Question

Determine the order of the reaction,

\[\ce{C12H22O11 + H2O ->[H+] C6H12O6 + C6H12O6}\],

from the following data:

Time (in minutes)	0	30	90	230	∞
Polarimeter reading (in degree)	+46.75	+41.0	+30.75	+12.75	−18.75

Also calculate the rate constant of the reaction.

Answer 1

If the given reaction is of first order, it must satisfy the following equation:

k = `2.303/t log_10  a/(a - x)`

= `2.303/t log_10  (r_0 - r_infty)/(r_t - r_infty)`

In the present case, r₀ = +46.75° and r_∞ = −18.75°

∴ r₀ − r_∞ = 46.75 − (−18.75)

= 65.5°

The values of k at different instants can be calculated as given below.

Time (min)	rt	rt − r∞	`bb(k = 2.303/t log_10  (r_0 - r_infty)/(r_t - r_infty))`
30	+41.0	41.0 − (−18.75) = 59.75	k = `2.303/30 log_10  65.5/59.45` = 3.06 × 10−3 min−1
90	+30.75	30.75 − (−18.75) = 49.5	k = `2.303/90 log_10  65.5/49.45` = 3.11 × 10−3 min−1
230	+12.75	12.75 − (−18.75) = 31.5	k = `2.303/230 log_10  65.5/31.5` = 3.18 × 10−3 min−1

The provided reaction is of first order since the values of k determined using the first order rate equation at various time periods are nearly identical.

The average value of k = `(3.06 xc 10^-3 + 3.11 xx 10^-3 + 3.18 xx 10^-3)/3`

= 3.12 × 10⁻³ min⁻¹