Units & Interconversion
The most common reason for losing marks in numericals is incorrect unit conversion.
1. The Metric System (Prefixes)
Powers of 10
Memorize these multipliers to jump between units instantly.
Small (Microscopic)
| Prefix | Symbol | Factor |
|---|---|---|
| deci | d | $10^{-1}$ |
| centi | c | $10^{-2}$ |
| milli | m | $10^{-3}$ |
| micro | $\mu$ | $10^{-6}$ |
| nano | n | $10^{-9}$ |
| pico | p | $10^{-12}$ |
| femto | f | $10^{-15}$ |
Large (Macroscopic)
| Prefix | Symbol | Factor |
|---|---|---|
| kilo | k | $10^{3}$ |
| mega | M | $10^{6}$ |
| giga | G | $10^{9}$ |
Crucial Length Unit for Chemistry:
1 Angstrom ($\mathring{A}$) = $10^{-10}$ m = $10^{-8}$ cm = 0.1 nm
2. Volume Conversions (Most Confusing)
Liter vs Meter Cubed
SI Unit is $m^3$, but Chemistry often uses Liters ($L$) or $cm^3$.
$$ 1 \text{ L} = 1000 \text{ mL} = 1000 \text{ cm}^3 = 1 \text{ dm}^3 $$
$$ 1 \text{ m}^3 = 1000 \text{ L} = 10^6 \text{ cm}^3 $$
The "cc" Trap:
1 cc = 1 cubic centimeter ($cm^3$) = 1 mL.
To convert $cm^3$ to SI ($m^3$), multiply by $10^{-6}$.
1 cc = 1 cubic centimeter ($cm^3$) = 1 mL.
To convert $cm^3$ to SI ($m^3$), multiply by $10^{-6}$.
3. Pressure and Energy
Pressure
SI Unit: Pascal (Pa) or $N/m^2$.
- 1 atm = 1.01325 bar $\approx$ 1 bar
- 1 atm = 101,325 Pa $\approx 10^5$ Pa
- 1 atm = 760 mmHg = 760 torr
Energy
SI Unit: Joule (J).
- 1 calorie (cal) = 4.184 J (Specific Heat)
- 1 L-atm = 101.3 J (Thermodynamics)
- 1 electron-volt (eV) = $1.602 \times 10^{-19}$ J (Atomic Structure)
- 1 erg = $10^{-7}$ J (CGS unit)
4. Temperature
Always use Kelvin for Calculation!
$$ K = ^\circ C + 273.15 $$
$$ ^\circ F = \frac{9}{5}(^\circ C) + 32 $$
Note: Difference in temperature ($\Delta T$) is the same in Celsius and Kelvin. $\Delta T(K) = \Delta T(^\circ C)$.
5. The Factor-Label Method
The foolproof way to convert units. Multiply by a fraction equal to 1.
Problem: Convert 72 km/h to m/s.
Step 1: Write given. $72 \frac{km}{h}$
Step 2: Multiply by conversion factors to cancel units.
$$ 72 \frac{\text{km}}{\text{h}} \times \left( \frac{1000 \text{ m}}{1 \text{ km}} \right) \times \left( \frac{1 \text{ h}}{3600 \text{ s}} \right) $$ (km cancels km, h cancels h)
$$ = \frac{72 \times 1000}{3600} \text{ m/s} = 20 \text{ m/s} $$
Step 1: Write given. $72 \frac{km}{h}$
Step 2: Multiply by conversion factors to cancel units.
$$ 72 \frac{\text{km}}{\text{h}} \times \left( \frac{1000 \text{ m}}{1 \text{ km}} \right) \times \left( \frac{1 \text{ h}}{3600 \text{ s}} \right) $$ (km cancels km, h cancels h)
$$ = \frac{72 \times 1000}{3600} \text{ m/s} = 20 \text{ m/s} $$
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