Hello, I am having problem with two lab questions and was wondering if someone can help!
1. Calculate the percentage of the empty space in a face-centered cubic lattice, and show that it does not depend on the edge length of the unit cell ot on the size of the atoms in the unit cell. It says I need to find the edge length in terms of the radii of the atoms in the unit cell, the total volumme of the unit cell in terms of the edge length, and filled the volume from the total volume of the atoms in the unit cell.
What equation will you use to calculate heat of fusion of ice? The specific heat of water is 4.184J/ (g x c) and the heat capacity of your calorimeter is 1.0 x 10^1 J/C. Explain the reasoning behind your equation.
There are four atoms per cell.
Packing factor: volumeatoms/volumecell
= 4*4/3 PI r^3 / s^3
Now, on any face diagonal, one has to have 4r, so 4r= s*sqrt2
packing factor: 16/3 PI 1/64 * 2sqrt2
= 1/6 PI sqrt 2= you do it.
b. I have no idea what you did, but suspect you melted ice of some mass.
Heatabsorbed=Hfusion*mass
Sure! I can help you with both of these questions. Let's start with the first one.
To find the percentage of empty space in a face-centered cubic (FCC) lattice, we need to calculate the volume occupied by the atoms in the unit cell and compare it to the total volume of the unit cell. The equation we can use is as follows:
Empty space percentage = (1 - filled volume / total volume) * 100
To find the edge length in terms of the radii of the atoms in the unit cell, we can assume that the atoms in the unit cell are identical spheres. In an FCC lattice, each corner is shared by eight unit cells, and each face is shared by two unit cells. This implies that each unit cell contains the equivalent of four atoms.
The edge length of the unit cell (a) can be expressed in terms of the atomic radius (r) as follows:
a = 4r
The total volume of the unit cell (V_total) can be calculated by cubing the edge length:
V_total = a^3 = (4r)^3 = 64r^3
To calculate the filled volume from the total volume of the atoms in the unit cell, we need to determine how much space the atoms occupy. In an FCC lattice, each atom is present at the center of a cubic face with each face shared by two unit cells. Therefore, the volume occupied by each atom is:
V_atom = (1/2) * (a^2) * (a/2) = (1/8) * a^3 = (1/8) * (4r)^3 = r^3
Since each unit cell contains four atoms, the total volume occupied by the atoms in the unit cell (V_filled) is:
V_filled = 4 * V_atom = 4 * r^3
Now we can substitute the expressions for V_total and V_filled into the empty space percentage equation. The edge length of the unit cell and the size of the atoms cancel out, showing that the percentage of empty space does not depend on these factors:
Empty space percentage = (1 - V_filled / V_total) * 100 = (1 - (4r^3 / 64r^3)) * 100 = (1 - (1/16)) * 100 = (15/16) * 100 = 93.75%
Therefore, the percentage of empty space in a face-centered cubic lattice is always 93.75% regardless of the edge length of the unit cell or the size of the atoms.
Now let's move on to the second question about calculating the heat of fusion of ice.
The equation to calculate the heat of fusion of ice is:
Q = m * ΔH_fusion
Here, Q represents the heat energy, m is the mass of ice, and ΔH_fusion is the enthalpy change associated with the fusion of ice.
To find Q, we can use the equation:
Q = (m_water * C_water * ΔT_water) + (C_calorimeter * ΔT_calorimeter)
In this equation, m_water is the mass of water, C_water is the specific heat capacity of water, ΔT_water is the change in temperature of water, C_calorimeter is the heat capacity of the calorimeter, and ΔT_calorimeter is the change in temperature of the calorimeter.
The reasoning behind this equation is that the heat energy gained by the water is equal to the heat energy lost by the calorimeter. The first term on the right side of the equation calculates the heat energy gained by the water, and the second term calculates the heat energy lost by the calorimeter.
By rearranging the equation, we can solve for ΔH_fusion:
ΔH_fusion = Q / m_ice
Here, m_ice is the mass of ice.
So, to find the heat of fusion of ice, you would need to measure the masses and temperatures involved, and use the specific heat capacity and heat capacity values given in the question. Plug these values into the equations and calculate ΔH_fusion.
I hope this helps! Let me know if you have any further questions.