300K তাপমাত্রায় 500 mL আয়তনের পাত্রে 1 mole কোনো গ্যাসের চাপ (atm), এককে গণনা কর ।

[ যেখানে, a = 1.15 atmL²mol^-1 ও b = 0.03 Lmol^-1 ]

Gas Pressure Calculation at 300K

Given Data:

• Temperature, T = 300 K
• Volume, V = 500 mL = 0.5 L
• Number of moles, n = 1 mol
• Constants: a = 1.15 atm·L²/mol², b = 0.03 L/mol

Using van der Waals Equation:

[P + a(n²/V²)](V - nb) = nRT

Rearranged for pressure P:

P = (nRT)/(V - nb) - a(n²/V²)

Calculations:

• Universal gas constant, R = 0.0821 atm·L/(mol·K)
• Calculate each term:

V - nb = 0.5 - (1)(0.03) = 0.5 - 0.03 = 0.47 L

nRT = (1)(0.0821)(300) = 24.63 atm·L

First term: P₁ = (nRT)/(V - nb) = 24.63 / 0.47 ≈ 52.4 atm

Second term: a(n²/V²) = 1.15 * (1² / (0.5)²) = 1.15 / 0.25 = 4.6 atm

Final pressure:

P = P₁ - a(n²/V²) = 52.4 - 4.6 = 47.8 atm

Rounded to two decimal places: 47.74 atm