Chromium is ametal that is added to steel to improve its resitance to corrosion. Calculate both the number of miles in a sample of Cr containing 5.00 x 10^20 atms and the mass of the sample.
Ok this is how I worked it.
1 mole of Cr = 51.996g = 6.022 x 10^23 atoms
(whatever mass is) 6.022 x 10^23 atom/51.996g = 5.00 x 10^20
After I solved that, I ended up with the mass being 4.32g
Okay now for mole.
4.32g 1 mole/51.996g = .0831 mole
Correct?
No, you have a math error.
moles= 5*E20/6.02E23=.000831 moles
mass=moles*51.996 which is not what you have.
So mass would be .0432?
the reason why i got the problem completely wrong was because i got the mass wrong?
Yes, your calculations are correct.
To calculate the mass of the sample, you used the conversion factor of 6.022 x 10^23 atoms per mole of chromium (Cr). By setting up a proportion, you found that the mass is 4.32 grams.
For the number of moles in the sample, you divided the mass of the sample (4.32g) by the molar mass of chromium (51.996g/mol), which gave you 0.0831 moles.
Therefore, the mass of the sample is 4.32 grams, and the number of moles in the sample is 0.0831 moles.
Yes, your calculations are correct. Let's go through the steps again to calculate both the number of moles and the mass of the sample:
Step 1: Determine the molar mass of chromium (Cr).
The molar mass of chromium is 51.996 g/mol.
Step 2: Calculate the number of moles of chromium in the given sample.
We are given that the sample contains 5.00 x 10^20 atoms. Since 1 mole of chromium contains 6.022 x 10^23 atoms, we can set up the following proportion:
(5.00 x 10^20 atoms) / (6.022 x 10^23 atoms/mol) = (x mol) / (1 mol)
Solving for x, we get:
x = (5.00 x 10^20 atoms) / (6.022 x 10^23 atoms/mol) ≈ 8.31 x 10^-4 mol
So, the number of moles in the sample is approximately 8.31 x 10^-4 mol.
Step 3: Calculate the mass of the sample.
Using the given information and the molar mass of chromium, we can set up another proportion:
(8.31 x 10^-4 mol) / (1 mol) = (mass) / (51.996 g)
Solving for mass, we get:
mass = (8.31 x 10^-4 mol) * (51.996 g/mol) ≈ 4.32 g
Therefore, the mass of the sample is approximately 4.32 g.
So, your final answers are:
- The number of moles in the sample is approximately 8.31 x 10^-4 mol.
- The mass of the sample is approximately 4.32 g.