The mixture does not maintain a uniform composition. A homogeneous mixture really is the same anywhere you sample it, while sand generally settles out of water when given the chance and there's likely more sand at the bottom than at the top.
You can say that if the volume of the gas is halved, the pressure is doubled.
The expression shows that pressure and volume are inversely proportional if temperature and amount of gas is held constant. This means that if volume goes down the pressure needs to go up. That also means that in order to maintain the K value, if pressure is doubled the volume needs to be halved and if the pressure is halved the volume needs to be doubled.
This relationship only works if we assume everything else (Temperature and moles of gas) to be constant.
