# 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.

交互版本：https://www.calcopenly.com/zh/science/ideal-gas-law-calculator
主题：科学计算器合集

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.

## 输入

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

## 结果

- 体积 (L) — 主要结果
- 压力 (kPa)
- 压力 (atm)
- Amount of gas (mol)
- 温度 (K)
- 温度 (°C)
- Molar volume V/n (L/mol)
- Number of molecules

## 公式

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

## 计算示例

### 1 mol at 0 °C and 1 atm

- Law: PV = nRT
- Solve for: 体积
- Pressure P: 1 atm
- Amount of gas n: 1
- Amount unit: mol
- Temperature T: 0 °C
- **体积: 22.414 L**
- 核验来源：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: 压力
- Volume V: 10 L
- Amount of gas n: 2
- Amount unit: mol
- Temperature T: 300 K
- **压力: 498.868 kPa**
- 核验来源：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**
- 核验来源：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: 温度
- Pressure P: 1 atm
- Volume V: 24.465 L
- Amount of gas n: 1
- Amount unit: mol
- **温度: 298.145 K**
- 核验来源：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: 温度
- 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
- **温度: 439.725 K**
- 核验来源：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: 体积
- 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
- **体积: 10 L**
- 核验来源：Combined gas law: V₂ = V₁ (P₁/P₂)(T₂/T₁) = 10 × ½ × 2

## 常见问题

### 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”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：6。 例如，“1 mol at 0 °C and 1 atm”根据CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol进行核验。

### 这种方法出自哪里？

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.

## 来源

- [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)