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

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

Step-by-step 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 = (P_(1)V_(1))/(T_(1))` (1)

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

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

By equating (1) with (2):

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

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