Meaning of “diagram of the 3 gas laws”
A diagram of the 3 gas laws summarizes three experimentally observed proportionalities for gases under clearly stated fixed conditions: Boyle’s law links pressure and volume, Charles’s law links volume and absolute temperature, and Avogadro’s law links volume and amount of gas. The diagram is a compact reminder of which variables change together and which remain constant.
Standard state assumptions used in the equations
- Constant amount of gas: a closed system with no gas entering or leaving (\(n\) fixed) for Boyle’s and Charles’s law statements.
- Absolute temperature scale: temperature expressed in kelvin, with \(T(\mathrm{K}) = T(^{\circ}\mathrm{C}) + 273.15\).
- Ideal-gas approximation: the relationships are exact in the limit of ideal behavior and remain accurate for many common conditions away from condensation.
Equations for the three laws
Each law compares two states of the same gas sample while holding specific variables constant.
| Law | Fixed variables | Proportionality | Two-state equation |
|---|---|---|---|
| Boyle’s law | \(T\) and \(n\) constant | \(P \propto \frac{1}{V}\) | \(P_1V_1 = P_2V_2\) |
| Charles’s law | \(P\) and \(n\) constant | \(V \propto T\) | \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\) |
| Avogadro’s law | \(P\) and \(T\) constant | \(V \propto n\) | \(\frac{V_1}{n_1} = \frac{V_2}{n_2}\) |
Unifying view through the ideal gas equation
\[ PV = nRT \]
Boyle’s, Charles’s, and Avogadro’s relationships are consistent with the ideal gas equation when the appropriate variables are held constant. With \(n\) fixed, the combined dependence on \(P\), \(V\), and \(T\) can be written as:
\[ \frac{PV}{T}=\text{constant}\quad(\text{fixed }n) \]
\[ \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\quad(\text{fixed }n) \]
Diagram: three characteristic graphs for the gas laws
Common pitfalls in gas-law work
- Kelvin temperature requirement: ratio forms such as \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\) require \(T\) in kelvin, not in degrees Celsius.
- Fixed-variable statements: each law changes meaning if a “constant” variable is allowed to vary (for example, Boyle’s law is not a general rule when temperature changes significantly).
- Unit consistency: pressure and volume units can vary, while equations such as \(P_1V_1=P_2V_2\) remain valid only when units are consistent within each variable.
- Real-gas limits: deviations become important at high pressure and low temperature, where intermolecular attractions and finite molecular volume matter.