A steam-methane reforming plant is consuming methane at a rate of 125 mol/h and converting itinto synthesis gas, which is a mixture of H2 and CO. The methane is being fed into the process atan absolute pressure of 2330 psi and a temperature of 25°C. A. Estimate the volumetric flowrate of methane using ideal gas EOS (report answer in liters/hr).B. Estimate the volumetric flowrate using the compressibility factor EOS.C. Does it make sense to use the ideal gas EOS? Why or why not? Justify your answer. This is a compressibility factor chart, which illustrates the relationship between the compressibility factor (Z), reduced pressure (${P_r}$), and reduced temperature (${T_r}$) for gases. The chart is plotted on a graph with reduced pressure (${P_r}$) on the x-axis ranging from 0.0 to 10.0 and compressibility factor (Z) on the y-axis ranging from 0.0 to 1.2.Key features of the chart include:- **Isotherms for Reduced Temperature (${T_r}$):** Each curve on the chart represents a different reduced temperature (${T_r}$). The curves are labeled with values ranging from 0.70 to 2.00, and include higher values such as 1.30, 1.50, and up to 3.00 for the rightmost curves.- **Compressibility Factor (Z):** The values on the y-axis represent the compressibility factor (Z), which is a dimensionless ratio indicating how much a real gas deviates from ideal gas behavior. A Z value of 1 corresponds to ideal gas behavior.- **Behavior at Different Conditions:** The chart provides insight into how gases behave under various combinations of pressure and temperature. For values of Z less than 1, the gas is more compressible than an ideal gas, while for values greater than 1, it is less compressible.- **Critical Point:** Near the central portion of the chart, typically around a reduced pressure of 1, the highest deviation from ideal behavior is observed. This area is significant in understanding phase changes and critical properties of substances.This chart is essential for engineers and scientists to predict how real gases will behave under different conditions, allowing for more accurate calculations in various applications such as chemical processes, thermodynamics, and fluid dynamics.

Molar flow rate of methane, ṅ = 125 mol/h Absolute pressure of the methane stream, P = 2330 psi = 158.55 atm = 160.65 bar Temperature of the methane stream, T = 25°C = 298 K The value of R to be used is 0.08206 (L.atm)/(mol.K)(A) Use the ideal gas equation of states to calculate the volumetric flow rate of methane as: PV˙id=n˙RTV˙id=n˙RTPV˙id=125 molh0.08206 L⋅atmmol⋅K298 K158.55 atmV˙id=19.28 Lh(B) From the standard table for physical properties of pure species, take the critical properties of methane as: PC=45.99 barTC=190.6 K Calculate the reduced temperature and reduced pressure for the given methane stream as: Pr=PPC=160.65 bar45.99 bar=3.49Tr=TTC=298 K190.6 K=1.56From the given graph, estimate the value of the compressibility factor (Z) corresponding to the calculated values of Tr and Pr. Z = 0.83 Now, calculate the volumetric flow rate of methane using this compressibility factor as: PV˙CF=Zn˙RTV˙CF=Zn˙RTPV˙CF=0.83125 molh0.08206 L⋅atmmol⋅K298 K158.55 atmV˙CF=16.00 Lh(C) The value of the compressibility factor calculated for methane at the given temperature and pressure is 0.83 which is considerably far from 1. Since there exists non-ideality in the behavior of methane gas, it does not make any sense to use the ideal gas equation of state to calculate the volumetric flow rate of methane.