Question

Question #c834a

Answer 1

Assuming that Gas Z behaves like an ideal gas over this pressure and temperature range, we can calculate the pressure and volume using the ideal gas equation.
`pV=kT`
That is, the pressure times the volume is a linear function of temperature.

We know initially that :
`V_i* 1" atm" = k * 273.15 ºK`

`V_i/k = 273.15(ºK)/(atm)`

In the compressed state:
`V_f * 50 " atm" = k * (1700ºK+273.15ºK)`

`V_f/k = (1973.15)/50 (ºK)/(atm) = 39.463 (ºK)/(atm)`

We can't calculate k without knowing the molar mass of the gas. It is equal to the number of atoms times the Rydberg constant. But we can calculate the ratio between the initial and final volume.

The final volume will be equal to :
`V_f = V_i * (39.463/273.15) = V_i * 0.144`
The gas has been compressed to a little more than one ninth its initial volume.