Physical Chemistry- Rates and Kinetics

[chanderjeet]

Homework Statement

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?

Homework Equations

Rate = k [NO]² [Cl2]

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

Am I going about this the right way or this completely wrong?

 

[Borek]

Close, but no cigar yet.

How much NO was consumed together with the chlorine?

 

[Yanick]

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

 

[chanderjeet]

Close, but no cigar yet.

How much NO was consumed together with the chlorine?

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

 

[Borek]

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

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

 

[chanderjeet]

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

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

 

[Borek]

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.

 

[chanderjeet]

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.

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?

 

[Borek]

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.