Derive the formula for the depletion force between two large particles (with a radius of ?) with a separation distance of ? in the presence of small molecules with a radius of ?. Hint: use the fact that the overlapping volume between two spheres is twice the overlapping volume between a sphere and a flat surface.

The image shows the example of finding the number of vacancies in 1 cubic meter of copper (Cu) at 1000 degrees celcius (1273 k) considering the image data. Replicating the problem in the image, calculate the number of vacancies but at room temperature.Explain why there is such a difference in the number of vacancies at both temperatures.

If we have 35.54L of O2 gas at STP, how many moles of this gas do we have?  Note:  it is understood that the unit of your answer is some number of moles, however do not explicitly include units in your answer.  Enter only a number.  If you do enter a unit ("mol" in this case), you answer will be counted wrong.  (STP means "standard temperature and pressure," which is 1 atmosphere of pressure or 101,325 Pa, and 273K).

The metal molybdenum becomes superconducting at temperatures below 0.90 K. Calculate the temperature at which molybdenum becomes superconducting in degrees Celsius. Round your answer to 2 decimal places .