Question

Determine the initial concentration of Al in experiment #4. Include your units. 4 Al(g) + 3 O2(g) ⟶ 2 Al2O3(g)

Experiment #	[O2]i, M	[Al]i, M	Initial Rate of Reaction, M/sec
1	0.10	0.20	4.80 x 10-3
2	0.30	0.20	4.35 x 10-2
3	0.30	0.40	8.70 x 10-2
4	0.20	?	1.95 x 10-2
5	0.15	0.30

Answer 1

4Al + 3O₂ = 2Al₂O₃

Rate, R = k [ Al]^a[O₂]^b......where, k = rate constant, a= order with respect to Al, b = order with respect to O₂

From experiment 1,

0.0048 = k [ 0.20]^a[0.10]^b                             eqn 1

From experiment 2,

0.0435 = k [ 0.20]^a[0.30]^b                             eqn 2

From experiment 3,

0.0870 = k [ 0.40]^a[0.30]^b                             eqn 3

(eqn 2) / (eqn 1) gives: 9.0625 = 3^b or, b=2

(eqn 3) / (eqn 2) gives: 2 = 2^a or, a=1

So, R = k [ Al][O₂]²

Let, unknown concentration of Al = x

From experiment 4,

0.0195 = k [ x]^a[0.2]^b                       eqn 4

(eqn 2) / (eqn 4) gives:

2.2307 = (0.2/x)^a (0.3/0.2)^b = (0.2/x) (0.3/0.2)^b

or, x = 0.20 M

Ans: Initial concentration of Al in experiment 4 : 0.20 M