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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.

Güncellendi Doğrulanan örnekler: 6

Dene
Hacim
L
Hacim: 22.414 L
Anlamlı basamaklar: 6; En yakına; eşit uzaklıkta sıfırdan uzağa
Basınç
101.325kPa / 1atm
Amount of gas
1mol
Sıcaklık
273.15K / 0°C
Molar volume V/n
22.414L/mol
Number of molecules
6.02214 × 10²³

1 mol of ideal gas at 273.15 K (0 °C) and 101.325 kPa occupies 22.414 L — 22.414 L per mole.

Isotherm through this state (P–V)

01002003004000204060Volume (L)Pressure (kPa)101.3 kPa, 22.41 L
Nasıl hesaplanır S

  1. Convert to SI units

    P=101,325 Pa, V=0.022414 m3, n=1 mol, T=273.15 KP = 101{,}325\ \mathrm{Pa},\ V = 0.022414\ \mathrm{m^3},\ n = 1\ \mathrm{mol},\ T = 273.15\ \mathrm{K}

    Temperature is always absolute in gas laws: K = °C + 273.15.

  2. Solve PV = nRT for V

    V=nRTP=(1)(8.314462618)(273.15)101,325=0.022414 m3=22.414 LV = \frac{nRT}{P} = \frac{(1)(8.314462618)(273.15)}{101{,}325} = 0.022414\ \mathrm{m^3} = 22.414\ \mathrm{L}

Ideal gas law calculator hakkında

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.

Çözümlü örnekler

1 mol at 0 °C and 1 atm

Law
PV = nRT
Solve for
Hacim
Pressure P
1 atm
Amount of gas n
1
Amount unit
mol
Temperature T
0 °C
Hacim
22.414 L

Doğrulama kaynağı: 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
Basınç
Volume V
10 L
Amount of gas n
2
Amount unit
mol
Temperature T
300 K
Basınç
498.868 kPa

Doğrulama kaynağı: 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

Doğrulama kaynağı: 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
Sıcaklık
Pressure P
1 atm
Volume V
24.465 L
Amount of gas n
1
Amount unit
mol
Sıcaklık
298.145 K

Doğrulama kaynağı: Python 3.8 decimal: 101325 × 0.024465 / 8.31446261815324 = 298.14508 K

Sorular

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” ne kadar doğru sonuç verir?

Doğruluk, girdilerinize ve yöntemin varsayımlarına bağlıdır. Ondalık aritmetik 50 anlamlı basamak kullanır; ancak tahminler, sayısal yöntemler ve kaynak veriler daha az hassas olabilir. Gösterilen değerin yuvarlanması bu sınırları ortadan kaldırmaz. Bağımsız kaynaklarla doğrulanan çözümlü örnek sayısı: 6. Örneğin “1 mol at 0 °C and 1 atm”, CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol ile karşılaştırılarak doğrulanır.

Yöntemin kaynağı nedir?

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.

Bu hesaplayıcı hakkında

PV=nRT, R=8.314 462 618… J mol−1 K−1 (exact);P1V1T1=P2V2T2PV = 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}

Kaynaklar

  1. 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)
  2. OpenStax Chemistry 2e, §9.2 Relating pressure, volume, amount, and temperature: the ideal gas law

Kaynaklarla doğrulandı

Bu hesaplayıcı, yanıtları bağımsız kaynaklardan alınan 6 çözümlü örnek içerir. Bunlar test paketinde çalıştırılır; burada da çalıştırabilirsiniz.

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