How many atoms of oxygen are contained in 47.6 g of #Al_2(CO_3)_3#? The molar mass of #Al_2(CO_3)_3# is 233.99 g/mol?

Question

Jeremiah Adams · Accepted Answer

#1.10 * 10^(24)#

The first thing that you need to do here is to convert the mass of aluminium carbonate to moles by using the compound's molar mass.

In this case, you know that aluminium carbonate has a molar mass of #"233.99 g mol"^(-1)#, which means that #1# mole of aluminium carbonate has a mass of #"233.99 g"#.

You can thus say that your sample will contain

#47.6 color(red)(cancel(color(black)("g"))) * ("1 mole Al"_2("CO"_3)_3)/(233.99color(red)(cancel(color(black)("g")))) = "0.2034 moles Al"_2("CO"_3)_3#

Now, the chemical formula of aluminium carbonate tells you that every mole of this salt contains

This means that your sample will contain

#0.2034 color(red)(cancel(color(black)("moles Al"_2("CO"_3)_3))) * "9 moles O"/(1color(red)(cancel(color(black)("mole Al"_2("CO"_3)_3)))) = "1.831 moles O"#

Finally, to convert this to atoms of oxygen, use Avogadro's constant, which tells you that in order to have #1# mole of atoms of oxygen, you need to have #6.022 * 10^(23)# atoms of oxygen.

#1.831 color(red)(cancel(color(black)("moles O"))) * (6.022 * 10^(23)color(white)(.)"atoms O")/(1color(red)(cancel(color(black)("mole O")))) = color(darkgreen)(ul(color(black)(1.10 * 10^(24)color(white)(.)"atoms O")))#

The answer is rounded to three sig figs, the number of sig figs you have for the mass of aluminium carbonate.

Mateo Aguilar · Answer

undefined To find the number of atoms of oxygen in 47.6 g of Al₂(CO₃)₃, first calculate the number of moles of Al₂(CO₃)₃ using its molar mass. Then, use the chemical formula to determine the number of oxygen atoms present. Finally, multiply the number of moles of oxygen atoms by Avogadro's number to find the total number of atoms.

1. Calculate moles of Al₂(CO₃)₃:
   $ \text{moles} = \frac{47.6 \, \text{g}}{233.99 \, \text{g/mol}} $

2. Determine moles of oxygen atoms in Al₂(CO₃)₃:
   $ \text{moles of O} = 3 \times \text{moles of Al}_2(\text{CO}_3)_3 $

3. Calculate the number of oxygen atoms:
   $ \text{Number of atoms of O} = (\text{moles of O}) \times (6.022 \times 10^{23} \, \text{atoms/mol}) $