Question

How many grams of sodium will have the same number of atoms as 6 grams of magnesium?
(Na=23, Mg=24)
A. 5.75 g
B. 5 g
C. 5.50 g
D. 5.25 g

Answer 1

Hint: Here in the question, it is given that the number of atoms of both the elements i.e., sodium and magnesium are equal. So, to find the number of moles and thus the number of atoms, we use the formula given below:
\[N = \dfrac{m}{M}\]
In the question, we are provided by the given mass of Mg and molar mass of both Na and Mg, from where we can find the number of moles for magnesium and thus the required mass of sodium.

Complete answer:
First of all, we know that if two species have the same number of atoms, they must have the same number of moles, because the number of atoms present in 1 mole is equal to \[6.022 \times {10^{23}}\]
To calculate the number of moles of any substance present in the sample, we use the formula given below:
\[N = \dfrac{m}{M}\]
Here, N is the number of moles present in the sample
m is the given mass,
M is the molar mass of the element.
Now, here we need to find the number of moles for magnesium (Mg):
By using the formula mentioned above:
Moles of Mg: \[N = {\text{ }}\dfrac{{given{\text{ }}mass{\text{ }}of{\text{ }}Mg}}{{molar{\text{ }}mass{\text{ }}of{\text{ }}Mg}}\] = \[\dfrac{6}{{24}}\] = \[\dfrac{1}{4}\] = 0.25 moles
Now, we know that, number of moles of magnesium = number of moles of sodium.
Thus, moles of Na: \[N = {\text{ }}\dfrac{{given{\text{ }}mass{\text{ }}of{\text{ Na}}}}{{molar{\text{ }}mass{\text{ }}of{\text{ Na}}}}\] = \[\dfrac{m}{{23}}\] = 0.25
Thus, \[m = 0.25 \times 23 = 5.75g\]

Hence, option A is the correct option..

Note: The mole is the unit to measure the quantity of substance present in any sample and number of atoms present in 1 mole is equal to \[6.022 \times {10^{23}}\] where \[6.022 \times {10^{23}}\] is NA called the Avogadro number.