The density of 2-methyl-2-butanol is 0.806 g/mL. How many milligrams represent an aliquot of 430 μL? How many millimoles represent an aliquot of 0.650 mL (2-methyl-2-butanol; formula weight is 88.15 g/mol)?
The Correct Answer and Explanation is:
Let’s solve both parts step by step.
Part 1: How many milligrams are in 430 µL of 2-methyl-2-butanol?
Given:
- Volume = 430 µL
- Density = 0.806 g/mL
- 1 mL = 1000 µL
- 1 g = 1000 mg
Step 1: Convert µL to mL430 μL=4301000=0.430 mL430 \, \mu L = \frac{430}{1000} = 0.430 \, mL430μL=1000430=0.430mL
Step 2: Use density to find mass in gramsMass=Density×Volume=0.806 g/mL×0.430 mL=0.34658 g\text{Mass} = \text{Density} \times \text{Volume} = 0.806 \, g/mL \times 0.430 \, mL = 0.34658 \, gMass=Density×Volume=0.806g/mL×0.430mL=0.34658g
Step 3: Convert grams to milligrams0.34658 g×1000=346.58 mg0.34658 \, g \times 1000 = 346.58 \, mg0.34658g×1000=346.58mg
Answer for Part 1:
346.58 mg
Part 2: How many millimoles are in 0.650 mL of 2-methyl-2-butanol?
Given:
- Volume = 0.650 mL
- Density = 0.806 g/mL
- Formula weight = 88.15 g/mol
Step 1: Calculate mass in gramsMass=Density×Volume=0.806 g/mL×0.650 mL=0.5239 g\text{Mass} = \text{Density} \times \text{Volume} = 0.806 \, g/mL \times 0.650 \, mL = 0.5239 \, gMass=Density×Volume=0.806g/mL×0.650mL=0.5239g
Step 2: Calculate molesMoles=MassMolar Mass=0.5239 g88.15 g/mol≈0.00594 mol\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{0.5239 \, g}{88.15 \, g/mol} \approx 0.00594 \, molMoles=Molar MassMass=88.15g/mol0.5239g≈0.00594mol
Step 3: Convert moles to millimoles0.00594 mol×1000=5.94 mmol0.00594 \, mol \times 1000 = 5.94 \, mmol0.00594mol×1000=5.94mmol
Answer for Part 2:
5.94 mmol
Explanation
To determine the amount of 2-methyl-2-butanol present in different volumes, we apply concepts from density and stoichiometry. Density provides a way to relate the volume of a substance to its mass. Since the density of 2-methyl-2-butanol is 0.806 g/mL, this means that every 1 mL of the alcohol weighs 0.806 grams.
In the first part, we convert microliters to milliliters to match the units used with density. Since 1000 µL equals 1 mL, 430 µL is 0.430 mL. Multiplying this volume by the density yields the mass in grams. To express the result in milligrams, which are thousandths of a gram, we multiply the gram value by 1000. This gives a total of 346.58 milligrams.
In the second part, we calculate the number of millimoles, a common unit in chemical analysis. The volume is given in milliliters, so we use the density directly to get the mass in grams. We then divide by the molar mass of the compound, which tells us how many grams are in one mole of the substance. This calculation gives the amount in moles. Since a millimole is one-thousandth of a mole, we multiply the mole value by 1000 to convert. The final result is 5.94 millimoles.
These calculations are essential in preparing solutions, determining reactant quantities, or analyzing sample compositions in both academic and professional laboratory settings.
