I need help writing a rate law

Question

(H₂O₂) decomposes into water and oxygen gas in the presence of light. [H₂O₂] was monitored in the data shown in the graph. What is the rate law for the decomposition of hydrogen peroxide?

Answer 1

For a 1st order chemical reaction

ln[A]=kt +C, t is the time, k is the rate constant, C Equation has for of y=mx+b

to find the equation of the line use the data point (0, -1.5) and (20, -3.25)

slope=(-3.25 +1.5)/(20-0) or -0.0875

Find the equation of the line using the point-slope formula and the coordinate pair (0, -1.5):

ln[A] -(-1.5)=-.0.075(t-0)

here is the equation of the line

ln[A]=-0.0875t - 1.5

Find the equation for [A] by the following method

e^(ln[A])=e^{(-0.0875t -1.5)}

[A]=0.223e^-0.0875t

Answer 2

The graph says that ln[H2O2] = -kt -1.5 (y = mx + y₀) here 1.5 is ln[H2O2]₀

or ln([H2O2]/ln[H2O2]₀ = -kt taking both sides to the e power [H2O2]/[H2O2] = e^-kt which is the

integrated rate law for a first order reaction. r_H2O2 = -k[H2O2] . This leads to exponential decay of the reactant concentration.

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