A 2500cm cube of hydrogen at S.T.P is subjected to 2.5 times increase in pressure. What volume will hydrogen now occupy?temperature remaining constant
If the pressure goes up, the volume goes down, assuming temperature is constant. This is Boyle's law. So the volume goes down by a factor of 2.5. Or, you can write v(1)xp(1) = v(2)xP(2). 2500/2.5 = 1000 mls of 1000 cubic centimeters.
It is simple. Just divided the volume of the hydrogen times the reciprocal of the pressure increase to get the answer.
By Boyle's Law, The product of pressure and volume of an ideal gas remains constant at a constant temperature. Or,P0V0 = P1V1, the temperature remaining constant.
Po = Pressure at the STP, V0 =2500cm^3, volume of hydrogen at STP and P1 =2.5 times P0 =2.5P0 on the hydrogen gas at the same STP Temperature and V1 is the resulting volume of the gas and is to be found out.
Substiting in the equation, we get.
P0 *2500 = (2.5P0)*v1
NB: Reading between words: If the increase of pressure is 2.5 times, then the actual pressure =P0+increase of 2.5P0 =3.5P0. Under this interpretation, the Volume, V1 under the pressure is 2500/3.5=714.29 cm^3.
For any gas including hydrogen the following formula holds true.
(P x V)/T = constant
Where P = Pressure, V = Volume and T = Temperature of the gas.
Therefore if given mass of a gas has Volume V1 at pressure P1 and temperature T1, and a volume of V2 at pressure P2 and Temperature T2:
(P1 x V1)/T1 = (P2 x V2)/T2
In the given problem it is assumed that the temperature remains unchanged, or T1 = T2. Therefore
P1 x V1 = P2 x V2
V2 = V1 x (P1/P2)
As P2 is 2.5 times P1, P1/p2 = 0.4
Therefore V2 = V1 x 0.4 = 2500 x 0.4 = 1000 cm cube.