You found an unknown metal sample shaped as a cube with each side measuring 2.00 cm. The cube's mass is 48.0 . Your colleague examined the mystery cube with X-ray diffraction and told you that it contains just one element arranged in a body-centered-cubic -lattice, and that the unit cell length is 304.4 pm. What element is the cube made of? Hint: determine the atomic weight and look it up in the periodic table.
My work:
2mol* 48g* 2 cm/ (6.022*10^23mol)(304.4*10^-10 cm)^3=
11.3 g
Boron
This is wrong! Could you please show me how to do this problem?
volume of the large cube is 2^3 = 8.0 cc
density = m/v= 48/8 = 6 g/cc
volume of unit cell = (3.044E-8 cm)^3 = 2.892E-23 cc
mass unit cell = v x d = 2.89E-23*6 = 1.69E-22
1.69E-22 = 2*atomic mass /6.022E23
Solve for atomic mass.
If a sugar cube measured 20cm by 20cm how much surface area would be exposed to the solvent(water)
To determine the element that the cube is made of, you need to calculate the atomic weight based on the given information. Here's the step-by-step process to find the correct solution:
Step 1: Calculate the volume of the cube:
Since each side measures 2.00 cm, the volume of the cube can be calculated as:
Volume = (2.00 cm)^3 = 8.00 cm^3
Step 2: Convert the volume to pm^3:
Given the unit cell length of the body-centered cubic lattice as 304.4 pm, convert the volume from cm^3 to pm^3:
Volume = 8.00 cm^3 * (10^8 pm / 1 cm)^3 = 8.00 × 10^24 pm^3
Step 3: Calculate the number of unit cells in the sample:
Since the cube contains a body-centered cubic lattice, there is 1 unit cell in the center and 8 additional unit cells at the corners. Therefore, the total number of unit cells is 9.
Step 4: Calculate the volume of one unit cell:
Divide the total volume of the cube by the number of unit cells:
Volume of one unit cell = (8.00 × 10^24 pm^3) / 9 = 8.89 × 10^23 pm^3
Step 5: Calculate the mass of a single atom in the unit cell:
Given that the mass of the cube is 48.0 g, and the cube contains 2 moles of the element:
Mass of one atom = (48.0 g) / (2 × 6.022 × 10^23 atoms) = 4.00 × 10^-23 g
Step 6: Convert the mass of one atom to atomic weight:
Since atomic weight is given in grams per mole, divide the mass of one atom by the Avogadro's number:
Atomic weight = (4.00 × 10^-23 g) / (6.022 × 10^23 atoms/mol) ≈ 0.0664 g/mol
Finally, take the atomic weight value (0.0664 g/mol) and look it up in the periodic table. By doing so, you will find that the element with this atomic weight is not Boron but rather Lithium (Li).