What mass of carbon has the same number of atoms as 76.78 g of chromium?
Answers
Answer:
We relate the two masses of the elements using their numbers of atoms by converting the mass (m) to the number of moles (n), then to a number of atoms. The molar mass (MM) of chromium is
51.996
g
/
m
o
l
. The molar mass of carbon is
12.011
g
/
m
o
l
. Value of Avogadro's number (Av) is
6.022
×
10
−
23
m
o
l
−
1
.
Number of moles of chromium:
n
C
r
=
m
C
r
M
M
C
r
n
C
r
=
45.27
g
51.996
g
/
m
o
l
n
C
r
=
0.8706
m
o
l
Number of chromium atoms:
No. of atoms
=
n
C
r
×
A
v
No. of atoms
=
0.8706
m
o
l
×
6.022
×
10
23
m
o
l
−
1
No. of atoms
=
5.243
×
10
23
Since both elements have the same number of atoms, we use the number of chromium atoms to calculate the number of moles of carbon.
Number of moles of carbon:
No. of atoms
=
n
C
×
A
v
5.243
×
10
23
=
n
C
×
6.022
×
10
23
m
o
l
−
1
n
C
=
5.243
×
10
23
6.022
×
10
23
m
o
l
−
1
n
C
=
0.8706
m
o
l
Mass of carbon:
n
C
=
m
C
M
M
C
0.8706
m
o
l
=
m
C
12.011
g
/
m
o
l
m
C
=
0.8706
m
o
l
×
12.011
g
/
m
o
l
m
C
=
10.46
g