14. what is the recipe to make 5000 ul of a 1:100 dilution?
15. what is the recipe to make 8 ml of a 1:8 dilution?
16. if my 1:100 diluted sample has a concentration of 0.4%, what was the concentration of the original sample?
17. if my 1:10 diluted sample has a concentration of 56 g/ml, what was the concentration of the original sample?
18. if i dilute my sample 1:100 then 1:10, what is the total dilution relative to the original?
19. if i dilute my sample 1:5 then 1:4, what is the total dilution relative to the original?
20. if i want to make 100 ul of a 2% red dye 40 solution, how much red dye 40 should i include?
21. if i want to make 600 ul of 17% red dye 40 solution, how much water should i add?
22. how do i write 1,500 in scientific notation?
23. how do i write 0.00067 in scientific notation?
24. what is 2.37 x 10^2 written fully out?
25. what is 7.6 x 10^-3 written fully out?
26. if my 1:10 diluted sample has a concentration of 5.5%, what was the concentration of the original sample?
27. if my 1:5 diluted sample has a concentration of 17%, what was the concentration of the original sample?

Question

Accepted Answer

### Question 14
# Explanation:
## Step1: Recall dilution formula
For a dilution, the ratio of the volume of the stock solution ($V_1$) to the volume of the final solution ($V_2$) is equal to the inverse of the dilution factor. The dilution factor ($DF$) for a 1:100 dilution is 100.
## Step2: Calculate volume of stock solution
We know $V_2 = 5000\ \mu L$ and $DF = 100$. Using the formula $V_1=\frac{V_2}{DF}$, we have $V_1=\frac{5000}{100}=50\ \mu L$. The volume of the diluent (usually water) is $V_2 - V_1=5000 - 50 = 4950\ \mu L$.
# Answer:
Take 50 $\mu L$ of the stock solution and add 4950 $\mu L$ of diluent.

### Question 15
# Explanation:
## Step1: Identify dilution factor
For a 1:8 dilution, the dilution factor ($DF$) is 8.
## Step2: Calculate volume of stock solution
We know $V_2 = 8\ mL=8000\ \mu L$. Using the formula $V_1=\frac{V_2}{DF}$, we get $V_1=\frac{8000}{8}=1000\ \mu L = 1\ mL$. The volume of the diluent is $V_2 - V_1=8000 - 1000 = 7000\ \mu L=7\ mL$.
# Answer:
Take 1 mL of the stock solution and add 7 mL of diluent.

### Question 16
# Explanation:
## Step1: Use dilution - concentration relationship
The concentration of the original sample ($C_1$) and the diluted sample ($C_2$) are related to the dilution factor ($DF$) by the formula $C_1 = C_2	imes DF$. For a 1:100 dilution, $DF = 100$ and $C_2 = 0.4\%$.
## Step2: Calculate original concentration
$C_1=0.4\%	imes100 = 40\%$
# Answer:
40%

### Question 17
# Explanation:
## Step1: Apply dilution - concentration formula
For a 1:10 dilution, the dilution factor ($DF$) is 10. Given $C_2 = 56\ g/L$, using the formula $C_1 = C_2	imes DF$.
## Step2: Compute original concentration
$C_1=56	imes10 = 560\ g/L$
# Answer:
560 g/L

### Question 18
# Explanation:
## Step1: Calculate total dilution factor
When we have a two - step dilution, the total dilution factor ($DF_{total}$) is the product of the individual dilution factors. For a 1:100 dilution (with $DF_1 = 100$) followed by a 1:10 dilution (with $DF_2 = 10$), $DF_{total}=DF_1	imes DF_2$.
## Step2: Find the value of total dilution factor
$DF_{total}=100	imes10 = 1000$
# Answer:
1:1000

### Question 19
# Explanation:
## Step1: Determine individual dilution factors
For a 1:5 dilution, $DF_1 = 5$, and for a 1:4 dilution, $DF_2 = 4$.
## Step2: Calculate total dilution factor
The total dilution factor ($DF_{total}$) is $DF_{total}=DF_1	imes DF_2=5	imes4 = 20$
# Answer:
1:20

### Question 20
# Explanation:
## Step1: Use percentage - volume relationship
A 2% solution means 2 g of solute per 100 mL (or 200 mg per 10 mL etc.). In terms of $\mu L$, a 2% solution has 20 mg per 1000 $\mu L$ or 0.02 mg per $\mu L$. For a 100 $\mu L$ of a 2% solution, we use the formula $m = C	imes V$, where $C$ is the concentration and $V$ is the volume.
## Step2: Calculate mass of Red Dye 40
$m=0.02\ mg/\mu L	imes100\ \mu L = 2\ mg$
# Answer:
2 mg

### Question 21
# Explanation:
## Step1: Calculate mass of Red Dye 40
For a 17% Red Dye 40 solution and $V = 600\ \mu L$, if we assume the percentage is by mass - volume, a 17% solution has 170 mg per 1000 $\mu L$. The mass of Red Dye 40, $m = 0.17\ mg/\mu L	imes600\ \mu L=102\ mg$.
## Step2: Calculate volume of water
The volume of the solution is 600 $\mu L$. Since the mass of the solute is already accounted for in the solution, the volume of water is 600 $\mu L$.
# Answer:
600 $\mu L$

### Question 22
# Explanation:
## Step1: Recall scientific notation form
Scientific notation is of the form $a	imes10^n$, where $1\leq a<10$ and $n$ is an integer. For 1500, we move the decimal point 3 places to the left.
## Step2: Write in scientific notation
$1500 = 1.5	imes10^3$
# Answer:
$1.5	imes10^3$

### Question 23
# Explanation:
## Step1: Recall scientific - notation rules
For a number less than 1, we move the decimal point to the right until we get a number between 1 and 10. For 0.00067, we move the decimal point 4 places to the right.
## Step2: Write in scientific notation
$0.00067=6.7	imes10^{- 4}$
# Answer:
$6.7	imes10^{-4}$

### Question 24
# Explanation:
## Step1: Expand scientific notation
$2.37	imes10^2$ means we move the decimal point 2 places to the right.
## Step2: Write the full number
$2.37	imes10^2=237$
# Answer:
237

### Question 25
# Explanation:
## Step1: Expand scientific notation
$7.6	imes10^{-3}$ means we move the decimal point 3 places to the left.
## Step2: Write the full number
$7.6	imes10^{-3}=0.0076$
# Answer:
0.0076

### Question 26
# Explanation:
## Step1: Apply dilution - concentration formula
For a 1:10 dilution, the dilution factor ($DF$) is 10. Given $C_2 = 5.5\%$, using the formula $C_1 = C_2	imes DF$.
## Step2: Calculate original concentration
$C_1=5.5\%	imes10 = 55\%$
# Answer:
55%

### Question 27
# Explanation:
## Step1: Use dilution - concentration relationship
For a 1:5 dilution, the dilution factor ($DF$) is 5. Given $C_2 = 17\%$, using the formula $C_1 = C_2	imes DF$.
## Step2: Compute original concentration
$C_1=17\%	imes5 = 85\%$
# Answer:
85%

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 14

Step1: Recall dilution formula

Step2: Calculate volume of stock solution

Step1: Identify dilution factor

Step2: Calculate volume of stock solution

Step1: Use dilution - concentration relationship

Step2: Calculate original concentration

Answer:

Question 15