When a gas is pumped into a small rigid container the pressure inside the container increases as more particles are added. if the number of particles is doubled then the pressure will double. what would happen if the number of particles were decreased by half?

Since the container of the gas is rigid, the volume of the gas will remain constant. Therefore, when the number of particles were decreased in half then the pressure will also be half of the original given they both are subjected to the same temperature.

PV = nRT

V, T and R are constants so they can be lumped together to a constant k.

P/n = k
P1/n1 = P2/n2

since n2 = n1/2
P1/n1 = P2/n1/2
P2 = P1/2

For cyclohexane compounds drawn in a chair conformation:   -axial bonds are vertical  -equatorial bonds are parallel to two bonds within the ring.  thus, as i assume the chair conformation is drawn:   -the x group is in an axial position, as are the five other vertical bonds.  -three axial bonds are on the top face of the ring  -the other three axial bonds are on the bottom face  the position of the second substituent on each ring carbon is equatorial.  gauche groups must be on an adjacent carbon such as carbon 6 and carbon 2, and also gauche groups are rotated by 60 degrees relative to each other.  drawing the newman projections for c1–c2 and c1–c6 aids in visualizing the groups that are gauche to the y group on c1.  click this link and watch some academic videos that may you more understand the topic