1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Brrunno [24]
3 years ago
8

The half-life for the radioactive decay of C-14 is 5730 years and is independent of the initial concentration. How long does it

take for 25% of the C-14 atoms in a sample of the C-14 to decay
Chemistry
1 answer:
DedPeter [7]3 years ago
3 0

Answer:

It will take 2378 years for 25% of the C-14 atoms in a sample of the C-14 to decay.

Explanation:

Radioactive decays/reactions always follow a first order reaction dynamic.

Let the initial amount of C-14 atoms be A₀ and the amount of atoms at any time be A

The general expression for rate of reaction for a first order reaction is

(dA/dt) = -kA (Minus sign because it's a rate of reduction)

k = rate constant

(dA/dt) = -kA

(dA/A) = -kdt

 ∫ (dA/A) = -k ∫ dt 

Solving the two sides as definite integrals by integrating the left hand side from A₀ to A and the right hand side from 0 to t.

We get

In (A/A₀) = -kt

(A/A₀) = e⁻ᵏᵗ

A(t) = A₀ e⁻ᵏᵗ

Although, we can obtain k from the information on half life.

For a first order reaction, the rate constant (k) and the half life (T(1/2)) are related thus

T(1/2) = (In2)/k

T(1/2) = 5730 years

k = (In 2)/5730 = 0.000120968 = 0.000121 /year.

So, the amount of C-14 atoms left at any time is given as

A(t) = A₀ e⁻⁰•⁰⁰⁰¹²¹ᵗ

How long does it take for 25% of the C-14 atoms in a sample of the C-14 to decay?

When 25% of C-14 atoms in a sample decay, 75% of C-14 atoms in the sample remain.

Hence,

A(t) = 75%

A₀ = 100%

100 = 75 e⁻⁰•⁰⁰⁰¹²¹ᵗ

e⁻⁰•⁰⁰⁰¹²¹ᵗ = (75/100) = 0.75

In e⁻⁰•⁰⁰⁰¹²¹ᵗ = In 0.75 = - 0.28768

-0.000121t = -0.28768

t = (0.28768/0.000121) = 2,377.54 = 2378 years

Hope this Helps!!!

You might be interested in
Kc for the reaction N2O4 <=> 2NO2 is 0.619 at 45 degrees C If 50.0g of N2O4 is introduced into an empty 2.10L container, w
Nadya [2.5K]

Answer:

p(N2O4) = 0.318 atm

p(NO2) = 7.17 atm

Explanation:

Step 1: Data given

Kc = 0.619

Temperature = 45.0 °C

Mass of N2O4 = 50.0 grams

Volume = 2.10 L

Molar mass N2O4 = 92.01 g/mol

Step 2: The balanced equation

N2O4 ⇔ 2NO2

Step 3: Calculate moles N2O4

Moles N2O4 = 50.0 grams / 92.01 g/mol

Moles N2O4 = 0.543 moles

Step 4: The initial concentration

[N2O4] = 0.543 moles/2.10 L = 0.259 M

[NO2]= 0 M

Step 5: Calculate concentration at the equilibrium

For 1 mol N2O4 we'll have 2 moles NO2

[N2O4] = (0.259 -x)M

[NO2]= 2x

Step 6: Calculate Kc

Kc = 0.619=  [NO2]² / [N2O4]

0.619 = (2x)² / (0.259-x)

0.619 = 4x² / (0.259 -x)

x = 0.1373  

Step 7: Calculate concentrations

[N2O4] = (0.259 -x)M = 0.1217 M

[NO2]= 2x = 0.2746 M

Step 8: The moles

Moles = molarity * volume

Moles N2O4 = 0.1217 M * 2.10  = 0.0256 moles

Moles NO2 = 0.2746 M * 2.10 = 0.577 moles

Step 9: Calculate partial pressure

p*V = n*R*T

⇒ with p = the partial pressure

⇒ with V = the volume = 2.10 L

⇒ with n = the number of moles

⇒ with R = the gas constant = 0.08206 L*atm/mol*K

⇒ with T = the temperature = 45 °C = 318 K

p = (nRT)/V

p(N2O4) = (0.0256 *0.08206 * 318)/ 2.10

p(N2O4) = 0.318 atm

p(NO2) = (0.577 *0.08206 * 318)/ 2.10

p(NO2) = 7.17 atm

6 0
3 years ago
Knowing that all three-sided figures are triangles is an example of:
pogonyaev

Answer:

B. Concept Formation

Explanation:

All the other answer choices are not equivalent.

Hope this helps!

Brainliest??

5 0
3 years ago
Read 2 more answers
Fill in the blank for the following statement: ________ is the movement of rocks, sand, or materials from a place?
Verizon [17]

Answer:

Erosion.

Explanation:

It can be as small as a grain of sand or as large as a boulder. Sediment moves from one place to another through the process of erosion. Erosion is the removal and transportation of rock or soil. Erosion can move sediment through water, ice, or wind.

3 0
3 years ago
Read 2 more answers
What volume of air is needed to burn completely 100cm of propane?
Evgesh-ka [11]

Answer:

See below

Explanation:

propane mole weight = 44 gm / mole

100 gm / 44 gm / mole = 2.27 moles

From the equation, 5 times as many moles of OXYGEN (O2)are required

   = 11.36 moles of oxygen

           at <u>STP</u> this is 254.55  liters of O2 (because 22.4 L = one mole) and

Using oxygen as 21 percent of air means that

      .21 x = 254.55 =       x = <u>1212.12 liters of air required </u>

5 0
2 years ago
What is the nuclear binding energy for thorium-234? 2.78 × 10-10 J 3.36 × 10-14 J 1.67 × 1017 J 5.35 x 10-23 J
grin007 [14]
The correct option is A.
To calculate the binding energy, you have to find the mass defect first.
Mass defect = [mass of proton and neutron] - Mass of the nucleus
The molar mass of thorium that we are given in the question is 234, the atomic number of thorium is 90, that means the number of neutrons in thorium is 
234 - 90 = 144.
The of proton in thourium is 90, same as the atomic number.
Mass defect = {[90 * 1.00728] +[144* 1.00867]} - 234
Note that each proton has a mass of 1.00728 amu and each neutron has the mass of 1.00867 amu.
Mass defect = [90.6552 + 145.24848] - 234 = 1.90368 amu.
Note that the unit of the mass is in amu, it has to be converted to kg
To calculate the mass in kg
Mass [kg] = 1.90368 * [1kg/6.02214 * 10^-26 = 3.161135 * 10^-27
To calculate the binding energy
E = MC^2
C = Speed of light constant = 2.9979245 *10^8 m/s2
E = [3.161135 * 10^-27] * [2.9979245 *10^8]^2
E = 2.84108682069 * 10^-10.
Note that we arrive at this answer because of the number of significant figures that we used.
So, from the option given, Option A is the nearest to the calculated value and is our answer for this problem.

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which acids caused the effects seen on the teeth in the study
    13·1 answer
  • What are some physical properties that could have helped to identify a mystery powder?
    13·1 answer
  • how many moles of potassium hydroxide are needed to completely react with 1.73 miles of aluminum sulfate according to the follow
    10·2 answers
  • What is the weight, on earth, if a book with a mass of 1.5kg 1.5N 6.5 N 11.3 N 14.7
    10·2 answers
  • Increasing the concentration of a reactant shifts the position of a chemical equilibrium towards formation of more products. wha
    13·1 answer
  • The naturally occurring isotopes of magnesium are magnesium-24. magnesium-25, and magnesium-26. Magnesium-24 has an abundance of
    9·2 answers
  • How do you know that an organism belongs to the animal kingdom
    6·1 answer
  • Tick (√) the statements that are correct.
    9·1 answer
  • In 1774, Joseph Priestly discovered oxygen gas by heating mercury(II) oxide powder with focused sunlight through a lens. How man
    7·1 answer
  • Sulfur is yellow, solid, nonmetal. what other elements is likely also a nonmetal?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!