Like all equilibrium constants, the value of kw depends on temperature. at body temperature (37∘c), kw=2.4⋅10−14. part a what is the [h3o+] in pure water at body temperature?

The concentration of  [ H3O^+] is 1.6 × 10^−7.

We know that the auto-ionization of water occurs as follows;

2H2O(l) ⇄ H3O^+(aq) + OH^-(aq)

The equilibrium constant for the auto-ionization of water is given as follows;

Kw = [ H3O^+] [ OH^-]/[H2O]^2

But water is a pure liquid hence;

Kw = [H3O^+] [ OH^-]

But  [H3O^+] =  [ OH^-] =

so Kw = [H3O^+] ^2

In this case Kw = 2.4 × 10^−14

[H3O^+] = √Kw

[H3O^+] = √2.4 × 10^−14

[H3O^+] = 1.6 × 10^−7 M

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what is the general relationship between a galaxy's distance from earth and its speed?

the answer is:

the farther away a galaxy is from us, the faster it is moving away from us.