solve for M2:

M2 = (0.124 M * 27.1 mL) / (27.1 mL + 52.3 mL)

(b) 110 mL of water is added to 54.2 mL of 0.808 M NaCl solution.

Step 1: Calculate the initial moles of solute (NaCl):
Initial moles = Initial molarity * Initial volume
Initial moles = 0.808 M * 54.2 mL

Step 2: Calculate the final volume (V2):
Final volume (V2) = Initial volume (V1) + Volume of water added
Final volume (V2) = 54.2 mL + 110 mL

Step 3: Plug the values into the formula and solve for M2:
M1 * V1 = M2 * V2
(0.808 M) * (54.2 mL) = M2 * (54.2 mL + 110 mL)

Now, you can solve for M2:

M2 = (0.808 M * 54.2 mL) / (54.2 mL + 110 mL)

Simply substitute the given values into the equations to calculate the new molarity (M2) in each case.