Question

How many grams are there in $4.6 \times {10^{24}}atoms$ of silver?

Answer 1

Here we need to determine the mass of a given number of atoms of an element. Hence , to determine it, we need to identify the equalities between moles of element and atoms of element and also between moles of element and its molar mass. Here also we need to remind that a mole is a collection of $6.023 \times {10^{23}}$ particles , ions or atoms. In the type of questions, we just use avogadro number to determine the number of atoms in a given gram.

Complete answer:
First of all we need to know atoms in $1mole$ of $Ag$.
Therefore , atoms in $1mole$ of $Ag$ $6.022 \times {10^{23}}atoms$ of $Ag$
Next we should know the molar mass of $Ag$ for doing further calculations.
Therefore, molar mass of $Ag$ $= 107.87 g/mol$
In next step we have to multiply the given number of atoms of silver by $\dfrac{{1mol Ag}}{{6.022 \times {{10}^{23}}atoms Ag}}$
Then the equation will be as follows,
$\dfrac{{1mol Ag}}{{6.022 \times {{10}^{23}}atoms Ag}} \times 4.6 \times {10^{24}}atoms Ag$
Then the above equation should be multiplied with molar mass of silver.
Then the equations become as follows,
$\dfrac{{1mol Ag}}{{6.022 \times {{10}^{23}}atoms Ag}} \times 4.6 \times {10^{24}}atoms Ag \times \dfrac{{107.87g Ag}}{{1molAg}}$
$= 820g Ag$

Therefore , $820g$ are there in $4.6 \times {10^{24}}atoms$of silver.

Note: So simply we can find the gram in particular number of atoms of a given element just by remembering the simple calculations we did above. So , if we need to calculate number of atoms in a sample , just we have to divide its weight in gram by atomic mass and then we have to multiply the result by avogadro number which is $6.022 \times {10^{23}}atoms$. If we have three pieces of information like number of atoms , molar mass and avogadro number , thus we can easily calculate the gram from the given sample.