Using deep-sea sediment cores found that Milankovitch cycles correspond with periods of major climate change over the past 450,000 years, with Ice Ages occurring when Earth was undergoing different stages of orbital variation.
Answer:
Elemental gold to have a Face-centered cubic structure.
Explanation:
From the information given:
Radius of gold = 144 pm
Its density = 19.32 g/cm³
Assuming the structure is a face-centered cubic structure, we can determine the density of the crystal by using the following:
![a = \sqrt{8} r](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%7B8%7D%20r)
![a = \sqrt{8} \times 144 pm](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%7B8%7D%20%5Ctimes%20144%20pm)
a = 407 pm
In a unit cell, Volume (V) = a³
V = (407 pm)³
V = 6.74 × 10⁷ pm³
V = 6.74 × 10⁻²³ cm³
Recall that:
Net no. of an atom in an FCC unit cell = 4
Thus;
![density = \dfrac{mass}{volume}](https://tex.z-dn.net/?f=density%20%3D%20%5Cdfrac%7Bmass%7D%7Bvolume%7D)
![density = \dfrac{ 4 \ atm ( 196.97 \ g/mol) (\dfrac{1 \ mol }{6.022 \times 10^{23} \ atoms})}{6.74 \times 10^{-23} \ cm^3}](https://tex.z-dn.net/?f=density%20%3D%20%5Cdfrac%7B%204%20%5C%20atm%20%28%20196.97%20%5C%20g%2Fmol%29%20%28%5Cdfrac%7B1%20%5C%20mol%20%7D%7B6.022%20%5Ctimes%2010%5E%7B23%7D%20%5C%20atoms%7D%29%7D%7B6.74%20%5Ctimes%2010%5E%7B-23%7D%20%5C%20cm%5E3%7D)
density d = 19.41 g/cm³
Similarly; For a body-centered cubic structure
![r = \dfrac{\sqrt{3}}{4}a](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B4%7Da)
where;
r = 144
![144 = \dfrac{\sqrt{3}}{4}a](https://tex.z-dn.net/?f=144%20%3D%20%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B4%7Da)
![a = \dfrac{144 \times 4}{\sqrt{3}}](https://tex.z-dn.net/?f=a%20%3D%20%5Cdfrac%7B144%20%5Ctimes%204%7D%7B%5Csqrt%7B3%7D%7D)
a = 332.56 pm
In a unit cell, Volume V = a³
V = (332.56 pm)³
V = 3.68 × 10⁷ pm³
V 3.68 × 10⁻²³ cm³
Recall that:
Net no. of atoms in BCC cell = 2
∴
![density = \dfrac{mass}{volume}](https://tex.z-dn.net/?f=density%20%3D%20%5Cdfrac%7Bmass%7D%7Bvolume%7D)
![density = \dfrac{ 2 \ atm ( 196.97 \ g/mol) (\dfrac{1 \ mol }{6.022 \times 10^{23} \ atoms})}{3.68 \times 10^{-23} \ cm^3}](https://tex.z-dn.net/?f=density%20%3D%20%5Cdfrac%7B%202%20%5C%20atm%20%28%20196.97%20%5C%20g%2Fmol%29%20%28%5Cdfrac%7B1%20%5C%20mol%20%7D%7B6.022%20%5Ctimes%2010%5E%7B23%7D%20%5C%20atoms%7D%29%7D%7B3.68%20%5Ctimes%2010%5E%7B-23%7D%20%5C%20cm%5E3%7D)
density =17.78 g/cm³
From the two calculate densities, we will realize that the density in the face-centered cubic structure is closer to the given density.
This makes the elemental gold to have a Face-centered cubic structure.
Answer:
The balanced chemical equation:
![C_6H_5OH(s)+7O_2(g)\rightarrow 6CO_2(g)+3H_2O(g)](https://tex.z-dn.net/?f=C_6H_5OH%28s%29%2B7O_2%28g%29%5Crightarrow%206CO_2%28g%29%2B3H_2O%28g%29)
Heat of combustion per gram of phenol is 32.454 kJ/g
Heat of combustion per gram of phenol is 3,050 kJ/mol
Explanation:
![C_6H_5OH(s)+7O_2(g)\rightarrow 6CO_2(g)+3H_2O(g)](https://tex.z-dn.net/?f=C_6H_5OH%28s%29%2B7O_2%28g%29%5Crightarrow%206CO_2%28g%29%2B3H_2O%28g%29)
Heat capacity of calorimeter = C = 11.66 kJ/°C
Initial temperature of the calorimeter = ![T_1= 21.36^oC](https://tex.z-dn.net/?f=T_1%3D%2021.36%5EoC)
Final temperature of the calorimeter = ![T_2= 26.37^oC](https://tex.z-dn.net/?f=T_2%3D%2026.37%5EoC)
Heat absorbed by calorimeter = Q
![Q=C\times \Delta T](https://tex.z-dn.net/?f=Q%3DC%5Ctimes%20%5CDelta%20T)
Heat released during reaction = Q'
Q' = -Q ( law of conservation of energy)
Energy released on combustion of 1.800 grams of phenol = Q' = -(58.4166 kJ)
Heat of combustion per gram of phenol:
![\frac{Q'}{1.800 g}=\frac{-58.4166 kJ}{1.800 g}=32.454 kJ/g](https://tex.z-dn.net/?f=%5Cfrac%7BQ%27%7D%7B1.800%20g%7D%3D%5Cfrac%7B-58.4166%20kJ%7D%7B1.800%20g%7D%3D32.454%20kJ%2Fg)
Molar mass of phenol = 94 g/mol
Heat of combustion per gram of phenol:
![\frac{Q'}{\frac{1.800 g}{94 g/mol}}=\frac{-58.4166 kJ\times 94 g/mol}{1.800 g}=3,050 kJ/mol](https://tex.z-dn.net/?f=%5Cfrac%7BQ%27%7D%7B%5Cfrac%7B1.800%20g%7D%7B94%20g%2Fmol%7D%7D%3D%5Cfrac%7B-58.4166%20kJ%5Ctimes%2094%20g%2Fmol%7D%7B1.800%20g%7D%3D3%2C050%20kJ%2Fmol)
The answears are in the attached photo.