The gases in a hair spray can are at a temperature of 27oC and a pressure of 30 lbs/in2. If the gases in the can reach a pressure of 90 lbs/in2, the can will explode. To what temperature must
the gases be raised in order for the can to explode? Assume constant volume. Show your work.

Using Gay Lussac's Law

Gay Lussac's Law:-

It states that at constant volume (V),The pressure(P) of fixed amount of gas caries directly with its absolute temperature(T).

n+h→nh3

we must remember that nitrogen and hydrogen are both diatomic molecules in their standard gas form. this adjusts the equation to

n2+h2→nh3

now we need to adjust coefficients in order to balance the atoms on each side of the equation. currently we have 2 atoms of nitrogen and 2 atoms of hydrogen on the reactant side and 1 atom of nitrogen and 3 atoms of hydrogen on the product side.

we can balance the hydrogens by placing a coefficient of 2 in front of ammonia and a coefficient of 3 in front of the hydrogen.

n2+3h2→2nh3

this gives us 6 hydrogen on each side and coincidentally the nitrogens now equal 2 on each side.

radioactive decay occurs in unstable atomic nuclei – that is, ones that don't have enough binding energy to hold

the nucleus together due to an excess of either protons or neutrons.