Question

Mass of a single atom of silver is $1.794 \times {10^{ - 22}}$. What is the atomic mass of silver?

Answer 1

Hint: Atomic mass of a substance is the mass of one mole particles or atoms of that substance. There are $6.022 \times {10^{23}}$ particles or atoms in one mole of a substance. Number of particles in one mole is fixed. This number doesn’t depend on temperature and pressure of the substance.

Formula used:
Atomic mass$ = $mass of single atom$ \times 6.022 \times {10^{23}}$

Complete step by step answer:
In this question we have to find the atomic mass of silver. We have given mass of one atom of silver. We know that there is an Avogadro number of particles in one mole of a substance and the mass of an Avogadro number of particles is the atomic mass of a substance. Avogadro number is equal to $6.022 \times {10^{23}}$. This means there are $6.022 \times {10^{23}}$ numbers of atoms in one mole of silver atoms. Mass of one atom of silver is $1.794 \times {10^{ - 22}}$. Therefore mass of Avogadro number of atoms of silver can be obtained by multiplying Avogadro number with mass of one silver atom. So,
Mass of Avogadro number of particles$ = $mass of single atom$ \times 6.022 \times {10^{23}}$
Mass of Avogadro number of particles$ = $ $1.794 \times {10^{ - 22}} \times 6.022 \times {10^{23}}$
(Mass of one atom is given in question)
Solving this we get:
Mass of Avogadro number of particles$ = $ $108$
As explained above, mass of Avogadro number of particles is equal to atomic mass of a substance. This means the atomic mass of silver is $108$.


Note:
According to the ideal gas equation, $PV = nRT$. Where, $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is gas constant and $T$ is temperature. From this equation we can observe that the number of moles of gas depends on temperature, pressure and volume of the gas.