Determine the rate constant for the hydrolysis of alpha-phenylethyl chloride in

Question

Determine the rate constant for the hydrolysis of alpha-phenylethyl chloride in 50% ethanol using the data provided. Also show the R^2 value. Report the rate constant k for this reaction in sec-1.

Could you please show the steps?

Thank you

Time (min:sec) Time (sec) Vol. NaOH /mL Vol. NaOH Used / mL V infinity -Vt (V infinity)/(V infinity - Vt) ln[(Vinfinity)/(Vinfinity-Vt) 0:00 0.20 0.00 6.90 1.00 0.000 8:27 507 2.20 2.00 4.90 1.41 0.343 18:15 1095 4.20 4.00 2.90 2.37 0.863 31:48 1908 5.90 5.70 1.20 5.75 1.750 47:43 2863 6.80 6.60 0.30 23.00 3.136 (infinity) 7.10 6.90 0.00 -- --

Explanation / Answer

In general, the equation for this is the following:

A = Ao e-kt

Where A = Final Concentration

Ao = innitial Concentration

k = rate constant

t = time (s)

In this case, you are not providing the concentrations. Instead you are providing the volume of base used and for infinity. So we are going to use this values to determine the constant.

V = Vo e-kt

lnV = lnVo - kt

lnV - lnVo = -kt

and lnV - lnVo = ln(V/Vo) = -kt

Now, with this expression, you can do a grah with the data provided. You can do it either with a calculator or excel. I'll put all the data in a calculator and these are the values I got:

r2 = 0.9817

B = k = 1.0969x10-3 s-1

Now if you want to obtain by yourself you may use the next expression:

k = Y2 - Y1/ x2 - x1

k = 1.750 - 0.863/1908 - 1095 = 1.09x10-3 s

There are only a few differences in the decimals. If you need more explanation or something you need to fix or a detail in specific, tell me and I'll gladly explain all what you want.

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