Question

elemental radon (M=222g/mol) is a radioactive gas found at low concentrations in some homes in Canada. The canadian nuclear safety commission specifies that radon concentrations higher than 2.7 X 10^-17 g/L are unhealthy. at this concentration, how many moles of radon would there be in a living room of volume 120m^3? how many atoms is this?

Answer 1

In a 120 m³ living room, at the concentration of 2.7 x 10^-17 g/L, there would be 1.459 x 10^-14 moles of radon, which corresponds to approximately 8.78 x 10^9 radon atoms.

Step-by-step explanation:

Elemental radon (Rn-222) is a concerning issue because it is a radioactive gas that can be found in homes and is capable of increasing the risk of lung cancer, especially for those with additional risk factors such as tobacco use.

The Canadian Nuclear Safety Commission has set the unhealthy threshold for radon concentration at 2.7 x 10-17 g/L. To calculate the number of moles of radon in a 120 m3 living room at this concentration, we first convert the volume to liters (since 1 m3 = 1000 L):

120 m3 x 1000 L/m3 = 120,000 L

Next, we can calculate the mass of radon in the room by multiplying the concentration by the volume:

2.7 x 10-17 g/L x 120,000 L = 3.24 x 10-12 g

Then, we determine the number of moles using the molar mass of radon (222 g/mol):

(3.24 x 10-12 g) / (222 g/mol) = 1.459 x 10-14 moles

To find the number of atoms, we use Avogadro's number (6.022 x 1023 atoms/mol):

1.459 x 10-14 moles x 6.022 x 1023 atoms/mol = 8.78 x 109 atoms of radon