# 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.

Phiên bản tương tác: https://www.calcopenly.com/vi/science/ideal-gas-law-calculator
Chủ đề: Máy tính khoa học theo chủ đề

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.

## Dữ liệu đầu vào

- **Law** (lựa chọn: PV = nRT, Combined gas law)
- **Solve for** (lựa chọn: Áp suất, Thể tích, Amount, Nhiệt độ)
- **Pressure P**
- **Volume V**
- **Amount of gas n**
- **Amount unit** (lựa chọn: µmol, mmol, mol, kmol)
- **Temperature T**
- **Find the new** (lựa chọn: Áp suất, Thể tích, Nhiệt độ)
- **Initial pressure P₁**
- **Initial volume V₁**
- **Initial temperature T₁**
- **New pressure P₂**
- **New volume V₂**
- **New temperature T₂**

## Kết quả

- Thể tích (L) — kết quả chính
- Áp suất (kPa)
- Áp suất (atm)
- Amount of gas (mol)
- Nhiệt độ (K)
- Nhiệt độ (°C)
- Molar volume V/n (L/mol)
- Number of molecules

## Công thức

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

## Ví dụ có lời giải

### 1 mol at 0 °C and 1 atm

- Law: PV = nRT
- Solve for: Thể tích
- Pressure P: 1 atm
- Amount of gas n: 1
- Amount unit: mol
- Temperature T: 0 °C
- **Thể tích: 22.414 L**
- Nguồn đối chiếu: 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: Áp suất
- Volume V: 10 L
- Amount of gas n: 2
- Amount unit: mol
- Temperature T: 300 K
- **Áp suất: 498.868 kPa**
- Nguồn đối chiếu: 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**
- Nguồn đối chiếu: 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: Nhiệt độ
- Pressure P: 1 atm
- Volume V: 24.465 L
- Amount of gas n: 1
- Amount unit: mol
- **Nhiệt độ: 298.145 K**
- Nguồn đối chiếu: 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: Nhiệt độ
- 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
- **Nhiệt độ: 439.725 K**
- Nguồn đối chiếu: 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: Thể tích
- 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
- **Thể tích: 10 L**
- Nguồn đối chiếu: Combined gas law: V₂ = V₁ (P₁/P₂)(T₂/T₁) = 10 × ½ × 2

## Câu hỏi

### 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.

### “Ideal gas law calculator” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 6. Ví dụ, “1 mol at 0 °C and 1 atm” được kiểm tra bằng CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol.

### Phương pháp này lấy từ đâu?

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.

## Nguồn

- [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)