Intuition The big pictureEvery measurement is really a comparison to a standard . When you say "5 kg", you mean "5 times a fixed lump of mass we all agreed on." Science works only if everyone uses the same rulers . The SI system is that shared agreement — a small set of base units from which every other unit is built by multiplication and division . In chemistry we constantly juggle how much stuff (mol), how heavy (kg), how hot (K), and how much push (Pa) — and the "answers" (energy J, volume L) are just combinations of these.
Definition SI base quantities used in chemistryA base unit is defined independently (not built from others). The seven exist; chemistry leans on these four:
Mass: kilogram (kg)
Amount of substance: mole (mol)
Temperature: kelvin (K)
(Length: metre (m) — used to build volume & pressure)
WHY these? Chemistry is the science of matter reacting . To describe a reaction you must know how many particles (mol), their mass (kg), the thermal energy driving them (K), and often the pressure confining a gas (Pa, which is derived from m and kg).
Intuition Why kelvin, not Celsius?Temperature in chemistry appears in laws like p V = n R T pV=nRT p V = n R T T T T T = 0 T=0 T = 0 zero thermal motion — the absolute zero. Celsius puts 0 at the freezing point of water (arbitrary!), so ratios go wrong. Kelvin's zero is physical , so T T T multiplicatively meaningful .
Conversion: = = T K = T ∘ C + 273.15 = = ==T_{\text{K}} = T_{^\circ\text{C}} + 273.15== == T K = T ∘ C + 273.15 ==
Intuition Why we invented the moleAtoms are far too tiny and numerous to count one by one. But reactions happen atom-by-atom in fixed whole-number ratios. So we need a counting unit that (a) contains a huge, fixed number of particles, and (b) links that number to a weighable mass . The mole does both.
One mole is the amount of substance containing exactly N A = = = 6.022 × 10 23 = = N_A = ==6.022\times10^{23}== N A === 6.022 × 1 0 23 == N A N_A N A
Intuition Core idea of a derived unitA derived unit comes from putting base units into a physics equation. You don't memorise them — you read them off the formula .
The SI coherent volume unit is m 3 \text{m}^3 m 3 litre (L) is a convenient non-SI submultiple:
1 L = 1 dm 3 = ( 10 − 1 m ) 3 = 10 − 3 m 3 = 1000 cm 3 1\ \text{L} = 1\ \text{dm}^3 = (10^{-1}\,\text{m})^3 = 10^{-3}\ \text{m}^3 = 1000\ \text{cm}^3 1 L = 1 dm 3 = ( 1 0 − 1 m ) 3 = 1 0 − 3 m 3 = 1000 cm 3 Why? A cube 10 cm on a side. Chemists use it because lab glassware is that scale.
Worked example E1 — moles from massHow many moles in 18 g 18\ \text{g} 18 g M = 18 g/mol M=18\ \text{g/mol} M = 18 g/mol n = m / M = 18 / 18 = 1 mol n = m/M = 18/18 = 1\ \text{mol} n = m / M = 18/18 = 1 mol Why this step? Molar mass is grams-per-mole, so dividing grams by it cancels grams, leaving mol.
Particles: N = n N A = 1 × 6.022 × 10 23 = 6.022 × 10 23 N = nN_A = 1\times6.022\times10^{23} = 6.022\times10^{23} N = n N A = 1 × 6.022 × 1 0 23 = 6.022 × 1 0 23
Worked example E2 — pressure in SIA gas exerts 2000 N 2000\ \text{N} 2000 N 0.05 m 2 0.05\ \text{m}^2 0.05 m 2 p p p p = F / A = 2000 / 0.05 = 40000 Pa = 4 × 10 4 Pa = 0.4 bar p = F/A = 2000/0.05 = 40000\ \text{Pa} = 4\times10^4\ \text{Pa} = 0.4\ \text{bar} p = F / A = 2000/0.05 = 40000 Pa = 4 × 1 0 4 Pa = 0.4 bar Why this step? Direct from definition; then divide by 10 5 10^5 1 0 5
Worked example E3 — energy check with units onlyConfirm 1 2 m v 2 \tfrac12 mv^2 2 1 m v 2 m = 2 kg m=2\ \text{kg} m = 2 kg v = 3 m/s v=3\ \text{m/s} v = 3 m/s kg ⋅ ( m/s ) 2 = kg m 2 s − 2 = J \text{kg}\cdot(\text{m/s})^2 = \text{kg}\,\text{m}^2\text{s}^{-2}=\text{J} kg ⋅ ( m/s ) 2 = kg m 2 s − 2 = J 1 2 ⋅ 2 ⋅ 9 = 9 J \tfrac12\cdot2\cdot9 = 9\ \text{J} 2 1 ⋅ 2 ⋅ 9 = 9 J Why this step? Unit-analysis first tells you the answer can be an energy before you trust the number.
Worked example E4 — ideal gas, all SIn = 1 mol n=1\ \text{mol} n = 1 mol T = 273.15 K T=273.15\ \text{K} T = 273.15 K V = 22.7 × 10 − 3 m 3 V=22.7\times10^{-3}\ \text{m}^3 V = 22.7 × 1 0 − 3 m 3 R = 8.314 J mol − 1 K − 1 R=8.314\ \text{J mol}^{-1}\text{K}^{-1} R = 8.314 J mol − 1 K − 1 p p p p = n R T V = 1 ⋅ 8.314 ⋅ 273.15 22.7 × 10 − 3 ≈ 1.00 × 10 5 Pa = 1 bar p = \dfrac{nRT}{V} = \dfrac{1\cdot8.314\cdot273.15}{22.7\times10^{-3}} \approx 1.00\times10^{5}\ \text{Pa} = 1\ \text{bar} p = V n R T = 22.7 × 1 0 − 3 1 ⋅ 8.314 ⋅ 273.15 ≈ 1.00 × 1 0 5 Pa = 1 bar Why this step? Feed only SI units so R R R
Common mistake "Molar mass is in kg because kg is the SI base unit."Why it feels right: kg is the SI base mass unit, so surely M M M The fix: SI-coherent M M M is kg/mol, but chemists tabulate M M M g/mol because atomic masses come out as nice numbers (water = 18 g/mol, not 0.018 kg/mol). Just keep mass and M M M same mass unit and n n n
Common mistake "Use Celsius inp V = n R T pV=nRT p V = n R T Why it feels right: we live in °C; it "is" temperature.
The fix: the gas law needs an absolute scale so that T ∝ T\propto T ∝
Common mistake "1 L = 1 m³."Why it feels right: both are volumes and 'litre' sounds big.
The fix: 1 m 3 = 1000 L 1\ \text{m}^3 = 1000\ \text{L} 1 m 3 = 1000 L 10 cm cube , a tiny fraction of a cubic metre.
Common mistake "Pa and N/m² are different things."Why it feels right: they look like separate names.
The fix: they are identical — Pa is just the shorthand name for N·m⁻². Every derived unit has an equivalent base-unit spelling.
Recall Feynman: explain to a 12-year-oldImagine LEGO. The base bricks are mass (how heavy), amount (how many pieces — a "mole" is like saying "a giant box of 6-hundred-thousand-billion-billion pieces"), and how hot it is (kelvin, counting from the coldest possible cold). Bigger things like energy (joule) and push (pascal) aren't new bricks — you build them by clicking base bricks together in the right pattern. A litre is just a milk-carton-sized cube. Once you know the bricks, you can read any label by seeing which bricks were snapped together.
Mnemonic Remembering the base four"Kids Make Kold Presents" → K g (mass), M ol (amount), K elvin (temp), P a (pressure, though Pa is derived — the odd one out you want to remember is derived).
For derived: "Joules Push Litres" — Joule = force×distance, Pascal = force÷area, Litre = length³.
What is the SI base unit for amount of substance? the mole (mol)
Value of Avogadro's number N A N_A N A 6.022 × 10 23 6.022\times10^{23} 6.022 × 1 0 23 per mole
Express 1 joule in SI base units. 1 J = 1 kg m 2 s − 2 1\ \text{J}=1\ \text{kg}\,\text{m}^2\,\text{s}^{-2} 1 J = 1 kg m 2 s − 2 Express 1 pascal in SI base units. 1 Pa = 1 kg m − 1 s − 2 1\ \text{Pa}=1\ \text{kg}\,\text{m}^{-1}\,\text{s}^{-2} 1 Pa = 1 kg m − 1 s − 2 (= N/m²)
Convert Celsius to kelvin. T K = T ° C + 273.15 T_K = T_{°C}+273.15 T K = T ° C + 273.15 Why must p V = n R T pV=nRT p V = n R T T must be absolute so it's proportional to kinetic energy; Celsius zero is arbitrary
How many litres in 1 m³? 1000 L (1 L = 1 dm³ = 10⁻³ m³)
Formula linking moles, mass and molar mass. Formula linking moles and particle count. Derive the unit of force in SI. F=ma → kg·m·s⁻² = newton (N)
1 bar equals how many Pa? 1 atm equals how many Pa? 101325 Pa
Why is a derived unit "derived"? it's built by multiplying/dividing base units from a defining equation
absolute zero makes T meaningful
Intuition Hinglish mein samjhoDekho, SI units ka matlab hai ek common "ruler" jispe puri duniya agree karti hai. Chemistry me sabse important base units hain: kg (kitna heavy), mol (kitne particles — ek mole matlab 6.022 × 10 23 6.022\times10^{23} 6.022 × 1 0 23 K (kitna garam, par absolute zero se ginte hain). Kelvin isliye use karte hain kyunki gas law p V = n R T pV=nRT p V = n R T
Ab derived units ka funda simple hai: naya unit rattaana nahi, formula se banana hai. Force F = m a F=ma F = ma k g ⋅ m / s 2 = N kg\cdot m/s^2 = N k g ⋅ m / s 2 = N W = F × d W=F\times d W = F × d N ⋅ m = J = k g m 2 / s 2 N\cdot m = J = kg\,m^2/s^2 N ⋅ m = J = k g m 2 / s 2 p = F / A p=F/A p = F / A N / m 2 = P a N/m^2 = Pa N / m 2 = P a litre koi alag jaadu nahi — bas ek 10 cm ka cube, yaani 1 L = 10 − 3 m 3 1\ L = 10^{-3}\ m^3 1 L = 1 0 − 3 m 3 1 m 3 = 1000 L 1\ m^3 = 1000\ L 1 m 3 = 1000 L
Do formulae har jagah kaam aate hain: n = m / M n=m/M n = m / M n = N / N A n=N/N_A n = N / N A
Common galtiyan: Celsius ko seedha gas law me daal dena (pehle +273.15 karo), aur litre ko cubic metre samajhna (1000 ka farak hai!). Ek baar base bricks samajh gaye, to koi bhi unit ka label khud padh loge — yehi iska power hai.
