A standard solution is prepared for the analysis of fluoxymesterone (C20H29FO3), an anabolic steroid. A stock solution is first prepared by dissolving 10.0 mg of fluoxymestrone in enough water to give a total volume of 500.0 ml. A 100.0 micro liter aliquot (portion)of this solution is diluted to a final volume of 100.0 ml. Calculate the concentration of the final solution in terms of molarity.

Please show all steps because I actually understand and learn how to do this. Thanks!

We need the molarity so we will need to be working in moles and therefore need the molar mass of the steroid.

I make this
C. 12 x 20 = 240
H. 29 x 1 = 29
F. 19 x 1 = 19
O. 3 x 16 = 48

total = 336 i.e. 336 g mol^-1

If 10.0 mg is dissolved taken then this is

0.0100 g /336 g mol^-1
= 2.98 x 10^-5 mol

If this is dissolved in 500 ml which is 0.500 L then the concentration is

2.98 x 10^-5 mol / 0.500 L
= 5.95 x 10^-5 M

If 100 microlitre (0.100 ml) is diluted to 100 ml then this is a 1000x dilution (100 ml / 0.100 ml = 1000) so the final solution will be 1000 x more dilute. so

5.95 x 10^-5 M /1000
= 5.95 x 10^-8 M

(please check the maths, and you will need to decide on the final sig figs, which will be 3 sig figs I think)

Thank you! That was a giant help, I understand now!

solution

Well, I'm glad to hear that you're ready to learn! But let's break it down with a little clownish touch.

Step 1: Find the moles of fluoxymestrone in the stock solution.
To calculate moles, we use the formula: moles = mass (in grams) / molar mass

Given mass = 10.0 mg = 0.010 g
Molar mass of fluoxymestrone (C20H29FO3) = (12.01 x 20) + (1.01 x 29) + 19.00 + (16.00 x 3) = 376.45 g/mol

moles = 0.010 g / 376.45 g/mol

Step 2: Calculate the concentration of the stock solution.
Concentration (in molarity) = moles / volume (in liters)

Given volume = 500.0 ml = 0.500 L

Concentration = (0.010 g / 376.45 g/mol) / 0.500 L

Step 3: Calculate the concentration of the final solution.
To find the concentration of the final solution, we'll need to use the dilution formula: C1V1 = C2V2

Given C1 = concentration of the stock solution (which we just calculated)
V1 = volume of the stock solution taken (100.0 μL = 0.0001 L)
C2 = concentration of the final solution (what we're trying to find)
V2 = final volume of the solution (100.0 mL = 0.100 L)

Substituting the values into the dilution formula, we get:
C1V1 = C2V2
(Concentration of stock solution) x (0.0001 L) = C2 x (0.100 L)

Now, solve for C2:
C2 = (C1 x V1) / V2

Plug in the values:
C2 = [(0.010 g / 376.45 g/mol) / 0.500 L] x (0.0001 L) / 0.100 L

Now, calculate C2 to find the concentration of the final solution in terms of molarity.

I hope this explanation doesn't make your head spin like a circus clown, and that it helps you understand the steps involved!

To calculate the concentration of the final solution in terms of molarity, we need to follow these steps:

Step 1: Calculate the number of moles of fluoxymestrone in the stock solution.
To do this, we need to know the molar mass of fluoxymestrone, which is 376.45 g/mol.
The mass of fluoxymestrone in the stock solution is 10.0 mg (or 0.010 g).
We can use the formula: moles = mass / molar mass.
So, moles = 0.010 g / 376.45 g/mol = 2.66 × 10^-5 mol.

Step 2: Calculate the number of moles of fluoxymestrone in the 100.0 μL (microlitre) aliquot of the stock solution.
To convert μL to L, we divide by 1,000,000 because there are 1,000,000 μL in a liter.
So, 100.0 μL is equal to 100.0 × 10^-6 L.
Now, we can calculate the moles using the formula: moles = volume (L) × concentration (mol/L).
Since we don't know the concentration yet, we'll use the variable C.
moles = (100.0 × 10^-6 L) × C.

Step 3: Determine the concentration of the stock solution (C_stock).
We know that the stock solution has a volume of 500.0 mL (or 0.500 L) and contains 2.66 × 10^-5 mol of fluoxymestrone.
Using the formula: concentration = moles / volume, we can calculate the concentration.
C_stock = (2.66 × 10^-5 mol) / 0.500 L = 5.32 × 10^-5 mol/L.

Step 4: Calculate the concentration of the final solution (C_final).
For the final solution, we diluted the 100.0 μL aliquot to a final volume of 100.0 mL (or 0.100 L).
Using the formula: C1V1 = C2V2 (where C1 and V1 are the initial concentration and volume, and C2 and V2 are the final concentration and volume), we can solve for C_final.
(5.32 × 10^-5 mol/L) × (100.0 × 10^-6 L) = C_final × (0.100 L).
C_final = (5.32 × 10^-5 mol/L) × (100.0 × 10^-6 L) / (0.100 L).

Step 5: Calculate the final concentration in terms of molarity.
We need to move the decimal point three places to the right to convert from mol/L to mM (millimolar).
C_final = (5.32 × 10^-5 mol/L) × (1000 mM/mol).
C_final = 53.2 mM.

Therefore, the concentration of the final solution is 53.2 mM in terms of molarity.