The combined gas law is a fundamental principle in chemistry that illustrates the relationship between pressure, volume, and temperature of a gas. It is derived from three key gas laws: Boyle's law, Charles' law, and Gay-Lussac's law. Each of these laws describes how one variable affects another under specific conditions.
Boyle's law states that pressure (P) is inversely proportional to volume (V) when temperature is held constant, which can be expressed mathematically as:
$$ P \propto \frac{1}{V} $$
Charles' law indicates that volume is directly proportional to temperature (T) when pressure is constant, represented as:
$$ V \propto T $$
Gay-Lussac's law asserts that pressure is directly proportional to temperature when volume is constant, which can be written as:
$$ P \propto T $$
By combining these relationships, we arrive at the combined gas law, which can be expressed as:
$$ \frac{PV}{T} = k $$
where \( k \) is a constant. This equation highlights that the product of pressure and volume divided by temperature remains constant for a given amount of gas.
Furthermore, when comparing two sets of conditions, the combined gas law can be rearranged to:
$$ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} $$
This form allows for the calculation of changes in pressure, volume, or temperature when a gas undergoes a transformation, making it a versatile tool in thermodynamics and gas behavior analysis.
