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1 mole of Kr contains Avogadro's number of atoms, therefore, to calculate the number of moles containing 9.783 * 10^23 atoms, we will do cross multiplication as follows:
number of moles = (9.783 * 10^23 *1) / (6.022 * 10^23) = 1.625 moles
1 atm is equivalent to 101325 Pa, therefore:
9.25 atm = 937256.25 Pa

The ideal gas law states that:
PV = nRT where
P is the pressure = 937256.25 Pa
V is the volume we want to calculate
n is the number of moles = 1.625 moles
R is the gas constant =  8.31441
T is the temperature = 512 k

Substitute with the givens to get V as follows:
937256.25 V = 1.625 * 8.31441 * 512
Volume = 7.38 * 10^-3 liters
BladeRunner212

7.38 liters

Further explanation

Given:

  • N = 9.783 x 10²³ atoms of Kr
  • p = 9.25 atm
  • T = 512 K
  • Avogadro's number = 6.02 x 10²³

Question:

The volume of Kr (in liters)

The Process:

Step-1: moles of Kr

We use the conversion formula from the number of atoms to moles.

[tex]\boxed{ \ n = \frac{N}{6.02 \times 10^{23}} \ }[/tex]

[tex]\boxed{ \ n = \frac{9.783 \times 10^{23}}{6.02 \times 10^{23}} \ }[/tex]

Hence, we get 1.625 moles of Kr.

Step-2: the volume of Kr

We use the formula for an ideal gas:

[tex]\boxed{ \ pV = nRT \ }[/tex]

  • p = pressure in atm
  • V = volume in liters
  • n = amount of substance in moles
  • R = ideal gas constant, i.e., 0.082 L atm/mol K.
  • T = temperature in Kelvin  

Let us calculate the volume.

[tex]\boxed{ \ V = \frac{nRT}{p} \ }[/tex]

[tex]\boxed{ \ V = \frac{(1.625)(0.082)(512)}{9.25} \ }[/tex]

Thus, the volume of Kr is 7.38 liters.

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Keywords: the volume, Kr, krypton, atoms, avogadro's number, moles, atm, pressure, temperature, ideal gas law