Question

Calculate the P values for which Br2(g) is in a corresponding state to Xe(g) at 328 K and 73.2 bar .

Answer 1

The reduced values are defined by the following equations.

T_r = T/T_c

P_r = P / P_c

V_mr = V_m / V_mc

Where T is the temperature, P is pressure, V_m is the molar volume. The subscript r means reduced variable and c means the value at the critical point.

For Xenon gas, critical temperature is 289.74 K and critical pressure is 58.40 bar.

Now calculate the reduced pressure and temperature of Xe gas using the above equations.

T_r = 328K / 289.74

T_r = 1.13

P_r = 73.2 bar / 58.40 bar

P_r = 1.25

As Bromine and xenon gases exist in corresponding states, they have same reduced values.

Rearrange the equations for the reduced variables to solve for the variables T,P.

T_r = T / T_c

T = T_r T_c

P_r = P / P_c

P = P_r P_c

For bromine gas, critical temperature is 588K and critical pressure is 103.40 bar.

Now substitute the values for bromine and calculate as follows:

T = T_r T_c

= 1.13 x 588K

T = 664.44 K

P = P_r P_c

= 1.25 x 103.40 bar

P = 129 bar