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A gas system is cooled from 38.1 °C to 15.0 °C.

What was the initial volume of the system if the final volume is 4.50 L?

\[ V = [?] \, \text{L} \]

Answer :

Considering the Charles's Law, the initial volume of the system if the final volume is 4.50 L is 4.86 L.

Definition of Charles's Law

Charles's Law establishes the relationship between the temperature and the volume of a gas when the pressure is constant. This law states that the volume is directly proportional to the temperature of the gas: If the temperature increases, the volume of the gas increases, while if the gas temperature decreases, the volume decreases.

Mathematically, this law establishes that:

V÷ T=k

where:

  • T is the temperature.
  • V is the volume.
  • k is a constant.

Considering an initial state 1 and a final state 2, it is fulfilled:

V₁÷ T₁=V₂÷ T₂

Initial volume in this case

In this case, you know:

  • V₁= ?
  • T₁= 38.1 °C= 311.1 K (being 0°C= 273 K)
  • V₂= 4.50 L
  • T₂= 15 °C= 288 K

Replacing in the definition of Charles' law:

V₁÷ 311.1 K= 4.50 L÷ 288 K

Solving:

V₁= (4.50 L÷ 288 K)× 311.1 K

V₁= 4.86 L

Finally, the initial volume is 4.86 L.

Learn more about Charles' Law:

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