Concentration units — mass %, volume %, ppm, ppb, molarity (M), molality (m), mole fraction

1.1.15 · Chemistry › Matter, Measurement & the Mole

WHY itni saari units ki zaroorat hai?

Definitions (har ek = ek fraction)

Figure — Concentration units — mass %, volume %, ppm, ppb, molarity (M), molality (m), mole fraction

DERIVATION: molarity ↔ molality ↔ mole fraction convert karna

Molarity + density se molality derive karna. 1 L (1000 mL) solution lo jisme molarity $M$ aur density $ρ$ (g/mL) ho, solute molar mass $M_{w}$ (g/mol) ho.

Step 1 — 1 L mein solute ke moles: $n = M (since n = M \times 1 L) .$ Yeh step kyun? Molarity per litre hai, aur humne exactly 1 L choose kiya, toh moles = $M$ .

Step 2 — poore solution ka mass: $mass_{soln} = 1000 mL \times ρ g/mL = 1000 ρ g .$ Kyun? Density volume ko mass mein convert karti hai.

Step 3 — solute ka mass: $mass_{solute} = n \times M_{w} = M \cdot M_{w} g .$ Kyun? moles × molar mass = grams.

Step 4 — solvent ka mass = solution − solute: $mass_{solvent} = (1000 ρ - M M_{w}) g = \frac{1000 ρ - M M _{w}}{1000} kg .$

Step 5 — molality: $m = \frac{n}{mass _{solvent, kg}} = \frac{M \times 1000}{1000 ρ - M M _{w}}$ Yeh answer kyun hai: humne bas definition $m = n / kg solvent$ apply ki, upar banaye hue pieces ke saath. Dhyan do: agar solution bahut dilute hai, toh $M M_{w}$ chhota hoga, isliye $m \approx M / ρ \approx M$ (jab $ρ \approx 1$ ). Isliye dilute water solutions mein M ≈ m hota hai.

Worked examples

Common mistakes (Steel-man + fix)

Recall Feynman: 12-saal ke bachche ko samjhao

Socho paani mein juice powder hai. Concentration bas yeh batata hai "juice kitna strong hai?" Aap strength ko alag-alag tarike se measure kar sakte ho: ek cup mein kitne chamach powder (molarity — lekin cup garm hone par bada ho jaata hai!), ya ek kilogram paani mein kitne grams powder (molality — kilogram kabhi nahi badlata, toh yeh garmi mein bhi kaam karta hai). Percent bas "100 mein se" hai, ppm hai "ek million mein se" (bahut chhoti cheezein ke liye, jaise ek poori bori mein ek daana). Same juice — bas tum alag measuring stick choose kar rahe ho.

Flashcards

Molarity ke denominator mein kya jaata hai?

Solution ka volume litres mein.

Molality ke denominator mein kya jaata hai?

Solvent ka mass kilograms mein.

Molality temperature-independent kyun hai lekin molarity nahi?

Molality mass use karta hai (T se nahi badlata); molarity volume use karta hai (T ke saath expand hota hai).

Molarity M ko molality m mein convert karne ka formula (density ρ g/mL, molar mass Mw)?

m = \frac{1000 M}{1000 ρ - M M _{w}}

Dilute aqueous solution mein 1 ppm kiske barabar hota hai?

≈ 1 mg/L (kyunki ρ ≈ 1 g/mL).

Saare components ke mole fractions ka sum kya hota hai?

M ≈ m kab hota hai?

Dilute aqueous solutions mein jahan density ≈ 1 g/mL ho.

Mass % ko fraction denominator mein convert karo: kiske mass se?

Solution ka mass (solute + solvent).

Kya liquids mix karne par volumes additive hote hain?

Nahi — isliye molarity final solution volume par fix kiya jaata hai.

Mass aur molar mass se n kaise nikaalte hain?

n = mass / M_{w}

Connections

The Mole and Avogadro's Number — molarity/molality dono ko moles chahiye.
Molar Mass and Formula Mass — grams ↔ moles convert karne ke liye zaruri.
Density — mass-based aur volume-based units ke beech ka bridge.
Colligative Properties — isliye molality & mole fraction exist karte hain (T-independent).
Stoichiometry and Dilution — $M_{1} V_{1} = M_{2} V_{2}$ molarity use karta hai.
Ideal Gas Law — mole fraction wapas aata hai partial pressure mein ( $p_{A} = x_{A} P$ ).