How many moles of water are in 1.23 x 10 to the 18th power water molecules

Divide the number of molecules you have by, 6.022 x 10^23. This will give you the moles of water, or the moles of anything, since there is always 6.022 x 10^23 molecules in 1 mole of substance. 

1.23x10^24 atoms/6.022x10^23 atom/mole = 2.04 mole H20 

answer: the rate of diffusion increases with increase in temperature.

increase in temperature, increases the molecular/particles speed (kinetic energy. diffusion means movement of particles through the material.

generally, the heavier the particle the more it interacts with the environment and more the temperature matters. so higher temperature results in higher diffusion.