Scientific notation Transitional Reasoning Download PDF

Questions

1. 1.

   During a time-of-flight mass spectrometry demonstration, an ionized molecule travels through a drift tube with a length of 1.20 meters at a constant speed of $4.00 \times 10^5\text{ m/s}$. To set the detection window, a chemistry student must determine the time required, in seconds, for the ion to reach the detector. What is this flight time in seconds, expressed in standard scientific notation ($N \times 10^n$, where $1 \le N < 10$)?

   • A) $3.00 \times 10^{-4}\text{ s}$
   • B) $3.00 \times 10^{-5}\text{ s}$
   • C) $0.300 \times 10^{-5}\text{ s}$
   • D) $3.00 \times 10^{-6}\text{ s}$
2. 2.

   A chemistry student determines the thickness of a rectangular sheet of aluminum foil using laboratory measurements. The sheet has a length of $3.0 \times 10^1$ cm, a width of $2.0 \times 10^1$ cm, and a mass of 3.24 g. Given that the density of aluminum is 2.70 g/cm³, what is the thickness of the foil in centimeters, expressed in standard scientific notation ($N \times 10^n$, where $1 \le N < 10$)?

   • A) $2.0 \times 10^{-3}$ cm
   • B) $2.0 \times 10^{-2}$ cm
   • C) $5.0 \times 10^{-3}$ cm
   • D) $2.0 \times 10^{-4}$ cm
3. 3.

   To understand atomic scale in an introductory chemistry unit, a student compares the dimensions of a gold atom to its nucleus. The diameter of the gold atom is measured as $1.0 \times 10^{-10}\text{ m}$, while the diameter of its nucleus is $2.0 \times 10^{-15}\text{ m}$. How many times larger is the diameter of the atom than the diameter of the nucleus, expressed in standard scientific notation ($N \times 10^n$, where $1 \le N < 10$)?

   • A) $2.0 \times 10^4$
   • B) $5.0 \times 10^4$
   • C) $5.0 \times 10^5$
   • D) $5.0 \times 10^6$
4. 4.

   During a laboratory investigation of volatile liquids, a student records the total pressure inside a sealed flask as $1.04 \times 10^5\text{ Pa}$. After selectively condensing the vapor, the remaining non-condensable gas exerts a pressure of $9.6 \times 10^4\text{ Pa}$. What is the partial pressure of the condensed vapor in pascals, expressed in standard scientific notation ($N \times 10^n$, where $1 \le N < 10$)?

   • A) $8.0 \times 10^3\text{ Pa}$
   • B) $8.0 \times 10^4\text{ Pa}$
   • C) $8.56 \times 10^4\text{ Pa}$
   • D) $8.0 \times 10^2\text{ Pa}$
5. 5.

   An environmental chemist monitors airborne particulate matter by operating an air-sampling pump at a constant volumetric flow rate of $1.5 \times 10^{-2}\text{ m}^3\text{/min}$ for $8.0 \times 10^2\text{ min}$. Over this period, the collection filter traps a total particulate mass of $7.2 \times 10^{-4}\text{ g}$. What is the concentration of airborne particulates in grams per cubic meter ($\text{g/m}^3$), expressed in standard scientific notation ($N \times 10^n$, where $1 \le N < 10$)?

   • A) $6.0 \times 10^{-3}\text{ g/m}^3$
   • B) $6.0 \times 10^{-4}\text{ g/m}^3$
   • C) $6.0 \times 10^{-6}\text{ g/m}^3$
   • D) $6.0 \times 10^{-5}\text{ g/m}^3$
6. 6.

   During an experiment measuring evaporation rates in an introductory chemistry laboratory, a student monitors a liquid solvent placed on an electronic balance. Over a measured time interval of $4.5 \times 10^2\text{ s}$, the solvent mass decreases from $8.6 \times 10^{-1}\text{ g}$ to $5.0 \times 10^{-1}\text{ g}$. What is the average rate of mass loss in grams per second ($\text{g/s}$), expressed in standard scientific notation ($N \times 10^n$, where $1 \le N < 10$)?

   • A) $8.0 \times 10^{-2}\text{ g/s}$
   • B) $8.0 \times 10^{-3}\text{ g/s}$
   • C) $8.0 \times 10^{-4}\text{ g/s}$
   • D) $8.0 \times 10^{-5}\text{ g/s}$
7. 7.

   During an investigation of nanomaterials, a materials chemist synthesizes uniform cubic nanocrystals of titanium dioxide. Each nanocrystal has an edge length of $3.0 \times 10^{-8}\text{ m}$. To model surface interactions, the chemist must determine the volume of a single nanocrystal expressed in standard scientific notation $N \times 10^n$, where $1 \le N < 10$. What is the volume of one nanocrystal in cubic meters ($\text{m}^3$)?

   • A) $9.0 \times 10^{-24}\text{ m}^3$
   • B) $2.7 \times 10^{-25}\text{ m}^3$
   • C) $2.7 \times 10^{-23}\text{ m}^3$
   • D) $2.7 \times 10^{-24}\text{ m}^3$
8. 8.

   In an environmental water quality test, an analyst collects suspended particulate matter from two distinct runoff samples. The first filter traps $3.15 \times 10^{-2}\text{ g}$ of solid residue, while the second filter traps $4.5 \times 10^{-3}\text{ g}$ of solid residue. To document the total particulate yield, the analyst must sum these two quantities and report the result in proper scientific notation $N \times 10^n$, where $1 \le N < 10$. What is the total mass of the collected residue in grams?

   • A) $3.60 \times 10^{-2}\text{ g}$
   • B) $7.65 \times 10^{-2}\text{ g}$
   • C) $3.60 \times 10^{-3}\text{ g}$
   • D) $7.65 \times 10^{-5}\text{ g}$
9. 9.

   A chemist measures a 0.0480 g sample of a synthesized catalyst containing $1.2 \times 10^{19}$ identical micro-crystals. To assess particle uniformity, the chemist needs to determine the average mass of a single micro-crystal by dividing the total sample mass by the crystal count. What is the average mass of one micro-crystal expressed in grams in standard scientific notation?

   • A) $4.0 \times 10^{-17}\text{ g}$
   • B) $4.0 \times 10^{-20}\text{ g}$
   • C) $4.0 \times 10^{-21}\text{ g}$
   • D) $4.0 \times 10^{-22}\text{ g}$
10. 10.

    In an analytical chemistry procedure, a technician measures a 0.0025 L aliquot of a solution containing a dissolved dye at a concentration of $6.0 \times 10^{-4}$ g/L. To calculate the total mass of the dye present, the volume and concentration must be multiplied and the result expressed in standard scientific notation $N \times 10^n$, where $1 \le N < 10$. What is the total mass of the dye in grams?

    • A) $1.5 \times 10^{-6}$ g
    • B) $1.5 \times 10^{-7}$ g
    • C) $15 \times 10^{-7}$ g
    • D) $1.5 \times 10^{-8}$ g