Question

Potassium sulphate is isomorphous with potassium chromate which contains \[26.79\% \] by weight of chromium. Find out the atomic weight of chromium.
1) \[24\]
2) \[32\]
3) \[51.96\]
4) \[53.2\]

Answer 1

Hint: In chemistry, periodic tables play a vital role. In the periodic table there are totally \[118\] elements. In the periodic table there are totally \[18\] columns and \[7\] rows. The columns are called groups. Hence, \[18\] groups in the periodic table. The rows are called periods. Hence, totally \[7\] period in the table. The atomic number of the element is nothing but the number of electrons or number of protons. The mass number of the atom is nothing but the sum of the number of protons and number of neutrons.
Formula used:
The molecular weight of the molecule is nothing but the sum of atomic weight of the atom present in the molecule.
The weight percentage of the atom depends on the atomic weight of that atom and molecular weight.
\[{\text{The Weight Percentage Of The Atom = }}\dfrac{{{\text{the atomic weight of atom }}}}{{{\text{molecular weight}}}} \times {\text{100 }}\]

Complete answer:
Potassium sulphate is isomorphous with potassium chromate.
The molecular weight of Potassium sulphate is\[{{\text{K}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\].
The molecular weight of potassium chromate is\[{{\text{K}}_{\text{2}}}{\text{Cr}}{{\text{O}}_{\text{4}}}\].
The atomic weight of potassium is \[33.1g\]
The atomic weight of oxygen is \[16g\]
The atomic weight of chromium is \[{\text{x}}\].
Hence the molecular weight of potassium chromate is,
\[ = (39.1 \times 2) + {\text{x}} + (16 \times 4)\]
\[ = 78.2 + {\text{x}} + 64\]
\[ = 142.2 + {\text{x}}\]
The weight percentage of chromium in potassium chromate is \[26.79\% \].
We calculate the atomic weight of chromium in \[26.79\% \] of potassium chromate
\[{\text{The Weight Percentage Of The Atom = }}\dfrac{{{\text{the atomic weight of atom }}}}{{{\text{molecular weight}}}} \times {\text{100 }}\]
\[{\text{26}}{\text{.79 = }}\dfrac{{{\text{x }}}}{{142.2 + {\text{x}}}} \times {\text{100}}\]
\[{\text{0}}{\text{.2679 = }}\dfrac{{{\text{x }}}}{{142.2 + {\text{x}}}}\]
\[{\text{0}}{\text{.2679}} \times (142.2 + {\text{x) = x}}\]
\[{\text{x}} = 51.96\]
According to the above calculation, we conclude the atomic weight of chromium in \[26.79\% \] of potassium chromate is \[51.96\].

Hence, option C is correct.

Note:
In chemistry each element has a specific symbol in the periodic table. Inside the atom having electrons, protons and neutrons. The electrons revolve around the nucleus in the atom. The neutrons and protons are present inside the nucleus. The electrons are arranged in the energy level of the shell in the atom.