A pretty confusing question with weird wording:
If the concentration of a compound is 10mg/ml, and its molecular weight is 267.24, how would you make 10 ml, with the compound at 10 µM?
The concentration is .010g/ml=10g/l=10/267.24 M=.0374M
so you want to dilute it .0374M/10e-6M... = 3750 times
that means one part original, and 3749 parts water.
so in 10 ml, one part=.01/3740=2.67e-6 liters or 2.67e-3 ml of stock, add solvent (water?) to 10 ml
well, we need how many mols?
we need
10 *10^-6 mols/liter
we need 10^-2 liters of that concentration
so we need 10^-8 mols of compund
we have 10 grams/liter
10 grams/liter / 267 g/mol = .0375 mols/liter
10^-8 mols/ .0375 mols/liter = 26.7 *10^-8 liters = 0.267 µM
To solve this problem, we need to understand the relationship between concentration, quantity, and molecular weight. The concentration of a compound is usually given in terms of mass per unit volume, such as milligrams per milliliter (mg/ml). The molecular weight of a compound represents the mass of one mole of that substance.
To determine how much of the compound is needed to make a specific concentration, we can use the equation:
Quantity (in moles) = Concentration (in M) × Volume (in liters)
First, let's convert the concentration from milligrams per milliliter (mg/ml) to micromoles (µM). Since 1 mg = 1,000 µg and 1 µg = 1 µmol for this compound:
Concentration (in µM) = Concentration (in mg/ml) × 1,000 µg/mg × 1 µmol/µg
Plugging in the given concentration value of 10 mg/ml, we can calculate the concentration in micromoles (µM):
Concentration (in µM) = 10 mg/ml × 1,000 µg/mg × 1 µmol/µg = 10,000 µmol/l
Now, let's calculate the quantity of the compound needed:
Quantity (in moles) = Concentration (in µM) × Volume (in liters)
Rearranging the equation to solve for Volume:
Volume (in liters) = Quantity (in moles) / Concentration (in µM)
Plugging in the values, we have:
Volume (in liters) = 10 ml × 1 L/1,000 ml = 0.01 L
Quantity (in moles) = 0.01 L × 10,000 µmol/L = 100 µmol
Finally, since the molecular weight is given as 267.24 g/mol, we can convert the quantity from moles to milligrams:
Quantity (in mg) = Quantity (in moles) × Molecular weight (in g/mol) × 1,000 mg/g
Plugging in the values, we find:
Quantity (in mg) = 100 µmol × 267.24 g/mol × 1,000 mg/g = 26,724 mg
To summarize, to make 10 ml of the compound at a concentration of 10 µM, you would need to measure out 26,724 mg of the compound.