Question

Be sure to answer all parts. Radon (Rn) is the heaviest and the only radioactive member of Group 8A(18), the noble gases. It is a product of the disintegration of heavier radioactive nuclei found in minute concentrations in many common rocks used for building and construction. In recent years, health concerns about the cancers caused from inhaled residential radon have grown. If 1.00 × 1015 atoms of radium (Ra) produce an average of 1.373 × 104 atoms of Rn per second, how many liters of Rn, measured at STP, are produced per day by 1.08 g of Ra?

Answer 1

1.27 x 10⁻⁷L of Rn will be produced in a day

Explanation:

Given parameters:

Rate of production of Rn atoms from Ra:

       1.00 x 10¹⁵ atoms of Ra produce 1.373 x 10⁴atoms of Rn per seconds

Mass of Ra = 1.08g

Condition of reaction; at Standard Temperature and Pressure

Unknown:

Volume of Rn produced in a day = ?

Solution:

  Procedures:

• Find the number of atoms contained in the given mass of Ra by first evaluating the number of moles of Ra. Using the avogadro's constant, obtain the number of atoms.
• Compare this to the rate of decay of Ra to Rn.
• The number of atoms of Rn derived is used to solved for the number of moles of Rn.
• From this calculate the volume and converted the time from seconds to day.

##Solving

Step 1:    Number of atoms of Ra:

      Number of moles = $\frac{mass of Ra}{molar mass of Ra}$

          molar mass of Ra = 226.03g/mol

      Number of moles =  $\frac{1.08}{226.03}$ = 0.0048mole

   1 mole of a substance = 6.02 x 10²³ atoms

   0.0048mole of Ra will contain 0.0048 x 6.02 x 10²³ = 2.89 x 10²¹atoms

Step 2:

  We know that:

    1.00 x 10¹⁵ atoms of Ra produce 1.373 x 10⁴atoms of Rn per seconds

Therefore 2.89 x 10²¹atoms of Ra will produce $\frac{2.89 x 10^{21} x 1.373 x 10^ {4} }{1 x 10^{15} }$ = 3.97 x 10¹⁰ atoms of Rn per seconds

Step 3:

    The number of atoms of Rn produced is 3.97 x 10¹⁰ atoms

  Number of moles = $\frac{number of atoms }{6.02 x 10^{23 } }$

  Number of moles =  $\frac{ 3.97 x 10^{10}{6.02 x 10^{23 } }$

  Number of moles of Rn = 6.6 x 10⁻¹⁴moles

Step 4:

  Number of moles of Rn produced per seconds is 6.6 x 10⁻¹⁴moles

 At STP;

     Volume = number of moles x 22.4 = 6.6 x 10⁻¹⁴ x 22.4 = 1.47 x 10⁻¹²dm³

   This is the same as  1.47 x 10⁻¹²L of Rn per seconds

Now, express in L per day;

  In a day:

        60 seconds = 1 minute

        60 minute = 1 hour

        24 hours = 1 day

so: 60x60x24(seconds ) = 1 day

         86400 seconds are in a day

       if in  1 seconds  1.47 x 10⁻¹²L of Rn is produced

Therefore  in 86400 seconds(1 day),  86400 x 1.47 x 10⁻¹²L will be produced

                         ⇒  1.27 x 10⁻⁷L of Rn will be produced in a day

In a day, 1.27 x 10⁻⁷L of Rn will be produced in a day will be produced from  1.08g of Ra

Learn more:

radioactive decay brainly.com/question/4207569

stoichiometry brainly.com/question/7795301

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