Question

How to derive ideal gas law using Charle's and Boyle's law?

Answer 1

#73138

- How to derive Ideal gas law using charle's & Boyle's law?

Sol: Ideal gas equation,

$$V \propto \frac{1}{p} \quad \text{(Boyle's law)} \quad \cdots (i)$$ $$V \propto T \quad \text{(Charle's law)} \quad \cdots (ii)$$ $$V \propto n \quad \text{(Avogadro's law)} \quad \cdots (iii)$$

Combining (i), (ii) & (iii)

$$V \propto \frac{nT}{p}$$ $$P V \propto nT$$ $$P V = nRT$$

Where,

$R =$ universal gas constant

$R = 8.314 \frac{\text{ft}^2 \text{mol}^{-1}}{2}$

where $P'$ (pressure) is in $\text{Pa}$ or $\text{Nm}^2$

$V'$ in $\text{m}^3$

$R = 0.0821 \text{ atm lit/mol·K}$

$R = 1.987 \text{ cal/mol K}^{-1}$

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