Question

A vessel containing 200 ml hydrogen gas at pressure 500torr at temperature 10 degree C.Find its volume when pressure increased to 700 torr and temperature 20degree C.

Answer 1

Answer:

When the pressure and the temperature are increased the volume is 285.7 ml.

Explanation:

We can find the new volume by using the Ideal Gas Law:

$PV = nRT$

Where:

P: is the pressure

V: is the volume

n: is the number of moles

R: is the gas constant

T: is the temperature  

Initially, when V₁ = 200 ml, P₁ = 500 torr and T₁ = 10 °C, we have:

$nR = \frac{P_{1}V_{1}}{T_{1}}$   (1)  

And finally, when P₂ = 700 torr and T₂ = 20 °C, we have:

$nR = \frac{P_{2}V_{2}}{T_{2}}$   (2)

By equating (1) with (2):

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

$V_{2} = \frac{P_{1}V_{1}T_{2}}{T_{1}P_{2}} = \frac{500 torr*200 ml*20 ^{\circ} C}{10 ^{\circ} C*700 torr} = 285.7 ml$

Therefore, when the pressure and the temperature are increased the volume is 285.7 ml.                                                

I hope it helps you!