18 mols of gold are shaped like a sphere. What is the sphere’s diameter. Note the atomic mass of gold is 0.197 kg/mol and its density is 19,300 kg/m3.
volumesphere=mass/density=
18*.197/19,300 m^3
but volume= 4/3 PI r^3
r= cubrt(3*19,300/(4PI * 18*.197)) meters.
multiply by 2 to get diameter.
Well, gold sure is heavy! If we have 18 moles of gold, we can use Avogadro's number (6.022 x 10^23) to find the total number of atoms. Since gold is an element and not a molecule, each mol contains the same number of atoms as there are mols. So, we have 6.022 x 10^23 atoms of gold.
Now, to find the volume of the sphere, we'll need to use the density of gold. The formula for density is density = mass/volume. So, rearranging the formula, we can find the volume: volume = mass/density.
The mass of 18 moles of gold can be calculated as follows: (18 mol) x (0.197 kg/mol) = 3.546 kg.
Now we'll find the volume of the sphere: volume = (3.546 kg) / (19,300 kg/m3) ≈ 0.183 m3.
Since we know the formula for the volume of a sphere is (4/3)πr^3, we can rearrange it to solve for the radius: r = (3*volume / (4π))^(1/3).
Plugging in the numbers, we get r ≈ (3 * 0.183 / (4π))^(1/3) ≈ 0.133 m.
And finally, since the diameter is twice the radius, the diameter of the sphere would be approximately 2 * 0.133 m ≈ 0.27 meters.
So, the diameter of the sphere made up of 18 mols of gold is approximately 0.27 meters. Just don't juggle it, unless you're really strong!
To find the sphere's diameter, we need to use the given information about the number of moles, atomic mass, and density of gold. Here are the steps to calculate the diameter:
Step 1: Determine the mass of the gold sphere.
To find the mass of the gold sphere, multiply the number of moles by the atomic mass of gold:
Mass of gold = Number of moles × Atomic mass
Mass of gold = 18 mol × 0.197 kg/mol
Step 2: Calculate the volume of the sphere.
The volume of a sphere can be calculated using the formula:
Volume = (4/3) × π × r^3
Since we need to find the diameter, we will use the equation:
Volume = (4/3) × π × (d/2)^3
Step 3: Relate volume, mass, and density equations.
The mass of the gold sphere is equal to the volume multiplied by the density of gold:
Mass of gold = Volume × Density of gold
Step 4: Solve for the diameter.
Now we can equate the volume equations from step 2 and step 3, and solve for the diameter:
(d/2)^3 = (Mass of gold) / (Density of gold)
d/2 = cuberoot((Mass of gold) / (Density of gold))
d = 2 × cuberoot((Mass of gold) / (Density of gold))
Let's calculate the diameter using these steps:
Step 1: Calculate the mass of the gold sphere:
Mass of gold = 18 mol × 0.197 kg/mol
Mass of gold = 3.546 kg
Step 2: Calculate the volume of the sphere:
Volume = (4/3) × π × (d/2)^3
Step 3: Relate volume, mass, and density equations:
Mass of gold = Volume × Density of gold
Step 4: Solve for the diameter:
d = 2 × cuberoot((Mass of gold) / (Density of gold))
Using these calculations, we can determine the diameter of the gold sphere.
To find the diameter of the sphere made up of 18 mols of gold, we need to use the given information about the molar mass of gold and its density.
First, let's calculate the mass of gold in the sphere. We know that 1 mol of gold has a mass of 0.197 kg/mol. So, for 18 mols, the mass would be:
Mass = (0.197 kg/mol) x (18 mol) = 3.546 kg
Now, we can determine the volume of the gold sphere using its mass and density. The formula to calculate the volume of an object is:
Volume = Mass / Density
Using the given density of gold (19,300 kg/m^3) and the mass we calculated (3.546 kg):
Volume = 3.546 kg / 19,300 kg/m^3
Simplifying this, we get:
Volume ≈ 0.0001837 m^3
Since we're dealing with a sphere, the volume can also be expressed as:
Volume = (4/3) * π * R^3
Where R is the radius of the sphere. To find the radius, we rearrange the equation and solve for R:
R = (Volume / (4/3)π)^(1/3)
Substituting the volume value we calculated:
R ≈ (0.0001837 m^3 / (4/3)π)^(1/3)
Evaluating this expression yields:
R ≈ 0.01112 m
Finally, to find the diameter, we multiply the radius by 2:
Diameter = 2 * R ≈ 2 * 0.01112 m ≈ 0.02224 m
Therefore, the diameter of the sphere made up of 18 mols of gold is approximately 0.02224 meters.