Convert the following from M (molarity) to μg/μL

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Convert the following from M (molarity) to μg/μL (microgram/microliter). Show all work for credit. MW = 37,000 g/mole a.) 3.338 x 10^-5 M b.) 8.567 x 10^-6 M

The Correct Answer and Explanation is:

To convert molarity (M) to micrograms per microliter (μg/μL), we need to follow these steps:

Formula to use:

Mass (μg)=Molarity (M)×Molecular Weight (g/mol)×106\text{Mass (μg)} = \text{Molarity (M)} \times \text{Molecular Weight (g/mol)} \times 10^6Mass (μg)=Molarity (M)×Molecular Weight (g/mol)×106

Here, we need to multiply by 10610^6106 because we’re converting from grams to micrograms (1 g = 10610^6106 μg) and from liters to microliters (1 L = 10610^6106 μL).

Step-by-Step Solution for each part:

a) For 3.338×10−5 M3.338 \times 10^{-5} \, M3.338×10−5M:

  1. Molarity (M) = 3.338×10−5 M3.338 \times 10^{-5} \, \text{M}3.338×10−5M
  2. Molecular Weight (MW) = 37,000 g/mol
  3. Convert to μg/μL: Mass (μg/μL)=3.338×10−5 M×37,000 g/mol×106\text{Mass (μg/μL)} = 3.338 \times 10^{-5} \, \text{M} \times 37,000 \, \text{g/mol} \times 10^6Mass (μg/μL)=3.338×10−5M×37,000g/mol×106 =3.338×10−5×37,000×106= 3.338 \times 10^{-5} \times 37,000 \times 10^6=3.338×10−5×37,000×106 =123,526 μg/μL= 123,526 \, \mu g/\mu L=123,526μg/μL

So, the answer for part (a) is: 123,526 μg/μL

b) For 8.567×10−6 M8.567 \times 10^{-6} \, M8.567×10−6M:

  1. Molarity (M) = 8.567×10−6 M8.567 \times 10^{-6} \, \text{M}8.567×10−6M
  2. Molecular Weight (MW) = 37,000 g/mol
  3. Convert to μg/μL: Mass (μg/μL)=8.567×10−6 M×37,000 g/mol×106\text{Mass (μg/μL)} = 8.567 \times 10^{-6} \, \text{M} \times 37,000 \, \text{g/mol} \times 10^6Mass (μg/μL)=8.567×10−6M×37,000g/mol×106 =8.567×10−6×37,000×106= 8.567 \times 10^{-6} \times 37,000 \times 10^6=8.567×10−6×37,000×106 =317,979 μg/μL= 317,979 \, \mu g/\mu L=317,979μg/μL

So, the answer for part (b) is: 317,979 μg/μL

Explanation:

To convert molarity (M, in mol/L) to micrograms per microliter (μg/μL), we use the formula that incorporates the molecular weight (MW) of the substance. By multiplying the molarity by the molecular weight in grams per mole and scaling up by a factor of 10610^6106 to account for the conversion from grams to micrograms and liters to microliters, we get the desired concentration in μg/μL.

Thus, we end up with the two final concentrations:

  • Part (a): 123,526 μg/μL
  • Part (b): 317,979 μg/μL

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