Question

Sulfuryl chloride undergoes first-order decomposition at 320.ºC with a half-life of 8.75 h (k = 2.20 × 10^-5 s^-1).

SO₂Cl₂(g) → SO₂(g) + Cl₂(g)

If the initial pressure of SO₂Cl₂ is 786 torr and the decomposition occurs in a 1.25-L container, how many molecules of SO₂Cl₂ remain after 11.8 h?

Answer 1

K = 2.20 * 10^-5 s-1

looking at the value of the rate constant it is first-order reaction

11.8 hr = 42480 sec

initial pressure = 786 torr

ln(initial pressure / final pressure) = rate constant * time ( in sec)

= ln (786 / final pressure) = 42480 * 2.20 * 10^-5

final pressure = 308.71 torr or 0.4062 atm

moles of SO2Cl2 = Pressure * volume ( in L) / R * temperature

= 0.4062 * 1.25 / 0.082 * 593.15 (320 in Kelvin)

= 0.01044

molecules = avagadro number * moles

= 6.022*10^23 * 0.01044

= 6.287*10^21

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