Calculate the density of CsCl. Use 169pm as the radius of Cs+.
rCs+= 169pm
length= 2*169= 338pm= 3.38*10^-8
v= l^3= (3.38*10^-8)^3 = 3.86*10^-23
m= 2* 168.36 g/mol / 6.022*10^23 = 5.59*10^-24g
d= m/v
d= 5.59*10^-24g/ 3.86*10^-23
d= 14.48 g/cm^3
BUT the correct answer is 4.24 g/cm^3. I can't figure out my mistake I've done it several times
Side of cube(unit cell) is root(3)×a=4r.
You are using 2r
Thats wrong.
Actually you have to use 4r=/3.a for volume then you get 1095.8 kg/m3 for one atom. and one unit cell has 4 cation (cs+) and 1 anion (cl-) and you have multiply 4x1x1095.8 = 4380 kg/m3.
You used the cation radius when calculating volume rather than the anion radius.
To calculate the density of CsCl, we need to know the molar mass of CsCl and the volume of the unit cell.
The molar mass of CsCl can be determined by summing the atomic masses of cesium (Cs) and chlorine (Cl). The atomic mass of Cs is 132.91 g/mol, and the atomic mass of Cl is 35.45 g/mol. Therefore, the molar mass of CsCl is:
Molar mass (CsCl) = 132.91 g/mol + 35.45 g/mol = 168.36 g/mol
Next, let's calculate the volume of the unit cell. The unit cell of CsCl is a simple cubic structure, and for a simple cubic lattice, the edge length of the unit cell is equal to twice the radius of the cation (in this case, Cs+).
The radius of Cs+ given in the question is 169 pm (picometers). To convert picometers to centimeters, we divide by 10000:
rCs+ = 169 pm = 169 x 10^-10 cm = 1.69 x 10^-8 cm
The length of the CsCl unit cell is equal to twice the radius of Cs+:
Length = 2 x 1.69 x 10^-8 cm = 3.38 x 10^-8 cm
Now, let's calculate the volume of the unit cell. Since the CsCl unit cell is a cube, the volume is given by:
Volume = Length^3 = (3.38 x 10^-8 cm)^3 = 3.86 x 10^-23 cm^3
Now that we have the molar mass and the volume of the unit cell, we can calculate the density of CsCl using the formula:
Density = Mass / Volume
First, we need to calculate the mass of the unit cell. To do this, we divide the molar mass of CsCl by Avogadro's number (6.022 x 10^23) to get the mass of one formula unit:
Mass = Molar mass (CsCl) / Avogadro's number
Mass = 168.36 g/mol / (6.022 x 10^23) = 2.797 x 10^-23 g
Finally, we can calculate the density:
Density = Mass / Volume
Density = (2.797 x 10^-23 g) / (3.86 x 10^-23 cm^3) = 0.724 g/cm^3
It seems like there was an error in your calculation. The correct density of CsCl is approximately 0.724 g/cm^3, not 4.24 g/cm^3. Please double-check your calculations and make sure you input all the values correctly.