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jek_recluse [69]
3 years ago
13

Metallic barium crystallizes in a body-centered cubic lattice, with one Ba atom per lattice point. If the metallic radius of Ba

is 217 pm, what is the volume of the unit cell in pm3 and in cm3?
Chemistry
1 answer:
Tema [17]3 years ago
3 0

Answer:

1.26 x 10⁸pm³ and 1.26 x 10⁻²²cm³

Explanation: Calculating for a body centered cubic lattice, the formula is

3d²= 16r²

where d =  edge length of unit cell

r=radius of atom

3d²= 16 x (217)²

3d²=753424

d²=251141.3

d= 501.1pm

volume of unit cell= d³= (501.1)³= 1.26 x 10⁸pm³

converting to cm³= 1.26 x 10⁸(10⁻¹²m)³

=1.26 x 10⁸(10⁻¹⁰cm)³ = 1.26 x 10⁻²²cm³

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<u>Answer:</u>

For a: The number of atoms of both the gases remains the same.

For b: The number of grams of 1 mole of argon is more than 1 mole of helium by 35.95 grams.

<u>Explanation:</u>

  • <u>For a:</u>

To calculate the number of atoms, we use mole concept.

According to mole concept:

1 mole of an element contains 6.022\times 10^{23} number of atoms.  

We are given two gases of same number of moles.

Therefore, 1 mole of helium gas will contain 1\times 6.022\times 10^{23}=6.022\times 10^{23} number of atoms.

and, 1 mole of argon gas will contain 1\times 6.022\times 10^{23}=6.022\times 10^{23} number of atoms.

Hence, number of atoms of both the given gases remains the same.

  • <u>For 2:</u>

As, the molar mass of both the gases are different, so their masses in 1 mole will be different.

To calculate the number of moles, we use the equation:

\text{Number of Moles}=\frac{\text{Given mass}}{\text{Molar mass}}

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Molar mass of helium = 4 g/mol

Putting the values in above equation, we get:  

1mol=\frac{\text{Given mass}}{4g/mol}=4grams

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Molar mass of Argon = 39.95 g/mol

Putting the values in above equation, we get:  

1mol=\frac{\text{Given mass}}{39.95g/mol}=39.954grams

Calculating the difference of masses of both the gases = (39.95 - 4)g = 35.95g

Therefore, the mass of argon is more than mass of helium by 35.95 grams.

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