A piece of copper contains 3.6 x 10^8 atoms. What is the volume of the sample in units of liters?
I know that first you have to get atoms to cancel out but them I do not know what to do!
To find the volume of the sample in liters, you need to know the number of atoms in the sample and some information about the properties of copper.
First, let's start by canceling out the atoms in the given information. The number of atoms, 3.6 x 10^8, is considered the Avogadro number (6.022 x 10^23) times the number of moles of copper. By dividing the given number of atoms by Avogadro's number, we can determine the number of moles of copper in the sample.
3.6 x 10^8 atoms ÷ 6.022 x 10^23 atoms/mol ≈ 5.98 x 10^-16 mol
Now, to proceed further, we need to know the molar mass of copper. The molar mass of copper is 63.55 grams/mole. By multiplying the number of moles we just calculated with the molar mass, we can find the mass of the copper sample.
5.98 x 10^-16 mol × 63.55 g/mol ≈ 3.8 x 10^-14 g
Next, we need to convert the mass from grams to kilograms. To do this, divide the mass by 1000.
3.8 x 10^-14 g ÷ 1000 ≈ 3.8 x 10^-17 kg
The next step is to find the density of copper. The density of copper is approximately 8.96 grams per cubic centimeter (g/cm³). To convert this to kilograms per liter, we need to divide by 1000 for the mass and multiply by 1000 for the volume.
8.96 g/cm³ × (1 kg/1000 g) × (1000 L/1 m³) ≈ 8.96 kg/m³
Now we have the density of copper in kilograms per liter.
Finally, to find the volume in liters, divide the mass (in kilograms) of the copper sample by the density (in kilograms per liter) of copper.
Volume = 3.8 x 10^-17 kg ÷ 8.96 kg/L ≈ 4.2 x 10^-18 L
Therefore, the volume of the copper sample is approximately 4.2 x 10^-18 liters.