Units and Measurements — Hard Practice Quiz

A Chemistry cheat sheet for Units and Measurements — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Temperature conversion: Celsius to Kelvin

$$K = ^\circ C + 273.15$$

Temperature conversion: Fahrenheit to Celsius

$$^\circ C = \frac{5}{9}(^\circ F - 32)$$

Temperature conversion: Celsius to Fahrenheit

$$^\circ F = \frac{9}{5}(^\circ C) + 32$$

Density = mass / volume

$$d = \frac{m}{V}$$

<table style="width:100%; border-collapse: collapse; font-size: 0.9em;"> <tr style="border-bottom: 1px solid #ccc;"><th>Quantity</th><th>Unit</th><th>Symbol</th></tr> <tr><td>Length</td><td>meter</td><td>m</td></tr> <tr><td>Mass</td><td>kilogram</td><td>kg</td></tr> <tr><td>Time</td><td>second</td><td>s</td></tr> <tr><td>Temperature</td><td>Kelvin</td><td>K</td></tr> <tr><td>Amount</td><td>mole</td><td>mol</td></tr> <tr><td>Current</td><td>Ampere</td><td>A</td></tr> <tr><td>Luminous int.</td><td>candela</td><td>cd</td></tr> </table>

$$\text{SI Base Units}$$

<table style="width:100%; border-collapse: collapse; font-size: 0.9em;"> <tr style="border-bottom: 1px solid #ccc;"><th>Prefix</th><th>Symbol</th><th>Factor</th></tr> <tr><td>Peta</td><td>P</td><td>10<sup>15</sup></td></tr> <tr><td>Tera</td><td>T</td><td>10<sup>12</sup></td></tr> <tr><td>Giga</td><td>G</td><td>10<sup>9</sup></td></tr> <tr><td>Mega</td><td>M</td><td>10<sup>6</sup></td></tr> <tr><td>Kilo</td><td>k</td><td>10<sup>3</sup></td></tr> <tr><td>Deci</td><td>d</td><td>10<sup>-1</sup></td></tr> <tr><td>Centi</td><td>c</td><td>10<sup>-2</sup></td></tr> <tr><td>Milli</td><td>m</td><td>10<sup>-3</sup></td></tr> <tr><td>Micro</td><td>&mu;</td><td>10<sup>-6</sup></td></tr> <tr><td>Nano</td><td>n</td><td>10<sup>-9</sup></td></tr> <tr><td>Pico</td><td>p</td><td>10<sup>-12</sup></td></tr> <tr><td>Femto</td><td>f</td><td>10<sup>-15</sup></td></tr> </table>

$$\text{SI Prefixes}$$

Practice quiz

  1. A chemical reaction occurs at $77 ^\circ F$. What is this temperature in Kelvin?

    • $298.15 \text{ K}$
    • $250.15 \text{ K}$
    • $350.15 \text{ K}$
    • $273.15 \text{ K}$

    Answer: $298.15 \text{ K}$

  2. A material has a density of $2.7 \text{ g/cm}^3$. What is the mass, in kilograms, of $0.05 \text{ m}^3$ of this material?

    • $135 \text{ kg}$
    • $13.5 \text{ kg}$
    • $1350 \text{ kg}$
    • $1.35 \text{ kg}$

    Answer: $135 \text{ kg}$

  3. A sample of liquid has a mass of $5.4 \text{ kg}$ and a density of $0.9 \text{ g/mL}$. What is its volume in liters? (Note: $1 \text{ mL} = 1 \text{ cm}^3$).

    • $6 \text{ L}$
    • $0.6 \text{ L}$
    • $60 \text{ L}$
    • $54 \text{ L}$

    Answer: $6 \text{ L}$

  4. For most substances, if the temperature increases, causing the substance to expand, how does its density change, assuming its mass remains constant?

    • It decreases.
    • It increases.
    • It remains constant.
    • It depends on the specific heat capacity.

    Answer: It decreases.

  5. Given the density formula $d = \frac{m}{V}$, if the mass $m$ of an object is equivalent to the mass of a liquid with density $d_L$ and volume $V_L$, express the volume $V$ of the object in terms of $d$, $d_L$, and $V_L$.

    • $V = \frac{d_L V_L}{d}$
    • $V = \frac{d V_L}{d_L}$
    • $V = d d_L V_L$
    • $V = \frac{d}{d_L V_L}$

    Answer: $V = \frac{d_L V_L}{d}$

  6. Two objects, A and B, have the same mass. Object A has a volume $V_A$ and density $d_A$. Object B has a volume $V_B = 3V_A$. What is the ratio of their densities, $d_A/d_B$?

    • $3$
    • $1/3$
    • $9$
    • $1$

    Answer: $3$

  7. A temperature change of $1.5 \text{ kK}$ (kilokelvin) is observed. What is this temperature change in degrees Celsius?

    • $1500 ^\circ C$
    • $1.5 ^\circ C$
    • $150 ^\circ C$
    • $1500 + 273.15 ^\circ C$

    Answer: $1500 ^\circ C$

  8. A block of material has a mass of $1.2 \text{ Mg}$ (megagrams) and a density of $2.0 \text{ g/cm}^3$. What is its volume in cubic meters?

    • $0.6 \text{ m}^3$
    • $600 \text{ m}^3$
    • $6 \times 10^{-4} \text{ m}^3$
    • $1.2 \times 10^6 \text{ m}^3$

    Answer: $0.6 \text{ m}^3$

  9. Density is a derived SI unit. Which combination of SI base units correctly defines density?

    • kilogram per cubic meter
    • gram per cubic centimeter
    • kilogram per liter
    • gram per milliliter

    Answer: kilogram per cubic meter

  10. At what numerical value do the Celsius and Fahrenheit temperature scales read the same?

    • $-40$
    • $0$
    • $32$
    • $100$

    Answer: $-40$

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