What is the different between a mole and a molecule?
A mole is in relationship to a mass unit. A molecule is in relationship with atoms.
What is a the integral of 1/x with respect to x?
The integral would be the natural log (x), so ln(x) + constant. The constant needs to be added in because when you take the derivative of a constant, it becomes zero and we do not know if a constant was there or not.
What is the fundamental equation for a mass balance and what are the meanings of the variables?
Input - Output +/- Reactions = Accumulation. Input in the mass going into the system, Output is the mass going out of the system, reactions are when mass can be created or destroyed, and accumulation happens when the system is not in steady state, if it is in steady state, accumulation equals zero.