Copper has an atomic radius of 0.128 nm, an FCC crystal structure, and an atomic weight of 63.5 g/mol. Compute its theoretical density and compare the answer with its measured density

d = 8.88 g/cm³

0.56 % difference

Explanation:

We need to compare the theoretical density of copper to its measured density which the literature says is 8.93 g/cm³.

The density is mass per volume so we need to determine the mass of the FCC unit cell and its volume.

In the face centered cubic unit cell we have 8 atoms at the 8 corners shared by 8 unit cells for a  total of one atom, and 6 atoms in the 6 faces of the cube shared by two face centered cubic unit cell, giving us a total of 4 atoms of copper per unit cell ( 8 x 1/8 + 6 x 1/2  = 4).

The mass of the unit cell will be the mass of 4 copper atoms:

mass = 4 atoms/unit cell x 63.5 g/mol x 1 mol /6.022 x 10²³ atoms

mass = 4.22 x 10⁻²² g

The volume of a cube is the length side, a , cubed.

There is the relation for a FCC unit cell which expresses this length as a function of the atomic radius as:

a =  √8 x r

converting r to cm for units consistency:

0.128 nm x 1 x 10⁻⁷ cm/nm = 1.28 x 10⁻⁸ cm

a = √8 x 1.28 x 10⁻⁸ cm = 3.62 x 10⁸ cm

V = a³ = ( 3.62 x 10⁸ cm)³ = 4.75 x 10⁻²³ cm³

Now we can finally compute the theoretical density as:

d = m/V = 4.22 x 10⁻²² g / 4.75 x 10⁻²³ cm³ = 8.88 g/cm³

finally comparing the theoretical with the measured density for copper, we get:

(8.93 - 8.88)/8.93 x 100 =0.56 %

There is a difference of just 0.56 % between the two values.

answer: - 3.) the oxidation state of nitrogen in no changes from +2 to 0, and the oxidation state of carbon in co changes from +2 to +4 as the reaction proceeds.

solution: - as per the rules, oxidation number of oxygen in its compounds is -2. the sum of oxidation numbers of all the elements of a molecule or compound is zero.

also, the oxidation number in elemental form is zero.

in no, the oxidation number of o is -2 so the oxidation number of n is +2 so that the sum is zero.

similarly, the oxidation number of c in co is +2 and o is -2.

on product side the oxidation number of n is 0 as it is in the elemental form() .

oxidation number of c in carbon dioxide is +4 as there are two oxygen in it and we know that each oxygen is -2.

so, oxidation number of n is changing from +2 to 0 and the oxidation number of c is changing from +2 to +4.

since nitrogen is reduced and hence no is acting as an oxidizing agent. carbon is oxidized and so co is acting as a reducing agent.

so, the right choice is number 3.)the oxidation state of nitrogen in no changes from +2 to 0, and the oxidation state of carbon in co changes from +2 to +4 as the reaction proceeds.

the potential energy of the reactants is 200j.

from the energy diagram, the energy of the product formed is 350j; this means that, this reaction is an endothermic reaction, because it absorbs energy from its environment.