Physical Chemistry- Rates and Kinetics

1. Dec 4, 2013

chanderjeet

1. The problem statement, all variables and given/known data

The Reaction; 2NO(g) + Cl2 (g) → 2NOCl (g)

Is second order in NO and first order in Cl2. Five moles of nitric oxide and two moles of Cl2 were brought together in a volume of 2dm3 and initial rate was 2.4x10-3 moldm-3sec-1. What will be the rate when one half of the chlorine has reacted?

2. Relevant equations

Rate = k [NO]2 [Cl2]

3. The attempt at a solution

Initial Rate= 2.4x10-3 moldm-3sec-1

2.4x10-3 = k [NO]2 [Cl2]

5mols of NO in 2dm3
= 5mols in 2L
∴ 1L contains 2.5mols
[NO] = 2.5M

2mols of Cl2 in 2dm3
= 2mols in 2L
∴ 1L contains 1mol
[Cl2] = 1M

2.4x10-3 = k (2.5)2 (1)
k = 2.4x10-3/6.25
= 0.000384

When half of the chorine is used (1mol), molarity = 0.5M

∴ Rate = (0.000384) (2.5)2 (0.5)
Rate = 0.0012moldm-3sec-1

2. Dec 4, 2013

Staff: Mentor

Close, but no cigar yet.

How much NO was consumed together with the chlorine?

3. Dec 4, 2013

Yanick

Wait, sorry I read the question wrong. Don't mind me, listen to Borek.

4. Dec 4, 2013

chanderjeet

So does that mean that since half the Cl2 (0.5mols) is used then half the NO is used (2.5mols)?

[NO] 2.5mols in 2dm3
2.5mols in 2L
∴ 1L = 1.25mols
[NO] = 1.25M

Rate = (0.000384) (1.25)2 (0.5)
= 0.0003moldm-3sec-1

5. Dec 5, 2013

Staff: Mentor

No, it is not about "half". It is a trivial stoichiometry.

6. Dec 5, 2013

chanderjeet

From the balanced equation, a 2: 1 mol ratio is noted between NO and Cl2

So if one mol of Cl2 is used up then 2 mols NO would be used up

[NO] = 1M
[Cl2] = 0.5M

Rate= (0.000384) (1)2 (0.5)
= 0.000192moldm-3s-1

7. Dec 5, 2013

Staff: Mentor

No.

Please pay attention to what you are doing, you have made a second careless mistake. You were right up to 2 moles of NO being consumed.

8. Dec 5, 2013

chanderjeet

I thought the volume was given so that the concentration can calculated an utilized in the rate expression. Am I not supposed to calculate the concentration based on the mols being consumed?

9. Dec 5, 2013

Staff: Mentor

Using your logic once all chlorine is consumed, and there is no more chlorine present, its concentration is 1 M, as 2 moles were consumed. So all was consumed, but the concentration has the maximum value. Something doesn't sound right.