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vagabundo
6 days ago
8

Find the age t of a sample, if the total mass of carbon in the sample is mc, the activity of the sample is a, the current ratio

of the mass of 14 6c to the total mass of carbon in the atmosphere is r, and the decay constant of 14 6c is λ. assume that, at any time, 14 6c is a negligible fraction of the total mass of carbon and that the measured activity of the sample is purely due to 14 6c. also assume that the ratio of mass of 14 6c to total carbon mass in the atmosphere (the source of the carbon in the sample) is the same at present and on the day when the number of 14 6c atoms in the sample was set. express your answer in terms of the mass ma of a 14 6c atom, mc, a, r, and λ.
Chemistry
1 answer:
Alekssandra [968]6 days ago
6 0
N₀ signifies the quantity of C-14 atoms per kg of carbon in the original sample at time = 0 seconds, when the carbon composition matched that in today’s atmosphere. As time progresses to ts, the number of C-14 atoms per kg declines to N, due to radioactive decay. λ indicates the decay constant.
Hence, we have N = N₀e - λt, which is the equation for radioactive decay. Rearranging gives us N₀/N = e λt, or In(N₀/N) = - λt, which becomes equation 1.
The sample contains mc kg of carbon, leading to an activity measured as A/mc decay per kg. The variable r represents the initial mass of C-14 in the sample at t=0 relative to the total mass of carbon which is calculated as [(total number of C-14 atoms at t = 0) × ma] / total mass of carbon. Thus, N₀ equates to r/ma, which becomes equation 2.
The activity of the radioactive element is directly related to the atom count at the moment. The activity equation A = dN/dt = λ(N) indicates that: A = λ₁(N × mc). Rearranging provides N = A / (λmc), represented in equation 3.
By integrating equations 2 and 3, we can solve for t yielding
t = (1/λ) In(rλmc/m₀A).

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How many carbon atoms are contained in 84.3 g of ethyne (c2h2)?
alisha [964]
<span>To find the number of carbon atoms, begin by eliminating grams from the given 84.3 g of C2H2 by dividing it by ethyne's molar mass, which is 26.038 g/mol. This molar mass is computed by summing the atomic masses of 2 carbons (12.011 g/mol each) and 2 hydrogens (1.008 g/mol each). This calculation yields the amount in moles of ethyne. Then, multiply by Avogadro's constant (6.022x10^23 atoms/mol) to convert moles of ethyne to atoms of ethyne. Since each C2H2 molecule contains 2 carbon atoms, multiply by 2 carbon atoms per ethyne molecule to get the total carbon atoms, resulting in 3.90x10^24 atoms of carbon. This figure is rounded to three significant digits, consistent with the smallest number of significant figures (three in 84.3). The steps are: 84.3 g C2H2 × (1 mol C2H2 / 26.038 g C2H2) × (6.022×10^23 atoms C2H2 / 1 mol C2H2) × (2 atoms C / 1 atom C2H2) = 3.90×10^24 carbon atoms.</span>
7 0
14 days ago
Butane (c4h10) undergoes combustion in excess oxygen to generate gaseous carbon dioxide and water. given δh°f[c4h10(g)] = –124.7
KiRa [971]

The Δ H value for butane (g) is -124.7 kJ/mol.

The Δ H value for CO2 (g) is -393.5 kJ/mol.

The Δ H value for H2O (g) is -241.8 kJ/mol.

The mass of butane is 8.30 grams.

Butane has a molar mass of 58 g/mol.

Considering the reaction,

C₄H₁₀ + 6.5 O₂ = 4CO₂ + 5H₂O

To determine the Δ H° of the reaction:

ΔH°rxn = ∑nH° f (products) - ∑nH° f (reactants)

By substituting values, we find that

Δ H° rxn = 4 (-393.5) + 5 (-241.8) - (-124.7)

= -1574 -1209 + 124.7

= -2783 - 124.7

= -2658.3 kJ/mol

Now, we will calculate how many moles of butane are in 8.30 grams.

Number of moles = mass/molar mass

= 8.30 / 58

= 0.143 moles

Therefore, the total energy released during the reaction is given by,

Q = number of moles × ΔH° rxn

= 0.143 × (2658.3)

= 380.14 kJ

Thus, the total heat released in the reaction is 380.14 kJ.

6 0
6 days ago
What mass of carbon dioxide (co2) can be produced from 86.17 grams of c6h14 and excess oxygen?
lorasvet [956]
2C6H14 + 13O2 ---> 6CO2 +14H2O

Calculating the molar mass of C6H14: M(C6H14)=12.011*6 +1.008*14 ≈ 86.17 g/mol

Thus, 86.17 g of C6H14 corresponds to 1 mole.

                                  2C6H14 + 13O2 ---> 6CO2 +14H2O
based on the equation        2 mol                            6 mol
according to the question    1 mol                            3 mol

To determine M(CO2): M(CO2)= 12.011 + 2*15.999= 44.009 g/mol
Therefore, 3 mol CO2*44.009 g/1 mol CO2 ≈ 132.0 g CO2
Final answer: 132.0 g CO2


3 0
10 days ago
If angle ABE = 2n + 7 and angle EBF=4n-13,<br>find angle ABE.​
VMariaS [1037]

Answer:

Angle ABE measures 27°.

Explanation:

Refer to the attached diagram related to this question.

The given values are ∠ABE=2n+7 and ∠EBF=4n-13.

Clearly seen in the diagram, ∠ABE and ∠EBF are equal in measure.

m\angle ABE=m\angle EBF

2n+7=4n-13

Move variable components to one side of the equation.

7+13=4n-2n

20=2n

Split both sides by 2.

10=n

The solution for n arrives at 10.

The next step is to calculate ∠ABE.

\angle ABE=2(10)+7=20+7=27

Consequently, the measurement of angle ABE is 27°.

4 0
8 days ago
A sample of neon gas at STP is allowed to expand into an evacuated vessel. What is the sign of work for this process?
Alekssandra [968]

Answer:

The work done in this process will be considered Negative.

Explanation:

The energy transferred by the system to the environment is negative

Therefore, if work is done on the system, it is labeled as positive. Conversely, when work is done by the system, it is regarded as negative.

In this scenario, the argon gas is expanding, and the work is exerted by the system into the surroundings (container), making the sign Negative.

Thus, the result for the work pertaining to this process will carry a Negative sign.

3 0
9 days ago
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