There is a composite system consisting of

two rigid compartments separated by a barrier. Both compartments are at $25$C and $1$ atm pressure. The first compartment contains an ideal mixture of gases $1$ and $2,$ with molar compositions of $10\%$ and $90\%,$ respectively. The second compartment contains an ideal equimolar mixture of gases $1,2$ and $3.($a$)$ Determine the values of the partial pressures in each compartment and based on this, determine in which compartment gas$1$ is greater. Clearly justify your answer. $(50$ points$).$

$($b$)$ If the barrier were replaced by a rigid membrane permeable only to gas $1,$ in which direction would gas $1$ diffuse? Justify your answer and add a drawing.