How many atoms are present in 48.60 g of Mg?

Question

Naomi Aronson · Accepted Answer

#1.204xx10^(24) "atoms"# of magnesium are present

In order to go from mass of magnesium to atoms of magnesium, we have to do two things:

Convert mass of Mg to moles of Mg using the molar mass of Mg as a conversion factor
Convert moles of Mg to atoms of Mg using Avogadro's number (#6.02xx10^(23)#) as a conversion factor

#color(indigo)("Step 1:"#
Before we start, I should note that the molar mass of Mg is #24.31 g/(mol)#. We can go from mass to moles using dimensional analysis. The key to dimensional analysis is understanding that the units that you don't need any more cancel out, leaving the units that are desired:

#48.60cancelgxx(1mol)/(24.31cancelg)# #= 2.00 mol#

#color(gold)("Step 2:"#
We'll use this relationship:

Using the moles of Mg that we just obtained, we can use Avogrado's number to perform dimensional analysis in order to cancel out units of #mol# to end up with atoms of Mg:

#2.00cancel"mol"xx(6.02xx10^(23) "atoms")/(1cancel"mol")# #= 1.204xx10^(24) "atoms"#

#color(brown)("Thus, 48.60g of Mg is equivalent to"# #1.204xx10^(24) "atoms"#

Caleb Adams · Answer

undefined The following steps are used to find the number of atoms in 48.60 g of magnesium: 1. Calculate the number of moles of magnesium using its molar mass (24.305 g/mol). 2. Convert moles of magnesium to atoms using Avogadro's number (6.022 x 10^23 atoms/mol). This yields the following results: $ \text{Number of moles of magnesium} = \frac{48.60 \, \text{g}}{24.305 \, \text{g/mol}} $. Next, $ \text{Number of atoms of magnesium} = \text{Number of moles of magnesium} \times 6.022 \times 10^{23} \, \text{atoms/mol} $.

Axel Alvarado · Answer

undefined To determine the number of atoms present in 48.60 g of Mg, we'll first need to find the number of moles of Mg using its molar mass.

The molar mass of magnesium (Mg) is approximately 24.305 g/mol.

To find the number of moles of Mg, we use the formula:

$$ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} $$

Substituting the given mass of Mg:

$$ \text{Number of moles} = \frac{48.60 \, \text{g}}{24.305 \, \text{g/mol}} $$

$$ \text{Number of moles} \approx 2 \, \text{mol} $$

Now, using Avogadro's number, which is approximately $6.022 \times 10^{23}$ atoms/mol, we can find the number of atoms present in 2 moles of Mg:

$$ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} $$

$$ \text{Number of atoms} = 2 \times 6.022 \times 10^{23} $$

$$ \text{Number of atoms} \approx 1.204 \times 10^{24} $$

Therefore, there are approximately $1.204 \times 10^{24}$ atoms present in 48.60 g of Mg.