# what is the mass of chromium in this sample?

If the total number of atoms in a sample of potassium dichromate is $$2.13\cdot10^{24}$$ , then the amount of chromium in this sample is? the answer that I've come up with is $$367.64\ \mathrm g$$ but in fact the solution in my book is $$33.4\ \mathrm g$$.

• Well how did you come up with your answer? – bon Feb 17 '16 at 18:55
• 2.13*10^24/6.022*10^23=3.54 mol *2=7.07 since the molecular form of the compound is K2Cr2O7 , then I"v calculated the mass by multiplying moles by 52 – 119 j7fly Feb 17 '16 at 19:01

I like to solve such assignments using Python as a scientific calculator.

import scipy.constants

# number of atoms in sample
N_ATOMS_TOTAL = 2.13E+24

# atomic mass of chromium
M_CR = 51.9961 # g/mol

# ratio of chromium atoms to total atoms in K2Cr2O7
CR_RATIO = 2/11

# moles of Cr in sample
n_cr = N_ATOMS_TOTAL * CR_RATIO / scipy.constants.Avogadro

mass_cr = n_cr * M_CR # mass of chromium in g

mass_cr


Let me explain:

• You have an unknown mass (in gramm) of potassium dichromate, $\ce{K2Cr2O7}$.

• The total number of atoms in this sample is $2.13\cdot10^{24}$.

### How can you calculate the number of chromium atoms in the sample?

• You need to determine the ratio of $\ce{Cr}$ to all atoms in $\ce{K2Cr2O7}$, and that's $\frac{2}{11}$ atoms.

### I know the number of $\ce{Cr}$ atoms now, but how many moles is that?

• You know that 1 mol of an element has $6.02214129\cdot10^{23}$ atoms of that element (Avogadro's number).
• Divide the number of $\ce{Cr}$ atoms determined before by Avogadro's number to determine the number of moles of $\ce{Cr}$.

### I know the number of moles of $\ce{Cr}$ now, but what is the weight?

• You know that the standard atomic weight of $\ce{Cr}$ is 51.9961.
• Multiply the standard atomic weight with the number of moles to get the weight.
• Im so confused :( , I know that when a substance like H20 has 2.5 mol it means H has number of moles=2*2.5 . but If I used the way u solved the question it will be 2 H atoms+1 O atom=3 atoms , to calculate H it will be (2/3)*2.5 and the result is different then :( – 119 j7fly Feb 17 '16 at 19:49
• @119j7fly $\ce{K2Cr2O7}$ has 2 $\ce{K}$ + 2 $\ce{Cr}$ + 7 $\ce{O}$ atoms, that's 11 atoms in total. Two of these are $\ce{Cr}$ atoms. This means that the number of $\ce{Cr}$ atoms in the sample is 2/11 * the total number of atoms :) – Klaus-Dieter Warzecha Feb 17 '16 at 20:05
• its very clear right now thanx a lot mr Klaus. – 119 j7fly Feb 17 '16 at 20:58