[zaleron]

I have done an experiment on the hydrolysis of Aspirin, which is pseudo-first order. I need to find the rate constant, but I only have the final(0.0278 M) and initial (0 M) product (Salicylic Acid) concentrations in 0.06 L solution, the change in time (24 hours), and the temperature (25 degrees celsius). Is there a way to find the rate constant of this reaction?

[zaleron]

My main problem is that I do not have either initial or final reactant concentrations to calculate the k value through an integrated rate law or by plugging in values into the pseudo first order rate law.

[Plontaj]

So, if you are sure that it is first order as regards to Salicylic Acid, it is possible.

SA - Salicylic Acid
P - product of hydrolysis

If stoichiometric is simple as below:
SA -> P

C_SA(final) = C_SA(t=0) - C_P(final)

the rate law:
-d(C_SA)/d(t)=+d(C_P)/d(t)=k*C_SA

Now, you have to integrate it and put your data to obtained expression, only k is unknown.
BTW: it isn't good practice, you should try to get a kinetic curve (function of concentration in time) and try to fit the best value k to get the minimal sum of squared error (for example).