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3 years ago

Iodine-131 half life 8.040 how long will it take for a 40 gram sample of iodine-131 to decay to 0.75 grams

Chemistry

1 answer:

otez555 [7]3 years ago

3 0

Answer:

See explanation below

Explanation:

To get this, we need to apply the general expression for half life decay:

N = N₀e(-λt) (1)

Where:

N and N₀ would be the final and innitial quantities, in this case, masses.

t: time required to decay

λ: factor related to half life

From the above expression we need λ and t. To get λ we use the following expression:

λ = t₁₂/ln2 (2)

And we have the value of half life, so, replacing we have:

λ = 8.04 / ln2 = 11.6

Now, we can replace in (1) and then, solve for t:

0.75 = 40 exp(-11.6t)

0.75 / 40 = exp(-11.6t)

ln(0.01875) = -11.6t

-3.9766 = -11.6t

t = -3.9766 / -11.6

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By the stoichiometry of the reaction:

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$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Moles of calcium carbonate = $2.37\times 10^{-4}mol$

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Putting values in the above equation:

$\text{Mass of }CaCO_3=(2.37\times 10^{-4}mol)\times 100.01g/mol\\\\\text{Mass of }CaCO_3=0.0237g$

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