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# The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume.

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The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume.

SO2Cl2(g) → SO2(g) + Cl2(g)

Experiment   -  Time/s-1   -  Total pressure/atm

1             -          0         -   0.5

2             -         100      -    0.6

Calculate the rate of the reaction when total pressure is 0.65 atm.

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The thermal decomposition of SO2Cl2 at a constant volume is represented by the following equation.

SO2Cl2(g) → SO2(g) + Cl2(g)

At t = 0  P0              0             0

At t = t   P0 - p         p             p

After time, t, total pressure,

Pt = (P0 - p) + p + p

⇒ Pt = P0+ p

⇒ p = Pt - P0

Therefore, P0 - p = P0 -(Pt - P0)

= 2Pt - P0

For a first order reaction,

k = $$\frac{2.303}{t}$$log $$\frac{P_0}{P_0 - p}$$

= $$\frac{2.303}{t}$$log $$\frac{P_0}{2P_0 - P_t}$$

When t = 100 s

k = $$\frac{2.303}{100 \ s}$$log $$\frac{0.5}{2 \times 0.5 - 0.6}$$

= 2.231 × 10-3 s-1

When Pt = 0.65 atm,

P0 + p = 0.65

⇒ p = 0.65 - P0

= 0.65 - 0.5

= 0.15 atm

Therefore, when the total pressure is 0.65 atm, pressure of SO2Cl2 is

PSOCl2 = P0 - p

= 0.5 - 0.15

= 0.35 atm

Therefore, the rate of equation, when total pressure is 0.65 atm, is given by,

Rate = k(PSOCl2)

= (2.23 × 10-3 s-1) (0.35 atm)

= 7.8 × 10-4 atm s-1

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