Chemistry & PhysicsNCTB Chemistry Paper 2 Ch 1NCTB Physics Paper 1 Ch 10BUET & Medical Prep
Ideal Gas Law & Kinetic Solver
Online Ideal Gas Law (PV = nRT) solver, molecular RMS speed, kinetic energy, and combined gas law calculator for chemistry and physics.
Ideal Gas Law & Kinetic Solver
Real-time solver for PV = nRT, molecular RMS speed, total kinetic energy, and state transformations.
প্রিসেট:
Solve For:
গ্যাস সিলিন্ডার ও পিস্টন মডেলV = 22.4256 L
ধাপে ধাপে সমাধান:R = 0.0821 L·atm/(mol·K)
- ▸ V = (1 mol × 0.0821 L·atm/mol·K × 273.15 K) / 1 atm
- ▸ V = 22.4256 / 1 = 22.4256 L
Formula & Derivation
Theoretical foundation, dimensional analysis, and governing boundary conditions.
Solved Textbook Examples
Three fully worked pedagogical exemplars: standard textbook, advanced edge-case, and authentic past board examination.
Higher Secondary Chemistry (NCTB Class 12)Sample 1 • Ideal Gas Volume Calculation
Calculate the volume occupied by 2.0 moles of CO2 at 27°C and 1.5 atm pressure. [R = 0.0821 L·atm/(mol·K)]
Given Parameters:
- P = 1.5 atm
- n = 2.0 mol
- T = 27°C = 300.15 K
- R = 0.0821 L·atm/(mol·K)
Procedural Solution:
Ideal gas equation: PV = nRT
V = (nRT) / P
V = (2 × 0.0821 × 300.15) / 1.5
V = 49.2846 / 1.5 = 32.86 L
Final Answer:Gas volume = 32.86 Liters
Higher Secondary Physics (NCTB Class 11)Sample 2 • Oxygen Molecule RMS Speed
Determine the root-mean-square (RMS) velocity of oxygen (O2) molecules at 27°C. [R = 8.314 J/(mol·K), M = 32 g/mol]
Given Parameters:
- T = 27°C = 300.15 K
- M = 32 g/mol = 0.032 kg/mol
- R = 8.314 J/(mol·K)
Procedural Solution:
RMS formula: c_rms = √(3RT / M)
c_rms = √[(3 × 8.314 × 300.15) / 0.032]
c_rms = √233948.17 = 483.68 m/s
Final Answer:RMS velocity of O2 = 483.68 m/s
Engineering Admission (BUET / Medical)Sample 3 • Combined Gas Law Bubble Problem
A bubble of volume 2.0 mL at the bottom of a lake has a pressure of 1.5 atm and temperature 10°C. If the surface conditions are 1.0 atm and 25°C, find the bubble volume at the surface.
Given Parameters:
- P1 = 1.5 atm, V1 = 2 mL, T1 = 283 K
- P2 = 1.0 atm, T2 = 298 K
Procedural Solution:
Combined gas law: (P1 × V1) / T1 = (P2 × V2) / T2
V2 = (P1 × V1 × T2) / (P2 × T1)
V2 = (1.5 × 2 × 298) / (1.0 × 283)
V2 = 894 / 283 = 3.16 mL
Final Answer:Surface bubble volume = 3.16 mL
Board Exam & Laboratory Checklist
✓ Unit Conversion (SI)Convert all inputs to SI units prior to calculation.
✓ Formula & TranspositionExplicitly isolate target variable before substitution.
✓ Precision & RoundingPreserve required precision without premature truncation.
Practical Applications
How this scientific principle drives chemical engineering, aerospace, medicine, and research.
Frequently Asked Questions
Answers to common conceptual misconceptions and board examination guidelines.
When should R = 0.0821 L·atm/(mol·K) be used versus R = 8.314 J/(mol·K)?▼
Use R = 0.0821 L·atm/(mol·K) when pressure is in atmospheres (atm) and volume in liters (L). Use R = 8.314 J/(mol·K) (SI units) when working with pressure in Pascals (Pa), volume in cubic meters (m³), or computing kinetic energy and molecular RMS speed.
What is the difference between STP and SATP conditions?▼
STP (Standard Temperature and Pressure) is defined at 0°C (273.15 K) and 1 atm (101.325 kPa), where 1 mole of ideal gas occupies 22.414 L. SATP (Standard Ambient Temperature and Pressure) is at 25°C (298.15 K) and 1 bar (100 kPa), where 1 mole occupies 24.789 L.
How does gas molecular RMS speed depend on temperature and molar mass?▼
RMS speed is directly proportional to the square root of absolute temperature (c_rms ∝ √T) and inversely proportional to the square root of molar mass (c_rms ∝ 1/√M). Lighter gases at higher temperatures travel significantly faster.