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;

          $\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }$

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  = $\frac{120}{1000}$ dm³  = 0.12dm³ = initial volume

Final volume;

      1000ml = 1dm³

      180ml  = $\frac{180}{1000}$ 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;

         $\frac{1.2bar x 0.12 }{308} = \frac{P_{2} x 0.18 }{308}$

       Solving for P₂;

     P₂  = 0.8bar

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