Help!!
How many atoms in 3.45 mL of water?
(H2O only;mL=g)
and
If you are out panning for gold and discover a nugget that is exactly 2.50 moles, how many molecules, atoms, and grams would you have? At a cost of $375 per ounce, what would be the value of gold?
To calculate the number of atoms in a given volume of water, you need to know the molar mass of water and use Avogadro's number. Here's how you can find the answer:
1. Determine the molar mass of water (H2O):
- Hydrogen (H) has a molar mass of approximately 1.008 g/mol.
- Oxygen (O) has a molar mass of approximately 16.00 g/mol.
- Since water has two hydrogen atoms and one oxygen atom, the molar mass of water is: (2 * 1.008 g/mol) + (1 * 16.00 g/mol) = 18.016 g/mol.
2. Convert the given volume of water from milliliters (mL) to grams (g):
- Since 1 mL of water has a mass of 1 g (as stated in the question), we do not need to perform any conversion.
3. Determine the number of moles of water:
- Moles = Mass / Molar mass
- In this case, Moles = 3.45 g / 18.016 g/mol = 0.1913 mol (approximately)
4. Calculate the number of atoms in the given volume of water:
- Number of atoms = Moles * Avogadro's number
- Avogadro's number is approximately 6.022 x 10^23 atoms/mol.
- Number of atoms = 0.1913 mol * 6.022 x 10^23 atoms/mol = 1.152 x 10^23 atoms (approximately)
Therefore, there would be approximately 1.152 x 10^23 atoms in 3.45 mL of water (H2O).
Now, let's move on to the second question about panning for gold:
1. Determine the number of molecules:
- Since we have 2.50 moles of gold, we can use Avogadro's number to find the number of molecules.
- Number of molecules = Moles * Avogadro's number
- Number of molecules = 2.50 mol * 6.022 x 10^23 molecules/mol = 1.5055 x 10^24 molecules (approximately)
2. Calculate the number of atoms:
- Gold (Au) is an element, and in 1 mole of gold, there are 6.022 x 10^23 atoms.
- Number of atoms = Moles * Avogadro's number
- Number of atoms = 2.50 mol * 6.022 x 10^23 atoms/mol = 1.5055 x 10^24 atoms (approximately)
3. Convert the number of moles to grams:
- The molar mass of gold (Au) is approximately 197.0 g/mol.
- Mass = Moles * Molar mass
- Mass = 2.50 mol * 197.0 g/mol = 492.5 g
4. Calculate the value of gold:
- To find the value of gold, we need to know the cost per ounce.
- Since we have the mass in grams, we need to convert it to ounces by dividing by 28.35 (1 ounce = 28.35 grams).
- Number of ounces = Mass / 28.35
- Number of ounces = 492.5 g / 28.35 g/oz = 17.36 ounces (approximately)
- The value of gold can be calculated by multiplying the number of ounces by the cost per ounce:
- Value of gold = Number of ounces * Cost per ounce
- Value of gold = 17.36 oz * $375/oz ≈ $6510
Therefore, in this scenario, the value of the discovered gold nugget would be approximately $6510.