Question

For the system methane(1)/ethane(2)/propane(3) as a gas, estimate f ˆ 1 , fˆ 2 , fˆ 3 , ϕˆ 1, ϕˆ 2,

and ϕ ˆ 3 at t = 100°C, P = 35 bar, y1 = 0.21, and y2 = 0.43:
(a) Through application of Eq. (10.64).
(b) Assuming that the mixture is an ideal solution.

Answer 1

To estimate the fugacity and activity of each component in the gas system methane/ethane/propane, we can use equations (10.64) and assume an ideal solution.

Step-by-step explanation:

To estimate the fugacity and activity for each component in the system methane(1)/ethane(2)/propane(3) as a gas, we can use the equations (10.64) and the assumption of an ideal solution.

(a) According to equation (10.64), the fugacity (ƒ) for each component is given by:

ƒ^1 = y1 * P * exp((u^1 - u^*) / (RT))

ƒ^2 = y2 * P * exp((u^2 - u^*) / (RT))

ƒ^3 = y3 * P * exp((u^3 - u^*) / (RT))

Where y1, y2, and y3 are the mole fractions of methane, ethane, and propane respectively, P is the pressure, u^1, u^2, and u^3 are the fugacity coefficients for methane, ethane, and propane respectively, u^* is the standard state fugacity coefficient, R is the gas constant, and T is the temperature.

(b) Assuming that the mixture is an ideal solution, the activity (φ) for each component is equal to its mole fraction:

φ^1 = y1

φ^2 = y2

φ^3 = y3

Answer 2

To estimate the fugacity and fugacity coefficient of each component in a gas mixture, the mole fraction of each component must be calculated. The fugacity and fugacity coefficient can be determined using the Peng-Robinson equation of state or assuming the mixture is an ideal solution and using the ideal gas law.

Step-by-step explanation:

To estimate the fugacity (f) and fugacity coefficient (ϕ) of each component in the given system, we can use the Peng-Robinson equation of state. First, we need to calculate the mole fraction (X) of each component:

X1 = y1 * P1 / P = (0.21 * 35) / 151 = 0.0482

X2 = y2 * P2 / P = (0.43 * 35) / 151 = 0.0993

X3 = 1 - X1 - X2 = 1 - 0.0482 - 0.0993 = 0.8525

Now, we can calculate the fugacity and fugacity coefficient using the Peng-Robinson equation:

f1 = X1 * P1 * exp(ϕ1)

f2 = X2 * P2 * exp(ϕ2)

f3 = X3 * P3 * exp(ϕ3)

ϕ1, ϕ2 and ϕ3 can be calculated using correlation equations. Alternatively, if we assume the mixture to be an ideal solution, we can use the ideal gas law:

f1 = X1 * P1

f2 = X2 * P2

f3 = X3 * P3