Units & Interconversion
The most common reason for losing marks in numericals is incorrect unit conversion.
1. The Metric System (Prefixes)
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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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