Question

What is the percentage composition by weight of Ag in $Ag{{\left( N{{H}_{3}} \right)}_{2}}^{+}$ ?$\_Ag{{\left( N{{H}_{3}} \right)}_{2}}^{+}\to \_A{{g}^{+}}+\_N{{H}_{3}}$
[A] 4.2
[B] 19.7
[C] 76.1
[D] 80.3
[E] 95.8

Answer 1

Hint: To solve this firstly find the molecular weight of the given compound. To find the composition of a particular element in the compound, divide its molar mass by the molecular weight of the compound. Multiply it by 100 to get percentage composition by weight.

Complete step by step solution:
We know that the percentage composition by weight of any element is the total mass in that compound due to that element.
In simpler words, we can say that it is the percentage of mass occupied by a certain element in a compound.
Adding the percentage compositions of all the elements of a compound gives us the total mass of the compound, which is 100.
Now, let us discuss how to find out the percentage composition of a certain element.
Firstly, we will need the molar mass of the element that we are calculating the percentage composition for. We have to divide its molar mass by the molar mass of the compound. To find the molar mass of the compound, we have to add the masses of all the atoms in that compound. Lastly, multiplying it by 100 will give us the percentage composition.
Now let us calculate the percentage composition by weight for silver in $Ag{{\left( N{{H}_{3}} \right)}_{2}}^{+}$.
The mass of silver = 108.
Mass of nitrogen is 14.
For hydrogen, mass is 1 and since there are 3 hydrogen atoms therefore we can write 3.
Therefore, the formula mass of $Ag{{\left( N{{H}_{3}} \right)}_{2}}^{+}$ will be 108 + 2 $\times $ (12+3) = 142g/mol.
Therefore, the molecular weight of $Ag{{\left( N{{H}_{3}} \right)}_{2}}^{+}$ is 142g/mol.
And the molar mass of silver is 108g/mol
Therefore, the percentage composition of silver by weight will be $\dfrac{108}{142}\times 100=76.056%$
We can see from the above calculation that the percentage weight of silver is 76.056% which is almost equal to 76.1%.

Therefore, the correct answer is option [C] 76.1.

Note: We should not be confused between mass percentage composition and the atomic percentage composition. Here, the mass percentage composition is the highest for silver, followed by nitrogen and hydrogen as silver is the heavier from the two by mass. If we see the atomic composition, it is the highest for hydrogen as we have 6 atoms of hydrogen whereas for nitrogen and silver we only have 2 and 1 respectively.