The density of copper is 8.96 g cm^−3 and its molar
mass is 64 g mol^−1.
The mass of an atom of copper is 1.1*10^-22 g
Determine the number of copper atoms per
cubic metre.
1m^3 * 10^6cm^3/m^3 * 8.96g/cm^3 * 1atom/(1.1*10^-22 g) = ? atoms
the molar mass does not come into play
Thank you! I realized my problem was that I didn't convert g/cm^3 to g/m^3 correctly
The density of copper is 8.96 g cm^−3 and its molar
mass is 64 g mol^−1.
To determine the number of copper atoms per cubic meter, we need to follow a series of steps:
Step 1: Calculate the volume of one copper atom:
The given mass of a copper atom is 1.1 * 10^-22 g. Knowing the density of copper, which is 8.96 g cm^-3, we can calculate the volume of one copper atom using the formula:
Volume = Mass / Density
Volume = 1.1 * 10^-22 g / 8.96 g cm^-3
Step 2: Convert cm^3 to m^3:
Since we want to find the number of atoms per cubic meter, we need to convert the volume from cm^3 to m^3. Since 1 m = 100 cm, we can convert as follows:
Volume (m^3) = Volume (cm^3) / (100 cm)^3
Step 3: Calculate the number of moles in one copper atom:
Given that the molar mass of copper is 64 g mol^-1, we can calculate the number of moles in one copper atom using the formula:
Number of moles = Mass / Molar mass
Number of moles = 1.1 * 10^-22 g / 64 g mol^-1
Step 4: Calculate Avogadro's number:
Avogadro's number, denoted as N_A, is a constant equal to 6.022 * 10^23 mol^-1.
Step 5: Calculate the number of copper atoms per cubic meter:
To find the number of copper atoms per cubic meter, we need to multiply the number of moles in one copper atom by Avogadro's number and multiply the result by the conversion factor from cm^3 to m^3:
Number of atoms per m^3 = (Number of moles * Avogadro's number) / Volume (m^3)
By plugging in the values calculated in the previous steps, you can find the final answer.