理想气体定律计算器 — PV=nRT 求解器
The ideal gas law PV = nRTrelates the pressure, volume, moles, and temperature of a gas using the universal gas constant R = 0.08206 L·atm/(mol·K). Enter any three known values and this calculator instantly solves for the fourth variable — with support for both Kelvin and Celsius input.
PV = nRT
R = 0.08206 L·atm/(mol·K)
Leave one field blank to solve for it.
常见问题
理想气体定律计算器是如何工作的？
理想气体定律计算器基于公式 PV = nRT，其中 P 是压强，V 是体积，n 是物质的量（mol），R 是气体常数（8.314 J/mol·K），T 是绝对温度（K）。输入任意三个变量，即可求解第四个未知量。
理想气体定律的局限性是什么？
理想气体定律假设气体分子间无相互作用力且分子本身体积可忽略不计。在高压（> 10 atm）和低温（接近液化点）条件下，真实气体会偏离理想行为，此时应使用范德华方程等真实气体模型。
如何使用理想气体定律？
确保使用一致的单位制：压强用 Pa 或 atm，体积用 m³ 或 L，温度用开尔文（K = °C + 273.15），物质的量用 mol。气体常数 R 的值随单位制不同而变化（R = 8.314 J/mol·K = 0.08206 L·atm/mol·K）。
标准状态（STP）下气体的摩尔体积是多少？
在标准状态（STP：0°C，1 atm）下，1 mol 理想气体的体积约为 22.4 L。在标准环境（SATP：25°C，1 bar）下，摩尔体积约为 24.8 L/mol。
PV = nRT Formula
The ideal gas law combines Boyle's Law, Charles's Law, and Avogadro's Law into a single equation relating the four state variables of a gas:
PV = nRT
P — Pressure
Measured in atmospheres (atm). 1 atm = 101,325 Pa = 760 mmHg.
V — Volume
Measured in liters (L). 1 L = 0.001 m³ = 1000 mL.
n — Moles
Amount of gas in moles. 1 mol = 6.022 × 10²³ molecules (Avogadro's number).
T — Temperature
Must be in Kelvin (K). T(K) = T(°C) + 273.15. Absolute zero is 0 K.
Solved for each variable:
P = nRT / V
V = nRT / P
n = PV / RT
T = PV / nR
Gas Constant R Values
The universal gas constant R has the same value regardless of the gas, but its numerical value depends on the units you choose:
| Value | Units | Common Use |
|---|---|---|
| 0.08206 | L·atm/(mol·K) | Chemistry (this calculator) |
| 8.314 | J/(mol·K) | SI / Physics |
| 1.987 | cal/(mol·K) | Thermochemistry |
| 62.36 | L·mmHg/(mol·K) | Pressure in mmHg / torr |
| 83.14 | mL·bar/(mol·K) | Pressure in bar |
STP and SATP Conditions
Standard conditions are reference states used to compare gas properties:
STP — Standard Temperature and Pressure (IUPAC 1982)
T = 0 °C (273.15 K), P = 1 atm. Molar volume = 22.414 L/mol.
SATP — Standard Ambient Temperature and Pressure (IUPAC 1982)
T = 25 °C (298.15 K), P = 1 bar (0.9869 atm). Molar volume ≈ 24.789 L/mol.
NTP — Normal Temperature and Pressure
T = 20 °C (293.15 K), P = 1 atm. Molar volume ≈ 24.04 L/mol. Common in HVAC and engineering.
Real vs. Ideal Gases
The ideal gas law assumes that gas molecules have no volume and exert no intermolecular forces on each other. Real gases deviate from this behavior, especially at:
- High pressure — molecules are forced close together, so their own volume becomes significant.
- Low temperature — intermolecular attractive forces become dominant, causing condensation.
- Polar molecules (e.g., H₂O, NH₃) — strong dipole–dipole or hydrogen-bonding forces cause significant deviation even at moderate conditions.
For real-gas corrections, the van der Waals equation adds two correction terms:
(P + a·n²/V²)(V − nb) = nRT
where a corrects for intermolecular attractions and b corrects for molecular volume.
How to Use This Calculator
- Enter any 3 known values — fill in pressure, volume, moles, and/or temperature.
- Leave one field blank — the blank field is automatically solved.
- Toggle temperature units — switch between Kelvin (K) and Celsius (°C) using the buttons under the temperature field. The calculator converts to Kelvin internally.
- Read and copy results — the result card shows all 4 variables. Click Copy to copy all values to your clipboard.
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