A piece of copper contains 3.6 x 10^8 atoms. What is the volume of the sample in units of liters?
i have no idea how to start this. Please help thank you!!!
I assume you know the density of copper, and the mass of each atom.
massatom= molmassCu/avagradrosnumber
=\
massallatoms= 3.6E8*massatomabove
volume = massallatoms/densityCu.
if you density of Cu is in grams/cm^3, then you will have to divide the volume by a thousand (1E3) to have it in liters.
To find the volume of the copper sample, we need to have information about the density of copper. The density of copper is known to be 8.96 grams per cubic centimeter (g/cm³).
Given that the sample contains 3.6 x 10^8 atoms of copper, we can calculate the mass of the sample using the atomic mass of copper (approximately 63.55 grams/mole).
1. Calculate the mass of the copper sample:
To find the mass, we need to determine the number of moles and then multiply by the molar mass. The formula found on periodic table for copper is 63.55 g/mol.
Number of moles = Number of atoms / Avogadro's number (6.022 x 10^23)
Number of moles = (3.6 x 10^8) / (6.022 x 10^23)
2. Calculate the mass of the sample:
Mass = Number of moles x Molar mass
Mass = (3.6 x 10^8 / 6.022 x 10^23) x 63.55
3. Convert the mass to grams:
To convert grams to milliliters or liters, we need to know the density of the substance. As mentioned earlier, the density of copper is 8.96 g/cm³.
4. Calculate the volume of the sample:
Volume = Mass / Density
Now we have all the values required for calculation. Let's proceed to solve the problem:
Volume = (3.6 x 10^8 / 6.022 x 10^23) x 63.55 / 8.96
Volume = 0.955 x 10^-15 cm³
To convert cm³ to liters, divide by 1000:
Volume = 0.955 x 10^-15 cm³ / 1000
Volume = 9.55 x 10^-18 liters
Therefore, the volume of the copper sample is approximately 9.55 x 10^-18 liters.
To find the volume of the sample in units of liters, you need to follow these steps:
Step 1: Determine the formula mass of copper (Cu).
The atomic mass of copper (Cu) is approximately 63.55 grams per mole (g/mol). Therefore, one mole of copper weighs 63.55 grams.
Step 2: Calculate the number of moles of copper in the given sample.
Given that the sample contains 3.6 x 10^8 atoms, you can use Avogadro's number (6.022 x 10^23 atoms/mol) to convert the given number of atoms to moles.
Number of moles of copper = (3.6 x 10^8 atoms) / (6.022 x 10^23 atoms/mol)
Step 3: Calculate the mass of the sample.
Multiply the number of moles of copper by the formula mass of copper (Cu) to find the mass of the sample in grams.
Mass of the sample = Number of moles of copper x Formula mass of copper
Step 4: Convert the mass to liters.
1 liter of copper has a mass of 8.96 grams (the density of copper is 8.96 g/cm³). Therefore, you can convert the mass in grams to liters.
Volume of the sample = Mass of the sample (in grams) / 8.96 g/cm³
It is important to note that the density of copper is temperature-dependent. The given value assumes room temperature conditions, and if you need a more accurate result, you may need to consider the actual temperature at which the measurement is being made.