Density, molar mass, molar volume — Hinglish notes

1.1.7 · Chemistry › Matter, Measurement & the Mole

1. Density

HOW isko scratch se derive karein — isme derive karne jaisa kuch nahi; density ek definition hai (ek ratio jo humne choose ki kyunki ye useful hai). Lekin hum iska microscopic meaning derive kar sakte hain:

Agar kisi substance mein volume $V$ mein $N$ particles hain jinka mass $m_{0}$ hai: $ρ = \frac{N m _{0}}{V} = (number density) \times (mass per particle)$

To density tab zyada hoti hai jab particles bhaari hon YA tightly packed hon. Isliye gases liquids se ~1000× kam dense hoti hain: same particle mass, lekin per unit volume bahut kam particles.

2. Molar Mass

Mole–mass bridge ki derivation:

1 u $= 1.6605 \times 1 0^{- 24}$ g (atomic mass unit ki definition). $A$ u mass wala ek particle $A \times 1.6605 \times 1 0^{- 24}$ g weighs karta hai. One mole = $N_{A} = 6.022 \times 1 0^{23}$ aese particles: $M = A \times (1.6605 \times 1 0^{- 24} g) \times (6.022 \times 1 0^{23})$ $1.6605 \times 1 0^{- 24} \times 6.022 \times 1 0^{23} \approx 1.000$ $M \approx A g mol^{- 1}$

3. Molar Volume

Ideal gas law se derivation: $P V = n R T ⟹ V_{m} = \frac{V}{n} = \frac{R T}{P}$ $T = 273.15$ K, $P = 1 bar = 1 0^{5}$ Pa, $R = 8.314 J mol^{- 1} K^{- 1}$ par: $V_{m} = \frac{8.314 \times 273.15}{1 0 ^{5}} = 0.0227 m^{3} = 22.7 L mol^{- 1}$

Figure — Density, molar mass, molar volume

Worked Examples

Common Mistakes

Active Recall

Recall Khud ko test karo (answers chhupao)

Density, molar mass, molar volume kin teen pairs of quantities ko connect karte hain?
Molar mass g/mol mein numerically atomic mass u mein ke barabar kyun hoti hai?
$P V = n R T$ se $ρ = P M / R T$ derive karo.
Saare ideal gases same molar volume kyun share karte hain?

Density formula and units

ρ = m / V

; units g cm⁻³ (solids/liquids), g L⁻¹ (gases)

Molar mass ki definition

ek mole (6.022×10²³ particles) ka mass, g mol⁻¹ mein, numerically = relative atomic/molecular mass

Mass se moles

n = m / M

(grams ÷ grams per mole)

Ideal gas ka molar volume STP par (273.15 K, 1 bar)

22.7 L mol⁻¹ (22.4 L at 1 atm)

Gas molar volume gas ki identity se independent kyun hai

Avogadro's law — same T,P par equal volumes mein equal molecules hote hain; molecule ka size negligible hai

M ke terms mein gas ki density

ρ = M / V_{m} = P M / R T

Molar mass (g/mol) = atomic mass (u) kyun

kyunki

N_{A} \times 1.6605 \times 1 0^{- 24} g \approx 1

; mole isliye define hua ki 1 u/particle → 1 g/mol

Liquid water ka molar volume

≈18 mL mol⁻¹ (18 g ÷ 1 g/mL)

1 g cm⁻³ ko kg m⁻³ mein convert karo

1000 kg m⁻³

Recall Feynman: ek 12-saal ke bachche ko explain karo

Marbles imagine karo. Density = ek bag of marbles kitni bhaari hai compared to bag kitni badi hai. Molar mass = exactly ek giant standard bag ka weight jisme $6.022 \times 1 0^{23}$ marbles hain — aur trick ye hai, ek marble jo "44 little units" weighs karta hai, usse poora bag exactly 44 grams weighs karta hai. Molar volume = ek standard bag kitni jagah leti hai. Gas marbles ke liye jo door-door float karte hain, har tarah ki gas bag magically same room leti hai (lagbhag 22.7 litres), kyunki marbles barely touch karte hain — sirf unki spacing matter karti hai, unka size nahi.

Connections

The Mole & Avogadro's Number
Ideal Gas Law PV=nRT
Avogadro's Law
Relative Atomic Mass & Atomic Mass Unit
Stoichiometry & Mass-Mole-Volume Conversions
STP and Standard Conditions