Chemistry, 20.02.2020 22:22, skinniestoflegends

Strotium−90, a radioactive isotope, is a major product of an atomic bomb explosion. It has a half-life of 28.1 yr. (a) Calculate the first-order rate constant for the nuclear decay. (b) Calculate the fraction of 90Sr that remains after 10 half-lives. (c) Calculate the number of years required for 95.7 percent of 90Sr to disappear.

Answers: 3

Show answers

Answers

answered: FlayMaster101

Answer :

(a) The first-order rate constant for the nuclear decay is, $0.0247\text{ years}^{-1}$

(b) The fraction of 90-Sr that remains after 10 half-lives is, $\frac{a_o}{1024}$

Explanation :

Part (a) :

Half-life = 28.1 years

First we have to calculate the rate constant, we use the formula :

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{28.1\text{ years}}$

$k=0.0247\text{ years}^{-1}$

Thus, the first-order rate constant for the nuclear decay is, $0.0247\text{ years}^{-1}$

Part (b) :

Now we have to calculate the fraction of 90-Sr that remains after 10 half-lives.

Formula used :

$a=\frac{a_o}{2^n}$

where,

a = amount of reactant left after n-half lives

a_o = Initial amount of the reactant

n = number of half lives = 10

Now put all the given values in the above formula, we get:

$a=\frac{a_o}{2^{10}}$

$a=\frac{a_o}{1024}$

Thus, the fraction of 90-Sr that remains after 10 half-lives is, $\frac{a_o}{1024}$

Part (c) :

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant = $0.0247\text{ years}^{-1}$

t = time passed by the sample = ?

a = let initial amount of the reactant = 100

a - x = amount left after decay process = 100 - 95.7 = 4.3

Now put all the given values in above equation, we get

$t=\frac{2.303}{0.0247}\log\frac{100}{4.3}$

$t=127.4\text{ years}$

Therefore, the time passed in years is, 127.4 years.

answered: Guest

Note that 2 mol dm⁻³ = 2 mol/(dm³)outline: we're given the concentration of hcl, which is 2 mol dm⁻³ (cubic meters in the denominator can represent volume, so i know this is concentration). we're an amount of calcium carbonate caco₃, which is 5 g. we're presented with a chemical equation which includes caco₃ and hcl. we are told to find the volume of hcl. from what we see so far, this seems to be a stoichiometry problem. we'll have to use the given information about calcium carbonate to find the amount of moles of hcl needed to fully react with calcium carbonate. then we'll have information about the moles of hcl and the concentration of hcl; that will be enough to figure out volume according to the formula concentration = moles / volume.======all the answer choices are not in dm.convert the given concentration so that it uses cm⁻³.we can use conversion factors. we have to cube our conversion factors so that dimensional analysis works.we can convert to meters first, using the fact that 10 dm = 1 m ⇔ 10³ dm³ = 1 m³then we use the fact that 10² cm = 1 m ⇔ (10² cm)³ = (1 m)³ ⇔ 10⁶ cm³ = 1 m³so converting: $\dfrac{\text{2 mol}}{\text{dm}^{3}} \cdot \dfrac{\text{10}^3\text{ dm}^3}{\text{1 m}^3} \cdot \dfrac{\text{1 m}^3}{10^6\text{ cm}^3} \\ \\ = \dfrac{\text{2 mol}}{1} \cdot \dfrac{\text{10}^3}{1} \cdot \dfrac{1}{10^6\text{ cm}^3} \qquad \text{\footnotesize cancelling units} \\ \\ = \dfrac{2\text{ mol}}{10^3 \text{ cm}^3} \\ \\ = 0.002\text{ mol/cm}^3$ now we have to find the moles of hydrochloric acid neededfind the moles of calcium carbonate. we have to find the molar mass of calcium carbonate, caco₃, which can be found by molar mass = (mass ca) + (mass c) + 3(mass o) = 40 + 12 + 3(16) = 100 g/molconvert the given 5 g to moles: mol caco₃ = 5 g caco₃ * 1 mol/(100 g) = 0.05 mol caco₃use stoichiometry (ratios) to figure out the moles of hcl needed. ratio wise, there's 2 hcls for every caco₃, so use dimensional analysis mol hcl = mol caco₃ * (2 mol hcl) / (1 mol caco₃) = 0.05 mol hcl * 2 = 0.1 mol hcl we have 0.1 mol hcl and concentration of hcl (0.002 mol/cm³).we need to find volumesince concentration = moles / volume, rearrange to get volume = moles / concentration volume = 0.1 mol / (0.002 mol/cm³) volume = 50 cm³

answered: Guest

Answer//the law of conservation of mass.;