# Ideal gas law calculator

> Solve the ideal gas law PV = nRT for pressure, volume, moles or temperature in any units, or find a new state with the combined gas law.

النسخة التفاعلية: https://www.calcopenly.com/ar/science/ideal-gas-law-calculator
الموضوع: حاسبات العلوم

The ideal gas law, PV = nRT, links the pressure, volume, amount and absolute temperature of a gas through the molar gas constant R = 8.314 462 618… J/(mol·K). Choose the unknown and enter the other three in any units; the calculator converts to pascals, cubic metres, moles and kelvin before solving. The combined gas law mode holds the amount fixed and uses P₁V₁/T₁ = P₂V₂/T₂ to find a new pressure, volume or temperature.

Students use it to find the volume of gas a reaction gives off, and engineers use it to estimate how much gas a tank holds. With the defaults, 1 mol at 0 °C and 1 atm occupies 22.414 L, the CODATA molar volume of an ideal gas at those conditions.

The law ignores molecular size and attraction. Carbon dioxide at 25 °C and 1 atm deviates from it by about 0.5 %; the calculator warns above 100 bar or below 150 K, where a van der Waals or virial equation fits better.

## المدخلات

- **Law** (الخيارات: PV = nRT, Combined gas law)
- **Solve for** (الخيارات: الضغط, الحجم, Amount, درجة الحرارة)
- **Pressure P**
- **Volume V**
- **Amount of gas n**
- **Amount unit** (الخيارات: µmol, mmol, mol, kmol)
- **Temperature T**
- **Find the new** (الخيارات: الضغط, الحجم, درجة الحرارة)
- **Initial pressure P₁**
- **Initial volume V₁**
- **Initial temperature T₁**
- **New pressure P₂**
- **New volume V₂**
- **New temperature T₂**

## النتائج

- الحجم (L) — النتيجة الرئيسية
- الضغط (kPa)
- الضغط (atm)
- Amount of gas (mol)
- درجة الحرارة (K)
- درجة الحرارة (°C)
- Molar volume V/n (L/mol)
- Number of molecules

## الصيغة

$$
PV = nRT,\ R = 8.314\,462\,618\ldots\ \mathrm{J\,mol^{-1}\,K^{-1}}\ (\text{exact});\qquad \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}
$$

## أمثلة محلولة

### 1 mol at 0 °C and 1 atm

- Law: PV = nRT
- Solve for: الحجم
- Pressure P: 1 atm
- Amount of gas n: 1
- Amount unit: mol
- Temperature T: 0 °C
- **الحجم: 22.414 L**
- مصدر التحقق: ⁨CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol⁩

### Pressure of 2 mol in 10 L at 300 K

- Law: PV = nRT
- Solve for: الضغط
- Volume V: 10 L
- Amount of gas n: 2
- Amount unit: mol
- Temperature T: 300 K
- **الضغط: 498.868 kPa**
- مصدر التحقق: ⁨Python 3.8 decimal: 2 × 8.31446261815324 × 300 / 0.01 = 498867.757 Pa⁩

### Moles in 1 m³ at 100 kPa and 25 °C

- Law: PV = nRT
- Solve for: Amount
- Pressure P: 100 kPa
- Volume V: 1 m³
- Temperature T: 25 °C
- **Amount of gas: 40.3395 mol**
- مصدر التحقق: ⁨Python 3.8 decimal: 100000 / (8.31446261815324 × 298.15) = 40.3395455⁩

### Temperature of 1 mol in 24.465 L at 1 atm

- Law: PV = nRT
- Solve for: درجة الحرارة
- Pressure P: 1 atm
- Volume V: 24.465 L
- Amount of gas n: 1
- Amount unit: mol
- **درجة الحرارة: 298.145 K**
- مصدر التحقق: ⁨Python 3.8 decimal: 101325 × 0.024465 / 8.31446261815324 = 298.14508 K⁩

### Sealed can heated: pressure and temperature both change

- Law: Combined gas law
- Find the new: درجة الحرارة
- Initial pressure P₁: 100 kPa
- Initial volume V₁: 2 L
- Initial temperature T₁: 293.15 K
- New pressure P₂: 150 kPa
- New volume V₂: 2 L
- **درجة الحرارة: 439.725 K**
- مصدر التحقق: ⁨Python 3.8 decimal: T₂ = 293.15 × 150 × 2 / (100 × 2) = 439.725 K (Gay-Lussac)⁩

### Double the pressure and the absolute temperature: volume unchanged

- Law: Combined gas law
- Find the new: الحجم
- Initial pressure P₁: 1 atm
- Initial volume V₁: 10 L
- Initial temperature T₁: 300 K
- New pressure P₂: 2 atm
- New temperature T₂: 600 K
- **الحجم: 10 L**
- مصدر التحقق: ⁨Combined gas law: V₂ = V₁ (P₁/P₂)(T₂/T₁) = 10 × ½ × 2⁩

## الأسئلة

### What is the value of R in PV = nRT?

R = 8.314 462 618 153 24 J/(mol·K), exact since the 2019 SI revision because it is the product of two fixed constants, the Avogadro constant and the Boltzmann constant. In other units it is 0.082 057 L·atm/(mol·K), 8.314 L·kPa/(mol·K) and 62.364 L·mmHg/(mol·K). Use the version that matches your pressure and volume units, or convert everything to SI as this calculator does.

### What volume does one mole of gas occupy at STP?

It depends on which STP is meant. At 0 °C and 1 atm (101.325 kPa), one mole of ideal gas occupies 22.414 L; at 0 °C and 100 kPa, the standard pressure IUPAC has recommended since 1982, it occupies 22.711 L; at 25 °C and 1 atm it occupies 24.465 L. Check which definition your textbook or exam uses, since the first two differ by 1.3 %.

### Why does temperature have to be in kelvin?

Gas pressure and volume are proportional to absolute temperature, which starts at absolute zero, −273.15 °C. Going from 10 °C to 20 °C looks like doubling, but the absolute temperature only rises from 283.15 K to 293.15 K, a 3.5 % increase, so at constant pressure the gas expands by 3.5 %, not 100 %. The calculator converts °C and °F to kelvin before solving.

### What is the combined gas law?

P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas. It merges Boyle's law (PV constant at fixed temperature), Charles's law (V/T constant at fixed pressure) and Gay-Lussac's law (P/T constant at fixed volume). Heating a sealed rigid container from 20 °C to 40 °C raises 100 kPa to 106.8 kPa, because the pressure scales with 313.15 K ÷ 293.15 K.

### ما مدى دقة «⁨Ideal gas law calculator⁩»؟

تعتمد الدقة على مدخلاتك وافتراضات الطريقة. يستخدم الحساب العشري 50 رقمًا معنويًا، لكن التقديرات والأساليب العددية وبيانات المصدر قد تكون أقل دقة؛ تقريب القيم المعروضة لا يزيل هذه الحدود. أمثلة محلولة جرى التحقق منها بمصادر مستقلة: 6. مثلًا، يجري التحقق من «⁨1 mol at 0 °C and 1 atm⁩» بالرجوع إلى ⁨CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol⁩.

### ما مصدر هذه الطريقة؟

CODATA 2022 — molar gas constant R and molar volume of an ideal gas (22.413 969 54 L/mol at 273.15 K, 101.325 kPa); OpenStax Chemistry 2e, §9.2 Relating pressure, volume, amount, and temperature: the ideal gas law.

## المصادر

- [CODATA 2022 — molar gas constant R and molar volume of an ideal gas (22.413 969 54 L/mol at 273.15 K, 101.325 kPa)](https://physics.nist.gov/cgi-bin/cuu/Value?mvol)
- [OpenStax Chemistry 2e, §9.2 Relating pressure, volume, amount, and temperature: the ideal gas law](https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law)