A 5M solution is diluted 1/10 and again 1/5. What is the concentration of each dilution?

First dilution is 5M x 1/10 = 0.5 M

Second dil is 0.5 M x 1/5 = 0.1 M.

Ah, dilution, my favorite subject! Alright, let's break it down.

First, we have a 5M solution. Then it's diluted 1/10, which means we're making it one-tenth as concentrated. So, we're left with a solution that's 1/10 as much, or 0.5M (because 5M divided by 10 is 0.5M).

Now comes the exciting part! We dilute it again by 1/5. So, we're taking that 0.5M solution and making it one-fifth as concentrated. Quick math magic: 0.5M divided by 5 is 0.1M!

Ta-da! We end up with a final concentration of 0.1M. So, the concentration of each dilution is 0.5M and 0.1M, respectively. Cheers to dilution shenanigans!

To find the concentration of each dilution, we will first calculate the concentration after the first dilution and then use that result for the second dilution.

1. First dilution:
The solution is diluted 1/10, which means that 1 part of the original solution is mixed with 10 parts of a diluent (such as water).
To determine the concentration after the first dilution, we can use the dilution formula:
C1V1 = C2V2
Where:
C1 = initial concentration (5 M)
V1 = initial volume (unknown)
C2 = final concentration (unknown)
V2 = final volume (unknown)

Since C2 is the variable we want to find, we can rearrange the formula as:
C2 = C1V1/V2

Substituting the known values:
C2 = (5 M)(1)/(10)

Calculating:
C2 = 0.5 M

So, after the first dilution, the concentration is 0.5 M.

2. Second dilution:
The solution with a concentration of 0.5 M is now diluted 1/5, which means that 1 part of the 0.5 M solution is mixed with 5 parts of a diluent.
Using the same dilution formula, we can find the concentration after the second dilution:
C1 = 0.5 M
V1 = unknown
C2 = final concentration (unknown)
V2 = final volume (unknown)

C2 = C1V1/V2

C2 = (0.5 M)(1)/(5)

Calculating:
C2 = 0.1 M

So, after the second dilution, the concentration is 0.1 M.

Thus, the concentration of each dilution is 0.5 M after the first dilution and 0.1 M after the second dilution.

To find the concentration of each dilution, we need to understand how dilution works. Dilution involves adding a solvent (usually water) to a solution to decrease its concentration.

Let's break down the dilution process step by step:

Step 1: Diluted 1/10
To dilute the 5M solution by 1/10, we need to add 1 part of the solution to 9 parts of the solvent (water).

Formula: C1V1 = C2V2

C1 = Initial concentration = 5M
V1 = Initial volume = ?
C2 = Final concentration = ?
V2 = Final volume = 1/10th of the initial volume

Since we are diluting by 1/10, V2 will be 1/10 of V1.

Let's substitute the known values into the formula and solve for C2:

5M * V1 = C2 * (V1/10)

Dividing both sides by V1:

5M = C2/10

Multiplying both sides by 10:

50M = C2

Therefore, after diluting the 5M solution by 1/10, the concentration is 50M.

Step 2: Diluted 1/5
To dilute the previous 50M solution by 1/5, we again add 1 part of the solution to 4 parts of the solvent (water).

Using the same formula:

C1 = 50M
V1 = ?
C2 = ?
V2 = 1/5th of the previous volume

Since we are diluting by 1/5, V2 will be 1/5 of V1.

Let's substitute the known values into the formula and solve for C2:

50M * V1 = C2 * (V1/5)

Dividing both sides by V1:

50M = C2/5

Multiplying both sides by 5:

250M = C2

Therefore, after diluting the 50M solution by 1/5, the concentration is 250M.

In summary, after the two dilutions, the concentrations are:

- After the first dilution (1/10): 50M
- After the second dilution (1/5): 250M