How to determine K in the rate law by choosing one of the experiment from the da

Question

How to determine K in the rate law by choosing one of the experiment from the data table above and calculate k. Do this for two other experiment and then average the three valuse of k. Round to two significant figures.

Data and Calculations Exp # [HCI]Mass of Mg [Mg] mol/0.050 time (sec)rate A[Mg/At 1.01M -1.01M 1.01M 4 ~0.51M -1.01M -1.52M -2.02M 0.0329 g 0.0686 +0.0812 M 0.0987 g 0.0497 g0.0409 M 0.0497 g0.0409 M 66.4 s 63.9 s 65.1 s 335 s 65.2 s 30.5 s 14.8 s 1.18×10-2 -2.06×10-2 4.17×10-2 5.17×10-5 1.12 ×10-2 3.87×10-4 2.70 × 10-4 0.0270 M 0.0564 M 4 0.0497 g 0.0497 g0.0409 M 0.0409 M First exp Mg mole = 0.0329 L Second exp Mg mole = .2421÷ Mg mole-2 0.0329 ÷ 0.050 24.31 ÷ 0.0270 M le = 0.0686 0.050 0.0564 M )

Explanation / Answer

Dissolution of Mg in HCl follows first order kinetics, whose rate law -d[Mg]/dt = r = k[Mg]

(not sure the [Mg] given in table is the concentration of Mg measured after the given time, but it is assumed to be so)

k = r/[Mg] = 1.18x10-2/0.0270 = 0.437 s-1

Exp.3: k = 0.0417/0.0812 = 0.514 s-1

Exp 5: k = 0.0112/0.0409 = 0.274 s-1

Average k = 0.41 s-1

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