Question

A sample of nitrogen gas is at a temperature of 50 c and a pressure of 2 atm. If the volume of the sample remains constant and the pressure increases to 3.2 atm, what ist eh enw temperature of the nitrogen gas

Answer 1

The new temperature of the nitrogen gas is 516.8 K or 243.8 C.

Step-by-step explanation:

Gay-Lussac's law indicates that, as long as the volume of the container containing the gas is constant, as the temperature increases, the gas molecules move faster. Then the number of collisions with the walls increases, that is, the pressure increases. That is, the pressure of the gas is directly proportional to its temperature.

Gay-Lussac's law can be expressed mathematically as follows:

`(P)/(T) =k`

Where P = pressure, T = temperature, K = Constant

You want to study two different states, an initial state and a final state. You have a gas that is at a pressure P1 and at a temperature T1 at the beginning of the experiment. By varying the temperature to a new value T2, then the pressure will change to P2, and the following will be fulfilled:

`(P1)/(T1) =(P2)/(T2)`

In this case:

• P1= 2 atm
• T1= 50 C= 323 K (being 0 C= 273 K)
• P2= 3.2 atm
• T2= ?

Replacing:

`(2 atm)/(323 K) =(3.2 atm)/(T2)`

Solving:

`T2*(2 atm)/(323 K) =3.2 atm`

`T2=3.2 atm*(323 K)/(2 atm)`

T2= 516.8 K= 243.8 C

The new temperature of the nitrogen gas is 516.8 K or 243.8 C.