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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.

تازہ کاری جانچی گئی مثالیں: 6

آزمائیں
حجم
L
حجم: 22.414 L
بامعنی ہندسے: 6؛ قریب ترین؛ برابر فاصلے پر صفر سے دور
دباؤ
101.325kPa / 1atm
Amount of gas
1mol
درجۂ حرارت
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
حساب کا طریقہ 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 کے بارے میں

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.

حل شدہ مثالیں

1 mol at 0 °C and 1 atm

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

جانچ کا ماخذ: ⁨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
دباؤ
Volume V
10 L
Amount of gas n
2
Amount unit
mol
Temperature T
300 K
دباؤ
498.868 kPa

جانچ کا ماخذ: ⁨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

جانچ کا ماخذ: ⁨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
درجۂ حرارت
Pressure P
1 atm
Volume V
24.465 L
Amount of gas n
1
Amount unit
mol
درجۂ حرارت
298.145 K

جانچ کا ماخذ: ⁨Python 3.8 decimal: 101325 × 0.024465 / 8.31446261815324 = 298.14508 K⁩

سوالات

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” کتنا درست ہے؟

درستی آپ کی درج کردہ قدروں اور طریقے کے مفروضوں پر منحصر ہے۔ اعشاری حساب 50 بامعنی ہندسے استعمال کرتا ہے، مگر تخمینے، عددی طریقے اور ماخذ کا ڈیٹا کم درست ہو سکتے ہیں؛ دکھائی گئی قدروں کو راؤنڈ کرنے سے یہ حدود ختم نہیں ہوتیں۔ آزاد ذرائع کی حل شدہ مثالوں سے جانچ: 6۔ مثلاً، “⁨1 mol at 0 °C and 1 atm⁩” کو ⁨CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol⁩ سے جانچا جاتا ہے۔

اس طریقے کا ماخذ کیا ہے؟

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.

اس کیلکولیٹر کے بارے میں

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}

ماخذ

  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

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