The methanation reaction for the production of methane from CO and H is as follows:

CO$+3$H$2$H$2$O $+$ CH$4$

This reaction was carried out in a system of reactor with recycle. The fresh feed contains $30$ mol$\%$ Coand $70$ mol$\%$ H$2.$ The gross product from the reactor contains $15$ mol$\%$ CO$.$ The recycle stream contains $63$ mol$\%$ H$2,10$ MOL $\%$ HO and $27$ mol$\%$ CO while the net product contains CH$4,$ HO and CO$.$ If the fresh feed rate is $100$ kmol per hour,

a$.$ Calculate the net product rate in kmol per hour.

b$.$ Determine the flow rate in kmol per hour of the gross product and its composition.

c$.$ Determine the flow rate of the reactor feed in kmol per hour and its composition

d$.$ Determine the conversion per pass and the overall conversion of CO$.$

e$.$ What is the degree of completion of the reaction on a once through basis.