Unit conversions (dimensional analysis) Transitional Reasoning Practice

Questions

1. 1.

   An analytical chemist conducts an intrinsic dissolution test on a compressed drug tablet that exposes a flat circular face with an area of $4.50\text{ cm}^2$. The compound steadily dissolves from this surface into an aqueous buffer at a constant flux of $1.25 \times 10^{-2}\ \mu\text{g}/(\text{mm}^2\cdot\text{s})$. Given that $1\text{ cm} = 10\text{ mm}$, $1\text{ mg} = 10^3\ \mu\text{g}$, and $1\text{ h} = 3600\text{ s}$, how many hours will be required for exactly 81.0 mg of the active compound to dissolve?

   • A) 0.400 h
   • B) 4.00 h
   • C) 24.0 h
   • D) 40.0 h
2. 2.

   In an energy research laboratory, a prototype catalytic micro-combustor burns a liquid biofuel with an energy density of $2.68 \times 10^4\text{ kJ/kg}$ at a steady fuel feed rate of $4.50\text{ g/min}$. To evaluate the thermal efficiency of the device, an analytical chemist must determine the equivalent thermal power produced by this combustion process. Given that $1\text{ kg} = 10^3\text{ g}$, $1\text{ kJ} = 10^3\text{ J}$, and $1\text{ W} = 1\text{ J/s}$, what is the continuous thermal power output of the micro-combustor in watts ($\text{W}$)?

   • A) $2.01 \times 10^0\text{ W}$
   • B) $3.35 \times 10^1\text{ W}$
   • C) $2.01 \times 10^3\text{ W}$
   • D) $1.21 \times 10^5\text{ W}$
3. 3.

   An industrial hygiene chemist monitors airborne toluene vapor in a manufacturing facility using an air sampling pump operating at a calibrated flow rate of $250\text{ mL/min}$ over an $8.00\text{-hour}$ work shift. Quantitative analysis of the collection sorbent reveals that a total mass of $14.4\text{ mg}$ of toluene was captured during this period. Given that $1\text{ m}^3 = 10^6\text{ mL}$, $1\text{ h} = 60\text{ min}$, and $1\text{ mg} = 10^3\ \mu\text{g}$, what is the time-weighted average concentration of toluene in the facility air in $\mu\text{g/m}^3$?

   • A) $7.20 \times 10^6\ \mu\text{g/m}^3$
   • B) $1.20 \times 10^5\ \mu\text{g/m}^3$
   • C) $1.20 \times 10^2\ \mu\text{g/m}^3$
   • D) $7.20 \times 10^3\ \mu\text{g/m}^3$
4. 4.

   In a materials chemistry laboratory, a researcher monitors the growth of a single seed crystal suspended in a supersaturated aqueous solution. Over a continuous period of $2.50\text{ days}$, the length of the crystal increases along its growth axis by $1.08\text{ mm}$. Given that $1\text{ mm} = 10^6\text{ nm}$, $1\text{ day} = 24\text{ h}$, and $1\text{ h} = 3600\text{ s}$, what is the average linear growth rate of the crystal in nanometers per second ($\text{nm/s}$)?

   • A) $5.00 \times 10^{-3}\text{ nm/s}$
   • B) $0.432\text{ nm/s}$
   • C) $5.00\text{ nm/s}$
   • D) $120\text{ nm/s}$
5. 5.

   In high-performance liquid chromatography (HPLC), the linear velocity of a mobile phase through a column equals its volumetric flow rate divided by the column cross-sectional area. An analytical chemist operates a chromatography column with an internal cross-sectional area of $16.0\text{ mm}^2$ at an eluent flow rate of $1.44\text{ mL/min}$. Given that $1\text{ mL} = 1\text{ cm}^3$, $1\text{ cm} = 10\text{ mm}$, and $1\text{ min} = 60\text{ s}$, what is the linear velocity of the mobile phase in centimeters per second ($\text{cm/s}$)?

   • A) $0.0150\text{ cm/s}$
   • B) $1.50\text{ cm/s}$
   • C) $9.00\text{ cm/s}$
   • D) $0.150\text{ cm/s}$
6. 6.

   An environmental chemist operates a continuous-flow bioreactor that requires a trace nutrient to be dosed at $18.0\ \mu\text{g}$ per liter of treated wastewater. The facility processes wastewater at a rate of $2.40 \times 10^3\text{ m}^3\text{/day}$, and the nutrient is supplied from a stock solution with a concentration of $1.20\text{ g/L}$. Given that $1\text{ m}^3 = 10^3\text{ L}$, $1\text{ g} = 10^6\ \mu\text{g}$, and $1\text{ day} = 1440\text{ min}$, what metering flow rate of the stock solution, in milliliters per minute ($\text{mL/min}$), should be set?

   • A) 0.0250 mL/min
   • B) 1.50 mL/min
   • C) 36.0 mL/min
   • D) 25.0 mL/min
7. 7.

   To monitor environmental soil and watershed acidification, an atmospheric chemistry station measures a sulfate ion ($\text{SO}_4^{2-}$) deposition flux of $3.20 \times 10^{-3}\text{ g}\cdot\text{m}^{-2}\cdot\text{week}^{-1}$. To integrate this value into a regional ecological impact model, the measurement must be converted into standard annual metric landscape units. Given that $1\text{ km} = 10^3\text{ m}$ and $1\text{ year} = 52.0\text{ weeks}$, what is this deposition rate in $\text{kg}\cdot\text{km}^{-2}\cdot\text{year}^{-1}$?

   • A) $0.166\text{ kg}\cdot\text{km}^{-2}\cdot\text{year}^{-1}$
   • B) $3.20\text{ kg}\cdot\text{km}^{-2}\cdot\text{year}^{-1}$
   • C) $166\text{ kg}\cdot\text{km}^{-2}\cdot\text{year}^{-1}$
   • D) $1.66 \times 10^5\text{ kg}\cdot\text{km}^{-2}\cdot\text{year}^{-1}$
8. 8.

   A chemical engineering team is fabricating a catalytic membrane with an active surface area of $250\text{ cm}^2$. To achieve optimal performance, the membrane must be coated with platinum at a surface loading of $1.60 \times 10^{-2}\text{ mg/mm}^2$. If the laboratory prepares this coating using a stock solution containing platinum at a concentration of $8.00\text{ g/L}$, what volume of the stock solution, in milliliters ($\text{mL}$), is required to provide the necessary mass of platinum?

   • A) $0.500\text{ mL}$
   • B) $5.00\text{ mL}$
   • C) $500\text{ mL}$
   • D) $50.0\text{ mL}$
9. 9.

   A chemistry student determines the thickness of a rectangular sheet of aluminum foil using indirect measurement in the laboratory. The foil sample has a length of $25.0\text{ cm}$, a width of $12.0\text{ cm}$, and a mass of $4.05\text{ g}$. Given that the density of aluminum is $2.70\text{ g/cm}^3$ and $1\text{ cm} = 10^4\ \mu\text{m}$, what is the thickness of the foil in micrometers ($\mu\text{m}$)?

   • A) $0.0500\ \mu\text{m}$
   • B) $5.00\ \mu\text{m}$
   • C) $50.0\ \mu\text{m}$
   • D) $500\ \mu\text{m}$
10. 10.

    A laboratory technician dispenses a liquid reagent with a density of $1.25\text{ g/cm}^3$ into a reaction vessel at a constant flow rate of $48.0\text{ mL/min}$ for exactly $15.0\text{ minutes}$. Given that $1\text{ mL} = 1\text{ cm}^3$ and $1\text{ kg} = 1000\text{ g}$, what is the total mass of the reagent added to the vessel in kilograms?

    • A) 0.576 kg
    • B) 1.44 kg
    • C) 9.00 kg
    • D) 0.900 kg

Answers and step-by-step solutions appear after you finish the test.