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).
Answer:
The dependent variable in this experiment is the egg's position above the water.
Explanation:
The dependent variable refers to the factor that is influenced by another variable.
On the other hand, the independent variable is what can be altered, affecting the dependent variable's outcome.
The controlled variable remains constant throughout the experiment.
In this setup, the amount of salt added acts as the independent variable, while the flotation level of the egg is the dependent variable, and the water volume in each cup represents the controlled variable.
Option d is the correct choice, as both belong to the alkali metals category (group one).
1. The total moles of the solution is 0.3079193 mol.
2. The mole fraction for gold is 0.2473212, and for silver, it is 0.7526787.
3. The molar entropy of mixing for gold is 2.87285 j/K, while for silver, it is 1.77804 j/K.
4. The total entropy of mixing sums to 4.65089 j/K.
5. Molar free energy amounts to -2325.445 kJ.
6. Chemical potential for silver is -1750.31129 j/mol and for gold, it is -575.13185 j/mol. To elaborate:
(1) The molar mass of silver stands at 107.8682 g/mol, and gold's at 196.96657 g/mol. Hence, calculating moles leads to mass/molar mass for silver: 25 g/107.8682 g/mol = 0.2317643 mol and for gold: 15 g/196.96657 g/mol = 0.076155 mol, resulting in a total of 0.30791193 mol.
(2) For the mole fractions, silver's fraction is 0.2317643/0.3079193 = 0.7526787, and for gold, it's 0.076155/0.3079193 = 0.2473212.
(3) To find molar entropy mixing ∆Sm, we use the formula ∆Sm = -R * Xi * ln(Xi) where R = 8.3144598. For silver, substituting gives us 1.77804 j/K, while for gold, we get 2.87285 j/K.
(4) Overall entropy of mixing totals 4.65089 j/K thus calculated.
(5) The Gibbs free energy at 500 °C can be derived through G = H - TS, accounting to H = 0 (as T is 500 + 273 = 773 K and S is 4.65089), resulting in G equating to -3595.138 kJ.
(6) The chemical potentials calculated derive from multiplying the Gibbs free energy by their mole fractions.
Answer:
5.57 L
Explanation:
- Apply the combined gas law formula.
- Change Celsius to Kelvin.
- Convert mmHg into atm.
- Enter the variables into the equation.
- I hope this information was beneficial! If you want, I can guide you through the process step by step.
