Question

A pipe bursts in your kitchen and floods it. The water seeps into an old bottle of vinegar (a dilute solution of acetic acid in water) and dilutes it further. Before the flood, there were 100 g of vinegar, which contained 5 wt% acetic acid and the rest water. After the flood, both the volume of the vinegar and its composition are unknown. How many degrees of freedom are in this process? (Hint: treat this like any other material balance problem. Set up your diagram, eliminate unknowns where possible, and balance your unknowns against your independent equations).

Answer 1

Amount of vinegar =100 gms amonut of acetic acid =5% of 100 gms = 5 gm amount of water =100-5=95gms

Unknowns : amonut of water that gets mixed with vinegar

If amount of water is known, total mass after mixing= 100+x ( where x is mass of water that gets added due to spillage)

Acetic acid is tie substance that does not undergo any change, only thing is it gets diluted.

hence 5= (100+x)* y where y= percentage of acetic acid

percentage of water= 100*(x/100+x)

so only one degree of freedom is there, that is the amount of water added.