Answer:
For the purposes of your question, we can think of speed and velocity as being the same thing. Therefore, the potential energy of an object is proportional to the square of its velocity (speed). In other words, If there is a twofold increase in speed, the potential energy will increase by a factor of four.
For this problem, we use the formula for radioactive decay which is expressed as follows:
An = Aoe^-kt
where An is the amount left after time t, Ao is the initial amount and k is a constant.
We calculate as follows:
An = Aoe^-kt
0.5 = e^-k(5730)
k = 1.21x10^-4
An = Aoe^-kt
An = 200e^-1.21x10^-4(17190)
An = 25
Therefore, about 175g is produced.
Answer:
1.3 mol H₂O
Explanation:
Let's consider the decomposition reaction of ammonium perchlorate.
NH₄ClO₄(s) → 1/2 N₂(g) + 1/2 Cl₂(g) + O₂(g) + 2 H₂O(g)
As we can see in the balanced equation, the molar ratio of ammonium perchlorate to water is 1:2. The moles of water produced by the reaction of 2.5 mol of ammonium perchlorate.
2.5 mol NH₄ClO₄ × (2 mol H₂O / 1 mol NH₄ClO₄) = 1.3 mol H₂O
Convert the amount of substance in carat to grams.
(5.0 carat) x (0.200 g / 1 carat) = 1 g
The volume of the substance is obtained by dividing the mass by the density,
v = m / d
v = 1 g / (3.51 g/cm³) = 0.2849 cm³
Therefore, the volume of a 5.0 carat diamond is approximately 0.285 cm³.
