how do you solve this?
The candy indistry converts sucrose (C11H22O11,table sugar),a crystalline material, to invert sugar, a hydrolzyed [rpdict tjat os 50:50 frutose and glucose. The hydrolysis occurs in water, quite slowly, at an elevated temperature of 55¨¬C. The reaction is
C11H22O11 + H2)¡æC6H12O6(frutose)+C6H12O6(glucose)
from the following time course data, determine the ORDER of reaction.
Time/min [C11H22O11M]
0 0.50
60 0.40
137.4 0.30
180 0.26
274.8 0.18
300 0.16
I think the answer is 1st order
To determine the order of the reaction, we need to analyze the time course data. The order of the reaction can be determined by examining the concentration changes of the reactant (C11H22O11) over time.
First, let's calculate the concentration change of C11H22O11:
∆[C11H22O11] = [C11H22O11]final - [C11H22O11]initial
For each time interval, the concentration change is:
∆[C11H22O11]60 = 0.40 - 0.50 = -0.10
∆[C11H22O11]137.4 = 0.30 - 0.40 = -0.10
∆[C11H22O11]180 = 0.26 - 0.30 = -0.04
∆[C11H22O11]274.8 = 0.18 - 0.26 = -0.08
∆[C11H22O11]300 = 0.16 - 0.18 = -0.02
Next, let's calculate the ratio of concentration changes between different time intervals:
∆[C11H22O11]60 / ∆[C11H22O11]137.4 = -0.10 / -0.10 = 1
∆[C11H22O11]137.4 / ∆[C11H22O11]180 = -0.10 / -0.04 ≈ 2.5
∆[C11H22O11]180 / ∆[C11H22O11]274.8 = -0.04 / -0.08 = 0.5
∆[C11H22O11]274.8 / ∆[C11H22O11]300 = -0.08 / -0.02 = 4
If the reaction is first-order, the ratio of concentration changes should be constant. However, in this case, the ratio is not constant. Thus, the reaction is not first order.
To further analyze the data, let's plot the natural logarithm of the concentration changes (∆[C11H22O11]) as a function of time:
ln(∆[C11H22O11])60 = ln(-0.10) = undefined (negative value)
ln(∆[C11H22O11])137.4 = ln(-0.10) = undefined (negative value)
ln(∆[C11H22O11])180 = ln(-0.04) = undefined (negative value)
ln(∆[C11H22O11])274.8 = ln(-0.08) = undefined (negative value)
ln(∆[C11H22O11])300 = ln(-0.02) = undefined (negative value)
As seen from the calculations, we encounter undefined values when taking the natural logarithm of negative concentration changes. This suggests that the reaction may not follow a simple order and cannot be determined solely from the given data.
In conclusion, based on the data provided, it is not possible to determine the order of the reaction.