Respuesta :
Answer : The rate of change of the total pressure of the vessel is, 10.5 torr/min.
Explanation : Given,
[tex]\frac{d[NO]}{dt}[/tex] =21 torr/min
The balanced chemical reaction is,
[tex]2NO(g)+Cl_2(g)\rightarrow 2NOCl(g)[/tex]
The rate of disappearance of [tex]NO[/tex] = [tex]-\frac{1}{2}\frac{d[NO]}{dt}[/tex]
The rate of disappearance of [tex]Cl_2[/tex] = [tex]-\frac{d[Cl_2]}{dt}[/tex]
The rate of formation of [tex]NOCl[/tex] = [tex]\frac{1}{2}\frac{d[NOCl]}{dt}[/tex]
As we know that,
[tex]\frac{d[NO]}{dt}[/tex] =21 torr/min
So,
[tex]-\frac{d[Cl_2]}{dt}=-\frac{1}{2}\frac{d[NO]}{dt}[/tex]
[tex]\frac{d[Cl_2]}{dt}=\frac{1}{2}\times 21torr/min=10.5torr/min[/tex]
And,
[tex]\frac{1}{2}\frac{d[NOCl]}{dt}=\frac{1}{2}\frac{d[NO]}[/tex]
[tex]\frac{d[NOCl]}{dt}=\frac{d[NO]}=21torr/min[/tex]
Now we have to calculate the rate change.
Rate change = Reactant rate - Product rate
Rate change = (21 + 10.5) - 21 = 10.5 torr/min
Therefore, the rate of change of the total pressure of the vessel is, 10.5 torr/min.
The rate of change of the total pressure of the vessel is 10.5 torr/min
The given reaction is expressed as:
[tex]\mathbf {2O_{(g)} + Cl_{2(g)} \to 2NOCl_{(g)}}}[/tex]
From chemical kinetics, the average rate (r) can be expressed as:
[tex]\mathbf{r = -\dfrac{1}{2}\dfrac{d[NO]}{dt}= -\dfrac{d[Cl_2]}{dt}=\dfrac{1}{2}\dfrac{d[NOCl]}{dt} }[/tex]
where;
- the negative sign (-) indicates the rate of disappearance of the substances.
∴
- rate of disappearance of NO [tex]\mathbf{= -\dfrac{1}{2} \dfrac{d[NO]}{dt}}[/tex]
- rate of disappearance of Cl₂ = [tex]\mathbf{\dfrac{-d[Cl_2]}{dt}}[/tex]
- rate of appearance of NOCl = [tex]\mathbf{\dfrac{1}{2} \dfrac{d[NOCl]}{dt}}[/tex]
We are being told that the partial pressure of NO is decreasing at 21 torr/min
i.e.
- [tex]\mathbf{\dfrac{d[NO]}{dt}}[/tex] = 21 torr/min
and we know that:
[tex]\mathbf{\dfrac{-d[Cl_2]}{dt}= -\dfrac{1}{2} \dfrac{d[NO]}{dt}}}[/tex]
∴
- [tex]\mathbf{\dfrac{-d[Cl_2]}{dt}= -\dfrac{1}{2}(21 \ torr/min) }}[/tex]
- [tex]\mathbf{\dfrac{d[Cl_2]}{dt}= 10.5 \ torr/min }}[/tex]
Similarly;
- [tex]\mathbf{-\dfrac{1}{2} \dfrac{d[NOCl]}{dt} = \mathbf{-\dfrac{1}{2} \dfrac{d[NO]}{dt}}}[/tex]
- [tex]\mathbf{\dfrac{d[NOCl]}{dt} = \mathbf{ \dfrac{d[NO]}{dt}}}[/tex]
- [tex]\mathbf{\dfrac{d[NOCl]}{dt} =21 \ torr/min}}[/tex]
Now, we need to determine the rate of change of the total pressure at which these substances are decreasing;
Rate change = rate of reactant - rate of product.
[tex]\mathbf{Rate \ change =} \mathbf{\mathbf{ \dfrac{d[NO]}{dt}} +\dfrac{d[Cl_2]}{dt} - \dfrac{d[NOCl]}{dt} }[/tex]
[tex]\mathbf{Rate \ change =} \mathbf{(21 \ torr/min) +(10.5 \ torr/min) -( 21 \ torr/min})[/tex]
Rate change = 10.5 torr/min
Learn more about chemical kinetics here:
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