How much energy, in joules, must be absorbed to convert to Na all the atoms present in 1.00mg of gaseous Na? The first ionization energy of Na is 495.8kj/mol .
Assume you mean to Na+
Na is 23 grams/mole
so we have 10^-3 grams (1 mole/23 grams) = .0435 *10^-3 moles
.0435 * 10^-3 * 495.8 *10^3 J/mole = 21.6 Joules
Well, let's start by converting the mass of Na to moles. We know the molar mass of Na is approximately 22.99 g/mol. So, 1.00 mg is equal to 0.001 g, which is equivalent to 4.35 x 10^-5 moles of Na.
Now, we can use the first ionization energy of Na to calculate the energy required to convert all the atoms. The first ionization energy is given as 495.8 kJ/mol, which is equal to 495.8 x 10^3 J/mol.
Since we have 4.35 x 10^-5 moles of Na, we can multiply this by the ionization energy to get the total energy required:
Energy = 4.35 x 10^-5 moles * 495.8 x 10^3 J/mol
Now, let's do some quick math:
Energy = 2.16 J
Therefore, approximately 2.16 Joules of energy must be absorbed to convert all the atoms present in 1.00 mg of gaseous Na. It's not a huge amount of energy, but it's enough to make the atoms a bit jumpy. Careful, though – they might get salty!
To calculate the amount of energy required to convert all the atoms present in 1.00 mg of gaseous Na to Na+ ions, we need to follow these steps:
Step 1: Convert the mass of Na to moles:
We need to determine the number of moles by dividing the given mass by the molar mass of Na.
The molar mass of Na is 22.99 g/mol.
1.00 mg = 0.001 g
Number of moles = (0.001 g) / (22.99 g/mol)
Number of moles = 4.35 x 10^-5 mol
Step 2: Calculate the energy required:
The first ionization energy of Na is given as 495.8 kJ/mol.
To find the energy required for 4.35 x 10^-5 mol of Na, we can use the following calculation:
Energy = (First ionization energy) x (Number of moles)
Energy = (495.8 kJ/mol) x (4.35 x 10^-5 mol)
However, we need to convert kJ to Joules by realizing that 1 kJ = 1000 J.
Energy = (495.8 kJ/mol) x (4.35 x 10^-5 mol) x (1000 J/ 1 kJ)
Calculating this expression will give us the energy required in Joules.
To calculate the energy required to convert all the atoms present in 1.00 mg of gaseous Na, we need to use the following steps:
Step 1: Convert the mass of Na from milligrams to moles.
To do this, we need the molar mass of Na, which is approximately 22.99 g/mol.
1 mg = 0.001 g
So, 1.00 mg = 0.001 g
Now, we can calculate the number of moles:
moles = mass / molar mass
moles of Na = 0.001 g / 22.99 g/mol
Step 2: Calculate the total energy required to convert all the atoms.
The first ionization energy of Na is given as 495.8 kJ/mol.
Since we have determined the number of moles of Na in Step 1, we can now calculate the total energy required:
total energy = ionization energy × moles of Na
We will now substitute the values into the equation:
moles of Na = 0.001 g / 22.99 g/mol
moles of Na = 0.00004349847 mol (rounded to 8 decimal places)
total energy = 495.8 kJ/mol × 0.00004349847 mol
Now, we convert kJ to J by multiplying by 1000:
total energy = (495.8 kJ/mol × 0.00004349847 mol) × 1000
total energy = 21.54324646 J
Therefore, the total energy required to convert all the atoms present in 1.00 mg of gaseous Na is approximately 21.54 J.