Question

A vessel of 120ml capacity contains a certain amount of gas at 35°C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180ml at 35°C. What would be its pressure

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Answer 1

Given parameters:

Initial volume = 120ml

Initial temperature = 35°C

Initial pressure = 1.2bar

Final volume = 180ml

Final temperature = 35°C

Unknown:

Final pressure = ?

To solve this problem, we apply the combined gas law. The expression is given below;

`(P_(1)V_(1) )/(T_(1) ) = (P_(2)V_(2) )/(T_(2) )`

Where P₁ is the initial pressure

P₂ is the final pressure

V₁ is the initial volume

V₂ is the final volume

T₁ is the initial temperature

T₂ is the final temperature

We need to convert the parameters to standard units

take the volume to dm³;

1000ml = 1dm³

120ml =
`(120)/(1000)` dm³ = 0.12dm³ = initial volume

Final volume;

1000ml = 1dm³

180ml =
`(180)/(1000)` dm³ = 0.18dm³

Now, the temperature;

K = 273 + °C

Initial temperature = 273 + 35 = 308k

Final temperature = 308k

We then input the parameters into the equation;

`(1.2bar x 0.12 )/(308) = (P_(2) x 0.18 )/(308)`

Solving for P₂;

P₂ = 0.8bar

The new pressure or final pressure in the vessel is 0.8bar