Once the activity of americium in a smoke detector falls below 5 percent of its original activity, it's no longer able to effectively detect smoke and trigger the alarm. If the half-life of americium-241 is approximately 432.2 years, how many years will it take before the americium-241 is unable to detect smoke? Question 11 options:

A)

10 years

B)

20 years

C)

1,868 years

D)

2 years

C 1,868 years

Explanation:

I just took the test - I tried doing the math and was close but couldn't get it exact; so I guessed and I was correct :)

h let me think

n2(g) + 3h2-> 2nh3(g)   this is the balanced equation

note the mole ratio between n2, h2 and nh3.   it is 1 : 3 : 2   this will be important.

moles n2 present = 28.0 g n2 x 1 mole n2/28 g = 1 mole n2 present

moles h2 present = 25.0 g h2 x 1 mole h2/2 g = 12.5 moles h2 present

based on mole ratio, n2 is limiting in this situation because there is more than enough h2 but not enough n2.

moles nh3 that can be produced = 1 mole n2 x 2 moles nh3/mole n2 = 2 moles nh3 can be produced

grams of nh3 that can be produced = 2 moles nh3 x 17 g/mole = 34 grams of nh3 can be produced

note:   the key to this problem is recognizing that n2 is limiting, and therefore limits how much nh3 can be produced.