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Gas lawsChemistryHigh schoolabout 1:01

What volume does 0.5 mol of an ideal gas occupy at 2.5 atm and 100 °C?: animated lesson

A narrated, step-by-step gas laws video lesson with captions. Final answer: V = 6.12394 L.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    What volume does 0.5 mol of an ideal gas occupy at 2.5 atm and 100 °C?
  2. 2. Step by step
    1. T=100+273.15=373.15 KT = 100 + 273.15 = 373.15\ \text{K}
      Convert the temperature to kelvin
    2. R=0.082057366 L⋅atm/(mol⋅K)R = 0.082057366\ \text{L·atm/(mol·K)}
      Choose the gas constant to match the units
    3. V=nRTP=0.5×0.082057366×373.152.5=6.12394 LV = \frac{nRT}{P} = \frac{0.5 \times 0.082057366 \times 373.15}{2.5} = 6.12394\ \text{L}
      Rearrange PV = nRT for V and substitute
  3. 3. The answer
    V=6.12394 LV = 6.12394\ \text{L}

    V = 6.12394 L

  4. 4. Check
    • PV = 15.3099 and nRT = 15.3099, which agree.

Transcript

The problem. Here is the problem: What volume does 0.5 mol of an ideal gas occupy at 2.5 atm and 100 °C? Solve PV equals nRT for V, with pressure in atm, volume in litres, amount in moles and temperature in kelvin.

Step by step. Convert the temperature to kelvin. The gas law needs absolute temperature. Choose the gas constant to match the units. Pressure is in atm and volume in litres. Rearrange PV equals nRT for V and substitute.

The answer. So the answer is V equals 6.12394 L. An ideal gas obeys PV equals nRT: pressure times volume is proportional to the amount of gas and its absolute temperature. Real gases follow it closely at low pressure and high temperature.

Check. PV equals 15.3099 and nRT equals 15.3099, which agree.

About gas laws

Use the ideal gas law and the combined gas law to find pressure, volume, temperature or moles.

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