The nuclide as-76 has a half-life of 26.0 hours. if a sample of as-76 weighs 344 g, what mass of as-76 remains after 538 minutes? a) 67.8 g b) 271 g c) 144 g d) 437 g e) 251 g 26.

B) 271 g.

Explanation:

It is known that the decay of a radioactive isotope isotope obeys first order kinetics.Half-life time is the time needed for the reactants to be in its half concentration.If reactant has initial concentration [A₀], after half-life time its concentration will be ([A₀]/2).Also, it is clear that in first order decay the half-life time is independent of the initial concentration.The half-life of As-76 = 26.0 hours.For, first order reactions:

k = ln(2)/(t1/2) = 0.693/(t1/2).

Where, k is the rate constant of the reaction.

t1/2 is the half-life of the reaction.

∴ k =0.693/(t1/2) = 0.693/(26.0 hours) = 0.02665 hour⁻¹.

Also, we have the integral law of first order reaction:

kt = ln([A₀]/[A]),

where, k is the rate constant of the reaction (k = 0.02665 hour⁻¹).

t is the time of the reaction (t = 538 min = 8.97 hour).

[A₀] is the initial concentration of (As-76) ([A₀] = 344 g).

[A] is the remaining concentration of (As-76) ([A] = ??? g).

∴ (0.02665 hour⁻¹)(8.97 hour) = ln((344 g)/[A])

∴ 0.239 = ln((344 g)/[A]).

Taking exponential for both sides:

∴ 1.27 = ((344 g)/[A]).

∴ [A] = (344 g)/(1.27) = 270.88 g ≅ 271 g.

So, the right choice is: B) 271 g.

False, as a substance changes from a solid to a liquid and from a liquid to a gas the molecules get farther apart from each other

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