Answer:
[tex]\boxed{\boxed {\sf 23.0 \ g \ Ba(NO_3)_2}}[/tex]
Explanation:
We are asked to find the mass of 5.30 ×10²² formula units of barium nitrate.
First, we convert formula units to moles using Avogadro's Number or 6.022×10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this case, the particles are formula units of barium nitrate.
Set up a conversion factor using Avogadro's Number.
[tex]\frac{6.022 \times 10^{23} \ formula \ units \ Ba(NO_3)_2}{ 1 \ mol \ Ba (NO_3)_2}[/tex]
We are converting 5.30×10²² formula units, so we multiply by this value.
[tex]5.30 \times 10^{22} \ formula \ units \ Ba(NO_3)_2 *\frac{6.022 \times 10^{23} \ formula \ units \ Ba(NO_3)_2}{ 1 \ mol \ Ba (NO_3)_2}[/tex]
Flip the conversion factor so the units of formula units of barium nitrate cancel.
[tex]5.30 \times 10^{22} \ formula \ units \ Ba(NO_3)_2 *\frac{ 1 \ mol \ Ba (NO_3)_2}{6.022 \times 10^{23} \ formula \ units \ Ba(NO_3)_2}[/tex]
[tex]5.30 \times 10^{22} *\frac{ 1 \ mol \ Ba (NO_3)_2}{6.022 \times 10^{23}}[/tex]
[tex]\frac{5.30 \times 10^{22} }{6.022 \times 10^{23}} \ mol \ Ba(NO_3)_2[/tex]
[tex]0.0880106276984 \ mol \ Ba(NO_3)_2[/tex]
Next, convert moles to grams using the molar mass. The molar mass of barium nitrate is 261.35 grams per mole.
Set up a conversion factor using the molar mass.
[tex]\frac{ 261.35 \ g \ Ba(NO_3)_2} {1 \ mol \ Ba(NO_3)_2}[/tex]
Multiply by the number of moles we calculated.
[tex]0.0880106276984 \ mol \ Ba(NO_3)_2 *\frac{ 261.35 \ g \ Ba(NO_3)_2} {1 \ mol \ Ba(NO_3)_2}[/tex]
The units of moles of barium nitrate cancel.
[tex]0.0880106276984*\frac{ 261.35 \ g \ Ba(NO_3)_2} {1}[/tex]
[tex]23.001577549 \ g \ Ba(NO_3)_2[/tex]
If this is rounded to the tenths place, the 0 in the hundredth place tells us to leave the 0 in the tenths place.
[tex]23.0 \ g \ Ba(NO_3)_2[/tex]
The mass of 5.30 ×10²² formula units of barium nitrate is approximately 23.0 grams.
