Question

A tank containing 200 L of hydrogen gas at 0.0 Celsius is kept at 10 kPa. The pressure is raised to 95C, and the volume is decreased to 175L. What is the new pressure of the gas?

Answer 1

The new pressure of the gas is 15.40 kPa.

Step-by-step explanation:

Gay-Lussac's law indicates that when there is a constant volume, as the temperature increases, the pressure of the gas increases. And when the temperature is decreased, the pressure of the gas decreases. Mathematically this law indicates that the quotient between pressure and temperature is constant:

`(P)/(T)=k`

On the other hand, Boyle's law says that the volume occupied by a certain gaseous mass at constant temperature is inversely proportional to the pressure. This law is expressed mathematically as:

P*V=k

Finally, Charles's law indicates that as the temperature increases, the volume of the gas increases and as the temperature decreases, the volume of the gas decreases. Mathematically, this law says that when the amount of gas and pressure are kept constant, the quotient that exists between the volume and the temperature will always have the same value:

`(V)/(T)=k`

Combined law equation is the combination of three gas laws called Boyle's, Charlie's and Gay-Lusac's law:

`(P*V)/(T)=k`

Studying an initial state 1 and a final state 2, it is fulfilled:

`(P1*V1)/(T1)=(P2*V2)/(T2)`

In this case:

• P1= 10 kPa
• V1= 200 L
• T1= 0 C= 273 K
• P2=?
• V2= 175 L
• T2= 95 C= 368 K

Replacing:

`(10 kPa*200 L)/(273 K)=(P2*175 L)/(368 K)`

Solving:

`P2=(368 K)/(175 L) *(10 kPa*200 L)/(273 K)`

P2= 15.40 kPa

The new pressure of the gas is 15.40 kPa.