Question

The molar mass of barium nitrate (Ba(NO3)2) is 261. 35 g/mol. What is the mass of 5. 30 × 1022 formula units of Ba(NO3)2? 0. 0900 g 12. 0 g 23. 0 g 3,130 g.

Answer 1

`\boxed{\boxed {\sf 23.0 \ g \ Ba(NO_3)_2}}`

Step-by-step explanation:

We are asked to find the mass of 5.30 ×10²² formula units of barium nitrate.

1. Formula Units to Moles

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.

`(6.022 * 10^(23) \ formula \ units \ Ba(NO_3)_2)/( 1 \ mol \ Ba (NO_3)_2)`

We are converting 5.30×10²² formula units, so we multiply by this value.

`5.30 * 10^(22) \ formula \ units \ Ba(NO_3)_2 *(6.022 * 10^(23) \ formula \ units \ Ba(NO_3)_2)/( 1 \ mol \ Ba (NO_3)_2)`

Flip the conversion factor so the units of formula units of barium nitrate cancel.

`5.30 * 10^(22) \ formula \ units \ Ba(NO_3)_2 *( 1 \ mol \ Ba (NO_3)_2)/(6.022 * 10^(23) \ formula \ units \ Ba(NO_3)_2)`

`5.30 * 10^(22) *( 1 \ mol \ Ba (NO_3)_2)/(6.022 * 10^(23))`

`(5.30 * 10^(22) )/(6.022 * 10^(23)) \ mol \ Ba(NO_3)_2`

`0.0880106276984 \ mol \ Ba(NO_3)_2`

2. Moles to Grams

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.

`\frac{ 261.35 \ g \ Ba(NO_3)_2} {1 \ mol \ Ba(NO_3)_2}`

Multiply by the number of moles we calculated.

`0.0880106276984 \ mol \ Ba(NO_3)_2 *\frac{ 261.35 \ g \ Ba(NO_3)_2} {1 \ mol \ Ba(NO_3)_2}`

The units of moles of barium nitrate cancel.

`0.0880106276984*\frac{ 261.35 \ g \ Ba(NO_3)_2} {1}`

`23.001577549 \ g \ Ba(NO_3)_2`

If this is rounded to the tenths place, the 0 in the hundredth place tells us to leave the 0 in the tenths place.

`23.0 \ g \ Ba(NO_3)_2`

The mass of 5.30 ×10²² formula units of barium nitrate is approximately 23.0 grams.