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Question

State Ideal gas equation and law.


Solution

Ideal gas law is a law relating the pressure, temperature and volume of an ideal gas. Ideal gas equation is combination of three laws (Boyle's law, Charles law and Avogadro law) and gives a single equation $$(PV=nRT)$$ called as Ideal gas equation.
Mathematically,
According to Boyle's law, at constant $$T$$ and $$n$$,
$$V\propto 1/P............(1)$$
According to Charle's law, at constant $$P$$ and $$n$$,
$$V\propto T..............(2)$$
According top Avogadro law, at constant $$T$$ and $$n$$,
$$V\propto n..............(3)$$
From equation $$1,2$$ and $$3$$, we get
$$V\propto nT/P...........(4)$$
or, $$V=RnT/P.............(5)$$
or, $$PV=nRT..............(6)$$
Then, $$R=PV/nT...........(7)$$
Where, $$R$$ is a gas constant which is same for all gases and known as Universal gas constant and equation $$(6), PV=nRT$$ is known as ideal gas equation.

Chemistry

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