Compound D can be prepared from compounds A and B according to the following reaction equation:

$2$A$+$ B $->$ D

Starting material A is available as a gas at $100(=373$ K$)$ which is condensed to $50(=323$ K$)$ liquid before feeding into the mixer. The current supplied to the condenser is pure A and fed at a flow rate of $100$ mol$/$h$.$ In the mixer, the stream coming from the condenser is mixed with a liquid reactant B at a temperature of $25(=298$ K$).$ The mixer works adiabatically. Mixers output stream is fed to the reactor where the above reaction takes place. The reactor feed stream contains $70$ mol$-\%$ component A$.$ The reactor is operated so that the conversion of starting material A is $60\%.$ Reactors output streams temperature is $30(=303$ K$).$ The pressure remains constant at $1$ atm throughout the process.

a$)$ Create component balances and energy balances for all process units. $($Note$.$ Without numerical values added.$)$

b$)$ Determine whether the balance problem can be solved with the help of degree of freedom analysis. From which process unit is it worth starting to solve the problem and how to proceed?

c$)$ Solve for the flow rates, compositions $($mole fractions$)$ and temperatures of all the streams and the condenser required cooling capacity. Also find out if the reactor needs to be heated or cooled and what it entails

required power.

d$)$ Could the balance of the overall process be solved without information about the internal flows of the process?