Question

The average mass of one gold atom in a sample of naturally occurring gold is $\text{3}\text{.257x1}{{\text{0}}^{-22}}$g. Using this, the molar mass of gold calculated is:
(a) 196.136g
(b) 193.124g
(c) 197.169g
(d) 198.269g

Answer 1

Hint: We know that the mass of an atom is equal to the ratio of atomic mass to Avogadro’s number. One mole of molecules or ion refers to the quantity in number possessing a mass equal to its atomic or molecular mass in grams. Number of particles present in one mole of any substance is $\text{6}\text{.022x1}{{\text{0}}^{23}}$. This value is called Avogadro’s number.

Complete step by step solution:
As we know that mass of one mole of atoms is known as molar mass.
Therefore, 1 mole = $\text{6}\text{.022x1}{{\text{0}}^{23}}$(Avogadro’s number of atoms)
And mass of one mole of a molecule or ion is equivalent to its relative atomic or molecular mass in grams.
Mathematically, we can express the definition of Avogadro’s number relating to the question as mentioned below:
Molar Mass of Gold=Average Mass of one atom of gold x Avogadro’s Number
Here, the average mass of one atom of gold in the question is given as $\text{3}\text{.257x1}{{\text{0}}^{-22}}$
Therefore, Mass of gold=$\text{6}\text{.022x1}{{\text{0}}^{23}}$x $\text{3}\text{.257x1}{{\text{0}}^{-22}}$= 196.136g
So, as per the calculation, we get the answer as 196.136g
Therefore, the correct option is (a) 196.136g.

Note: The mole allows scientists to calculate the number of elementary entities (usually atoms or molecules) in a certain mass of a given substance.
Avogadro’s number is an absolute number: there are $\text{6}\text{.022x1}{{\text{0}}^{23}}$elementary entities in 1 mole. This can also be written as $\text{6}\text{.022x1}{{\text{0}}^{23}}$ $\text{mo}{{\text{l}}^{-1}}$.
The mass of one mole of a substance is equal to that substance’s molecular weight. For example, the mean molecular weight of water is 18.015 atomic mass units (amu), so one mole of water weighs 18.015 grams.