The Ideal Gas Law
Introduced| English | Meaning |
|---|---|
| ideal gas law/aɪˈdɪəl ɡæs lɔː/ | The relation pV=nRT connecting pressure, volume, amount and absolute temperature in the ideal-gas model. |
| kelvin/ˈkelvɪn/ | The SI unit of thermodynamic temperature, with zero at absolute zero. |
One equation for all gases
- Squeeze a balloon and the pressure rises.
- Heat it and it swells.
- Every gas — air, helium, steam — follows the same simple rule.
- Four quantities, one tidy equation, tie them together.
The ideal gas law
- The ideal gas law 理想气体定律 is:
- $P$ is pressure, $V$ volume, $n$ moles, $T$ temperature, and $R$ the gas constant.
- Know any three and you can find the fourth.
An ideal gas is a model of point particles with no forces between them
How many variables does $PV = nRT$ contain (counting P, V, n, T but not the constant R)?
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$P$, $V$, $n$, $T$ are the four variables; $R$ is a constant.
The gas constant and units
- $R = 8.314\ \text{J/(mol}\cdot\text{K)}$, or $0.0821\ \text{L}\cdot\text{atm/(mol}\cdot\text{K)}$.
- Temperature must be in kelvin 开尔文, never Celsius.
- Match your units to the $R$ you choose.
Before using $PV = nRT$, temperature must be converted to...
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The gas laws require an absolute temperature in kelvin.
How the variables trade
- At fixed $T$ and $n$: squeeze the volume and the pressure rises.
- At fixed $P$ and $n$: heat it and the volume grows.
- More moles at fixed $T$ and $V$ means more pressure.
Squeeze the gas
At fixed temperature, pressure and volume are inversely related.
At fixed temperature and moles, halving the volume halves the pressure.
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False. $P$ and $V$ are inversely related at fixed $n$ and $T$, so halving the volume doubles the pressure.
At fixed pressure and moles, heating a gas causes its volume to...
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At fixed $P$, $V$ is directly proportional to $T$.
Find the pressure of $2\ \text{mol}$ of gas in $10\ \text{L}$ at $300\ \text{K}$ (use $R = 0.0821$).
- $P = \dfrac{nRT}{V} = \dfrac{(2)(0.0821)(300)}{10}$.
- $P \approx 4.9\ \text{atm}$.
Find P for $1\ \text{mol}$ in $2\ \text{L}$ at $300\ \text{K}$ ($R = 0.0821$), in atm (1 decimal).
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$P = nRT/V = (1)(0.0821)(300)/2 \approx 12.3\ \text{atm}$.
The ideal gas model works best at high temperature and ____ pressure.
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Low pressure keeps molecules far apart, so attractions are negligible.
Always convert the temperature to kelvin (add 273) before using $PV = nRT$ — Celsius gives nonsense. Keep units consistent with your $R$ (L and atm, or m$^3$ and Pa). And "ideal" assumes point particles with no attractions, an approximation that is best at high temperature and low pressure.
The ideal gas law $PV = nRT$ ties pressure, volume, moles, and temperature through the gas constant $R$. Know any three to find the fourth. Temperature must be in kelvin, and units must match your $R$. The model is ideal — best at high $T$ and low $P$.