Question

Assume that thermal decomposition of mercuric oxide, HgO, obeys first-order kinetics. It can be followed by the production of oxygen gas as a product: 2 HgO(s) --> 2 Hg(l) + O2 (g) At a particular temperature, k = 6.02 x 10-4 sec-1. If 1.00 gram of HgO were present initially, how long would it take to produce to produce 1 ml of O2 (g) at STP?

Answer 1

2 HgO(s) --> 2 Hg(l) + O2 (g)

At a particular temperature, k = 6.02 x 10-4 sec-1. If 1.00 gram of HgO were present initially, how long would it take to produce to produce 1 ml of O2 (g) at STP?

Mass of 1 litre or 1000 ml of oxygen at STP = 1.429 g

1000 ml = 1.429 g

1 ml = 1.429 *140^-3 g

Now calcualte the number of moles in 1.429 *140^-3 g

1.429 *140^-3 g /32 g/mol = 4.46 *10^-5 mol

This can be produced by 8.92 *10^5 mol HgO

Which can be converted into g as follows:

216.59 g·mol⁻¹ * 8.92 *10^5 mol HgO

= 0.02 g

ln ([A]t / [Ao]) = -kt .

ln ([0.02 / [1.0]) = - 6.02 x 10-4 sec-1 *t

t= 6498.4 s

108.3 min or 1.8 hr