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Sagot :
Use integrated first order rate law, which give you the concentration of reactant sulfuryl chloride as function of time t:
ln[SO₂Cl₂] = ln[SO₂Cl₂]₀ - k∙t
([SO₂Cl₂]₀ i the initial concentration and k is the rate constant)
=> [SO₂Cl₂] = e^(ln[SO₂Cl₂]₀ - k∙t) = e^(ln[SO₂Cl₂]₀) ∙ e^( - k∙t)
= [SO₂Cl₂]₀ ∙e^( - k∙t)
The decomposition of SO₂Cl₂ follows the reaction equation
SO₂Cl₂ → SO₂ + Cl₂
So per mole of sulfuryl chloride disappeared one mole of sulfur dioxide is formed. Hence the changes in concentrations of these compounds are related as:
-∆[SO₂Cl₂] = ∆{SO₂] <=> [SO₂Cl₂]₀ - [SO₂Cl₂] = [SO₂] - [SO₂]₀
Assuming there was initially no sulfur dioxide you get for its concentration:
[SO₂] = [SO₂Cl₂]₀ - [SO₂Cl₂]
= [SO₂Cl₂]₀ - [SO₂Cl₂]₀ ∙e^( - k∙t)
= [SO₂Cl₂]₀ ∙(1 - e^( - k∙t))
after 210s starting with 0.150M of [SO₂Cl₂]
[SO₂]= 0.150M ∙(1 - e^( - 1.48×10⁻⁴s⁻¹k ∙ 240s) =
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