Unit conversions (dimensional analysis) Transitional Reasoning Download PDF

Questions

1. 1.

   During the chemical vapor synthesis of carbon nanotubes, methane gas is fed into a tube furnace at a constant rate of $2.50\text{ oz/h}$. To configure the furnace's automated digital mass flow controller, a chemical engineer must convert this rate into milligrams per second ($\text{mg/s}$). Given that $1\text{ lb} = 16.0\text{ oz}$, $1\text{ lb} = 453.6\text{ g}$, and $1\text{ h} = 3600\text{ s}$, what is the mass flow rate of methane in $\text{mg/s}$?

   • A) 315 mg/s
   • B) 5040 mg/s
   • C) 1180 mg/s
   • D) 19.7 mg/s
2. 2.

   An environmental remediation facility pumps contaminated groundwater through an activated carbon adsorption column at a steady flow rate of 15.0 L/min. The groundwater contains dissolved benzene at an average concentration of 4.80 mg/L. Assuming the column operates continuously for 28.0 days with 100% capture efficiency, what total mass of benzene, in kilograms, is removed from the water?

   • A) 0.0484 kg
   • B) 0.121 kg
   • C) 2900 kg
   • D) 2.90 kg
3. 3.

   During the characterization of a newly synthesized nickel-based superalloy for turbine components, a materials chemist determines its density to be $8.25\text{ g/cm}^3$. An aerospace engineering team requires this physical property to be reported in pounds per cubic foot ($\text{lb/ft}^3$) for structural weight modeling. Given that $1\text{ lb} = 453.6\text{ g}$, $1\text{ in} = 2.54\text{ cm}$, and $1\text{ ft} = 12\text{ in}$, what is the density of the superalloy expressed in $\text{lb/ft}^3$?

   • A) $79.8\text{ lb/ft}^3$
   • B) $515\text{ lb/ft}^3$
   • C) $0.554\text{ lb/ft}^3$
   • D) $2.34 \times 10^5\text{ lb/ft}^3$
4. 4.

   During the chemical evaluation of a drop-in aviation biofuel, a bomb calorimeter experiment determines that the fuel has an energy density of $42.8\text{ MJ/kg}$. To compare this result with international combustion specifications, an engineer needs to express this value in kilocalories per pound ($\text{kcal/lb}$). Given that $1\text{ MJ} = 10^6\text{ J}$, $1\text{ cal} = 4.184\text{ J}$, $1\text{ kcal} = 1000\text{ cal}$, and $1\text{ kg} = 2.205\text{ lb}$, what is the energy density of the biofuel in $\text{kcal/lb}$?

   • A) $2.26 \times 10^4\text{ kcal/lb}$
   • B) $4.64 \times 10^3\text{ kcal/lb}$
   • C) $1.02 \times 10^4\text{ kcal/lb}$
   • D) $8.12 \times 10^4\text{ kcal/lb}$
5. 5.

   In a materials chemistry laboratory, a silicon wafer is coated with a protective ceramic layer using chemical vapor deposition at a steady rate of 0.450 nm/s. The deposition chamber runs continuously for a total process duration of 8.00 hours. Given that 1 m = 100 cm = $10^9$ nm, 1 in = 2.54 cm, and 1 mil = $1.00 \times 10^{-3}$ in, what is the final thickness of the coating in mils?

   • A) 0.00850 mils
   • B) 0.142 mils
   • C) 0.510 mils
   • D) 3.29 mils
6. 6.

   A pediatric liquid medicine contains 12.5 mg of an active drug ingredient per 5.00 mL of oral suspension. A child weighing 33.0 lb is prescribed 4.00 mg of the drug per kilogram of body mass per day, divided evenly into two doses each day (given that 1 kg = 2.20 lb). Using dimensional analysis, what volume of the suspension, in milliliters, should be administered for a single dose?

   • A) 24.0 mL
   • B) 58.1 mL
   • C) 75.0 mL
   • D) 12.0 mL
7. 7.

   During an environmental monitoring assessment of a chemical manufacturing cleanroom, particulate matter is deposited on a collection filter at a constant flux of $7.50 \times 10^{-2}\text{ mg}/(\text{m}^2\cdot\text{h})$. To compare this result against surface contamination standards, an environmental chemist needs to convert this rate into micrograms per square centimeter per day ($\mu\text{g}/(\text{cm}^2\cdot\text{day})$). Using dimensional analysis, what is this deposition flux expressed in $\mu\text{g}/(\text{cm}^2\cdot\text{day})$?

   • A) $1.80 \times 10^{1}\text{ }\mu\text{g}/(\text{cm}^2\cdot\text{day})$
   • B) $1.80 \times 10^{-1}\text{ }\mu\text{g}/(\text{cm}^2\cdot\text{day})$
   • C) $3.13 \times 10^{-4}\text{ }\mu\text{g}/(\text{cm}^2\cdot\text{day})$
   • D) $1.80 \times 10^{-7}\text{ }\mu\text{g}/(\text{cm}^2\cdot\text{day})$
8. 8.

   In an analytical laboratory, an automated syringe pump dispenses a concentrated reagent solution with a density of $1.25\text{ g/cm}^3$ at a constant flow rate of $40.0\,\mu\text{L/s}$. The pump runs continuously for exactly $4.00\text{ minutes}$ into a reaction vessel. Using dimensional analysis, what is the total mass of the reagent solution delivered to the vessel in milligrams ($\text{mg}$)?

   • A) $1.20 \times 10^4\text{ mg}$
   • B) $7.68 \times 10^3\text{ mg}$
   • C) $2.00 \times 10^2\text{ mg}$
   • D) $1.20 \times 10^1\text{ mg}$