Consider the following equilibrium:

What will cause the pH to increase and the Kwto decrease?

increasing the temperature
decreasing the temperature
adding a strong base
adding a strong acid

and why

Adding a strong base will cause the pH to increase and the Kw to decrease.

Adding a strong base will increase the concentration of hydroxide ions (OH-) in the solution. As a result, the concentration of hydrogen ions (H+) will decrease, leading to an increase in pH.

The auto-ionization of water, which is responsible for the formation of hydroxide and hydrogen ions, is represented by the equilibrium equation: H2O ⇌ H+ + OH-. Increasing the concentration of hydroxide ions by adding a strong base will shift this equilibrium to the left, decreasing the concentration of hydrogen ions and reducing the value of Kw (the equilibrium constant of water).