Sucrose hydrolyzes into glucose and fructose. The hydrolysis is a first order reaction. the half life for the hydrolysis of sucrose is 64.2min at 25C. How many grams fo sucrose in 1.25L of a 0.389M solution are hydrolyzed in 1.73hrs?

I started off by finding k the constant
t1/2=0.693/k
64.2min=0.693/k
k=0.01079

I'm not sure what to do after this
I converted the 64.2min into hrs and got k as 0.6477

ln166.44-lnx=0.64766*1.73

-lnx=1.120-ln166.44
lnx=3.9942
x=E^3.9942
=54.27
166.54-54.27=112g

Since you want the answer in hours I would use the k in the hour units.

How many grams do you have in the solution? 1.25L x 0.389 moles/L x 342.3 grams/mole = ?? (about 166 but that is approximate).
ln(No/N) = kt
I would substitute 166 (or the actual number you obtain) for No, solve for N, and substitute 1.73 for t and the k you have in hr^-1. Solve for N which will be the grams REMAINING after 1.73 hours. That subtracted from the number of grams initially should be the amount decomposed.

That looks good to me.

merry christmas guys I love everyone on this site, all the staff, the students everything about this site just makes it more humble and unique

To calculate the amount of sucrose hydrolyzed in the given time period, you need to use the first-order reaction rate expression:

ln[A] = -kt + ln[A₀]

Where:
ln[A] is the natural logarithm of the concentration of sucrose at a given time (in mol/L),
[A₀] is the initial concentration of sucrose (in mol/L),
k is the rate constant of the reaction,
t is the time (in seconds).

Given:
Initial concentration of sucrose ([A₀]) = 0.389 M
Volume (V) = 1.25 L
Time (t) = 1.73 hrs = 1.73 x 60 x 60 seconds

First, convert the time from hours to seconds:
1.73 hrs x 60 min/hr x 60 s/min = 6228 seconds

Calculate the amount of sucrose hydrolyzed by substituting the values into the equation:

ln[A] = -k(6228) + ln[0.389]

Now, you need to solve for [A] (the concentration of sucrose at the end of the given time period).

But, since you're looking for the amount of sucrose hydrolyzed, you can subtract [A] from [A₀]:

[A₀] - [A] = ∆[A]

∆[A] will give you the change in concentration of sucrose.

Next, calculate [A₀] - ∆[A] to find the final concentration of sucrose:

[A₀] - ∆[A] = [A₂]

Now, multiply [A₂] by the volume (V) to get the final number of moles of sucrose:

[A₂] x V = moles of sucrose

Finally, convert moles to grams by multiplying by the molar mass of sucrose (342.3 g/mol):

moles of sucrose x molar mass of sucrose = grams of sucrose hydrolyzed

By following these steps, you should be able to find the answer to your question.