Question

When the contents of a 1000 cubic foot container full of basketballs is mixed with the contents of a 200 cubic foot container full of ping pong balls, the mixture does not completely fill a 1200 cubic foot container. explain this result in terms of the partial molar volumes of the basketballs and ping pong balls. state any assumptions you make.

Answer 1

The total volume occupied by basketball in 1000 cubic feet container includes the volume occupied by basketball and the interstitial space between the balls. The ping-pong balls are small enough to occupy the interstitial space created between the basketballs. Out of all the ping-pong balls that occupied 200 cubic feet volume, most of them would occupy the space available between the basketballs and only some of them would need any extra volume. Thus, the total volume occupied by basketball and ping-pong balls will not fill up the 1200 cubic feet container.

Let us assume a unit of basketball and ping-pong ball is considered as one mole of each of them respectively. In terms of partial molar volume, it can be considered that as the volume change upon addition of ping-pong balls is negligible as most of the balls, when added would occupy the interstitial space and would not lead to any increase or decrease in volume of the overall mixture of the balls. As the interstitial volume is occupied, the partial molar volume due to further addition of balls would increase the total volume but this volume will be less than the total of 1200 cubic feet.