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gavmur [86]
3 years ago
14

The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.

3 hours. If 1 gram of this isotope is present initially, how long will it take for 80% of the lead to decay
Chemistry
1 answer:
Marina86 [1]3 years ago
3 0

Answer:

Therefore it will take 7.66 hours for 80% of the lead decay.

Explanation:

The differential equation for decay is

\frac{dA}{dt}= kA

\Rightarrow \frac{dA}{A}=kdt

Integrating both sides

ln A= kt+c₁

\Rightarrow A= e^{kt+c_1}

\Rightarrow A=Ce^{kt}         [e^{c_1}=C]

The initial condition is A(0)= A₀,

\therefore A_0=Ce^{0.k}

\Rightarrow C=A_0

\therefore A=A_0e^{kt}.........(1)

Given that the Pb_{209}  has half life of 3.3 hours.

For half life A=\frac12 A_0 putting this in equation (1)

\frac12A_0=A_0e^{k\times3.3}

\Rightarrow ln(\frac12)= 3.3k     [taking ln both sides, ln \ e^a=a]

\Rightarrow k=\frac{ln \frac12}{3.3}

⇒k= - 0.21

Now A₀= 1 gram, 80%=0.8

and A= (1-0.8)A₀ = (0.2×1) gram = 0.2 gram

Now putting the value of k,A and A₀in the equation (1)

\therefore 0.2=1e^{(-0.21)\times t}

\Rightarrow e^{-0.21t}=0.2

\Rightarrow -0.21t= ln(0. 2)

\Rightarrow t= \frac{ln (0.2)}{-0.21}

⇒ t≈7.66

Therefore it will take 7.66 hours for 80% of the lead decay.

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Explanation:

solution has a pH of 2 is a strong acid.

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I need help with my homework.Calculate the number of formula units in: 41.5 grams CaBr2
lana66690 [7]

Answer:

\text{ }1.25\times10^{23}\text{ formula units}

Explanation:

Here, we want to calculate the number of formula units in the given molecule

We start by getting the number of moles

To get the number of moles, we have to divide the mass given by the molar mass

The molar mass is the mass per mole

The molar mass of calcium bromide is 200 g/mol

Thus, we have the number of moles as follows:

\frac{41.5}{200}\text{ = 0.2075 mol}

The number of formula units in a mole is:

1\text{ mole = 6.02 }\times10^{22}\text{ formula units}

The number of formula units in 0.2075 mole will be:

0.2075\text{ }\times6.02\times10^{23}\text{ = }1.25\times10^{23}\text{ formula units}

5 0
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Can someone plz help me? :(
Sveta_85 [38]

Answer:

it's C

Explanation:

because it exhaled the carbon dioxide

8 0
2 years ago
When 15.3 g of sodium nitrate, NaNO3,was dissolved in water in a calorimeter, the temperature fell from 25.00oC to 21.56oC. If t
satela [25.4K]

Answer:

20.468 kilo Joules is the enthalpy change when one mole of sodium nitrate dissolves.

Explanation:

Heat lost by solution ad calorimeter = Q

Heat capacity of solution ad calorimeter = C = 1071 J/°C

Change in temperature = ΔT = 21.56°C - 25.00°C = -3.44°C

Q=C\times Delta T

Q=1071 J/^oC\times (-3.44^oC)=-3,684.24 J

Heat gained by sodium nitrate = -Q = -(-3,684.24 J)=3,684.24 J

Moles of sodium nitrate = \frac{15.3 g}{85 g/mol}=0.18 mol

When 0.18 mole of sodium nitrate was dissolved in water 3,684.24 joulesof heat was absorbed by it.

Then heat absorbed by 1 mole of sodium nitrate :

\frac{3,684.24 J}{0.18}=20,468 J=20.468 kJ

1 J = 0.001 kJ

20.468 kilo Joules is the enthalpy change when one mole of sodium nitrate dissolves.

8 0
3 years ago
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