<u>Answer:</u> The sample of Carbon-14 isotope will take 2377.9 years to decay it to 25 %
<u>Explanation:</u>
The equation used to calculate rate constant from given half life for first order kinetics:

where,
= half life of the reaction = 5730 years
Putting values in above equation, we get:

Rate law expression for first order kinetics is given by the equation:
![k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B2.303%7D%7Bt%7D%5Clog%5Cfrac%7B%5BA_o%5D%7D%7B%5BA%5D%7D)
where,
k = rate constant = 
t = time taken for decay process = ? yr
= initial amount of the sample = 100 grams
[A] = amount left after decay process = (100 - 25) = 75 grams
Putting values in above equation, we get:

Hence, the sample of Carbon-14 isotope will take 2377.9 years to decay it to 25 %
Explanation:
a) The amount of heat released by coffee will be absorbed by aluminium spoon.
Thus, 
To calculate the amount of heat released or absorbed, we use the equation:

Also,
..........(1)
where,
q = heat absorbed or released
= mass of aluminium = 45 g
= mass of coffee = 180 g
= final temperature = ?
= temperature of aluminium = 
= temperature of coffee = 
= specific heat of aluminium = 
= specific heat of coffee= 
Putting all the values in equation 1, we get:
![45 g\times 0.80J/g^oC\times (T_{final}-24^oC)=-[180 g\times 4.186J/g^oC\times (T_{final}-83^oC)]](https://tex.z-dn.net/?f=45%20g%5Ctimes%200.80J%2Fg%5EoC%5Ctimes%20%28T_%7Bfinal%7D-24%5EoC%29%3D-%5B180%20g%5Ctimes%204.186J%2Fg%5EoC%5Ctimes%20%28T_%7Bfinal%7D-83%5EoC%29%5D)

80.30 °C is the final temperature.
b) Energy flows from higher temperature to lower temperature.Whenever two bodies with different energies and temperature come in contact. And the resulting temperature of both bodies will less then the body with high temperature and will be more then the body with lower temperature.
So, is our final temperature of both aluminium and coffee that is 80°C less than initial temperature of coffee and more than the initial temperature of the aluminum.
Answer:
The chemical equation needs to be balanced so that it follows the law of conservation of mass. A balanced chemical equation occurs when the number of the different atoms of elements in the reactants side is equal to that of the products side.
They move like waves since they're such a small particle
Answer: 2 mol
Explanation:
- According to the ideal gas law, One mole of an ideal gas at STP (standard temperature and normal pressure) occupies 22.4 liters.
- Using cross multiplication,
1 mol of (O2) → 22.4 L
? → 43.9 L
Therefore, the number of moles of oxygen in 43.9 L = (43.9 × 1)/ 22.4 = 1.96 mol≈ 2 mol..