If an oil molecule is 100*10^-10m in diameter,then can 10^24 molecules fit exactly in a cube 1m on a side? Please help me answer this showing working out.
If the diameter of an oil molecule is exactly 100 x 10^-10 m (better stated as 1.00E-8 meters) it will take up 1E-8 m space. Let's think of a square that is 1 meter on a side. How many molecules call be place in ONE row. We can place exactly 1E8 (because 1E8*1E-8 = 1 meter.
How many rows can we make? We can make 1E8 rows. So now we have a square of 1E8 rows. If we make a cube, then we can have 1E8*1E8*1E8 = 1E24. So yes. They can fit exactly. Of course these are round so there will still be spaces in the 1 m cube.
Dr.Bob, I cannot understand why you changed 100*10 ^-10 to 1E-8m? What is their relationship?
To determine if 10^24 oil molecules can fit exactly in a cube 1m on a side, we need to calculate the volume of one oil molecule and the volume of the cube and compare them.
The volume of one oil molecule can be calculated using the formula for the volume of a sphere:
V = (4/3) * π * r^3,
where V is the volume and r is the radius of the sphere.
Given that the diameter of one oil molecule is 100 * 10^-10 m, we can find the radius by dividing the diameter by 2:
r = (100 * 10^-10 m) / 2 = 50 * 10^-10 m.
Now we can calculate the volume of one oil molecule:
V_molecule = (4/3) * π * (50 * 10^-10 m)^3.
Next, let's calculate the volume of the cube:
V_cube = (1 m)^3.
Now we can compare the volumes:
V_molecule = (4/3) * π * (50 * 10^-10)^3 = X m^3 (approximate value).
V_cube = (1 m)^3 = 1 m^3.
If V_molecule * 10^24 = V_cube, then 10^24 molecules can fit exactly in the cube.
Hence, you need to calculate the volume of one oil molecule and then multiply it by 10^24. If the result is equal to the volume of the cube, then 10^24 molecules can fit exactly.
To determine if 10^24 oil molecules can fit exactly in a cube that is 1 meter on each side, we need to calculate the volume of the cube and the volume occupied by a single oil molecule, and then compare the two.
The volume of a cube can be calculated using the formula V = s^3, where V is the volume and s is the length of one side.
Given that the cube has a side length of 1 meter, we can substitute this value into the formula:
V = (1 m)^3
V = 1 m^3
So, the volume of the cube is 1 cubic meter (m^3).
Now, let's calculate the volume of a single oil molecule. The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where V is the volume and r is the radius.
The diameter of the oil molecule is given as 100*10^-10m. To find the radius, we divide the diameter by 2:
r = (100*10^-10m) / 2
r = 50*10^-10m
Substituting this radius value into the formula:
V = (4/3) * π * (50*10^-10m)^3
To simplify the calculation, let's approximate π to 3.14:
V = (4/3) * 3.14 * (50*10^-10m)^3
Now, we can simplify the calculation by converting the radius to scientific notation:
V = (4/3) * 3.14 * (5*10^-9m)^3
Expanding:
V = (4/3) * 3.14 * (5^3 * (10^-9m)^3)
Calculating:
V ≈ 4.19 * 125 * 10^-27 m^3
V ≈ 523.75 * 10^-27 m^3
V ≈ 5.2375 * 10^-25 m^3
So, the volume of a single oil molecule is approximately 5.2375 * 10^-25 cubic meters (m^3).
Now, let's see if 10^24 oil molecules can fit exactly in the cube.
To find the number of oil molecules that can fit in the cube, we divide the volume of the cube by the volume of a single oil molecule:
Number of molecules = Volume of cube / Volume of a single molecule
Number of molecules = (1 m^3) / (5.2375 * 10^-25 m^3)
Dividing these values:
Number of molecules ≈ 1.909 * 10^24
After performing the division, we get approximately 1.909 * 10^24.
Since this value is less than 10^24, it means that 10^24 oil molecules CANNOT fit exactly in a cube 1 meter on each side.