How many grams of neon $(Ne)$ will have the same number of atoms as $4 g$ of calcium $(Ca)$ ?

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Solution

Step 1: Calculate the number of moles in $4 g$ of calcium:
We know that one mole of any substance contains a mass equal to its atomic mass.
Therefore,
One mole of calcium $(Ca)$ = $40 g$ of $(Ca)$
$1 g$ of $(Ca)$ = $1 g \times (\frac{1 mol}{40 g})$
$1 g$ of $(Ca)$ = $4 g \times (\frac{1 mol}{40 g})$ = $0.1 mol$ of calcium.
Step 2: Calculate the number of atoms in one gram of calcium:
We know from Avagadro's number,
$1 mol$ of $(Ca)$ = $(6.022 \times 10^{23})$ atoms of calcium.
$0.1 mol$ of calcium = $0.1 \times (6.022 \times 10^{23})$ = $0.6022 \times 10^{23}$ atoms of calcium
$4 g$ of calcium = $0.6022 \times 10^{23}$ atoms of calcium
Now, the number of atoms of calcium is equal to the number of atoms of neon.
Thus, the number of atoms of neon $(Ne)$ = $0.6022 \times 10^{23}$
Step 3: Calculate the number of moles of neon in $0.6022 \times 10^{23}$ atoms of neon:
We know from Avagadro's number,
$1 mol$ of $(Ne)$ = $(6.022 \times 10^{23})$ atoms of neon.
$0.1 mol$ of $(Ne)$ = $\frac{(6.022 \times 10^{23})}{10}$ = $0.6022 \times 10^{23}$
Step4: Calculate the mass of neon in $0.1 mol$ :
We know that one mole of any substance contains a mass equal to its atomic mass.
Therefore,
$1 mol$ of neon = $20 g$ of $(Ne)$
$0.1 mol$ of $(Ne)$ = $\frac{20 g}{10}$ = $2 g$
Hence, $2 g$ of neon $(Ne)$ will have the same number of atoms as $4 g$ of calcium $(Ca)$ .

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