Why does a mixture of hydrogen and oxygen in a balloon not spontaneously explode at room temperature

Because the molecules of the mixture would be compact or bond together at room temperature. In this case, both gases will condense to form water (or ice, if the room temperature is prolonged) and such droplets of water will not cause a balloon to spontaneously explode at room temperature.

Explanation:

A mixture of hydrogen and oxygen will form water. Recall that the chemical formula for water is H₂O, where H represents Hydrogen and O represents Oxygen.

A balloon is a light (not thick) solid substance with a thin membrane when blown or filled with some elements or gases.

Room Temperature means cool or cold temperature. You already know that generally at room temperature, the molecules of any substance will stick together or will become less mobile (less spontaneous).

In this case, hydrogen gas and oxygen gas will go through a process called condensation - to form water - and then through the process called freezing - to form ice.

At room temperature, the gases will first change state (state of matter) from gaseous to liquid and then from liquid to solid.

This is why the balloon will NOT spontaneously explode.