Introduction To Health Physics
Introduction To Health Physics
5th Edition
ISBN: 9780071835275
Author: Johnson, Thomas E. (thomas Edward), Cember, Herman.
Publisher: Mcgraw-hill Education,
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Chapter 3, Problem 3.23P

If 9 g of NaC1 were dissolved in 1 L of water, what would be concentration, in atoms per milliliter, of each of the constituent elements in the solution?

Expert Solution & Answer
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To determine

The concentration in atoms per millilitre of each of the constituent elements in the solution.

Answer to Problem 3.23P

Concentrations:

Number of atoms of Na added to the solution in 9 gm = 9.27×1019atoms Na/mL

Number of atoms of Cl added to the solution in 9 gm = 9.27×1019atoms Cl/mL

Number of atoms of H in 1 millilitre of water = 6.69×1022atoms H/mL

Number of atoms of O in 1 millilitre of water = 3.34×1022atoms O/mL

Explanation of Solution

Given Information:

9 g of NaCl were dissolved in 1 L of water

Calculation:

Na = 22.99 g/mole

Cl = 35.45 g/mole

NaCl = 58.43 g/mole

Calculating the number of atoms of Na added to the solution in 9 gm,

  (9g NaCl1L)×(mol NaCl58.43g NaCl)×(1 mol Na1mol NaCl)×(6.02×1023atoms Na1mol Na)×(1L1000mL = 9.27×1019atoms Na/mL

Calculating the number of atoms of Cl added to the solution in 9 gm,

  (9g NaCl1L)×(mol NaCl58.43g NaCl)×(1 mol Cl1mol NaCl)×(6.02×1023atoms Cl1mol Cl)×(1L1000mL)

  = 9.27×1019atoms Cl/mL

H = 1 g/mole

O = 16 g/mole

H2O = 2(1 g/mole) + 16 g/mole = 18 g/mole

Calculating the number of atoms of H in 1 millilitre of water (assume 1 litter = 1000 g water),

  (1000g H2O1L)×(mol H2O18g H2O)×(2 mol H1mol H2O)×(6.02×1023atoms H1mol H)×(1L1000mL) = 6.69×1022atoms H/mL

Calculating the number of atoms of O in 1 millilitre of water (assume 1 litter = 1000 g water),

  (1000g H2O1L)×(mol H2O18g H2O)×(2 mol O1mol H2O)×(6.02×1023atoms O1mol O)×(1L1000mL) = 3.34×1022atoms O/mL

Conclusion:

The concentration, in atoms per millilitre, of each of the constituent elements in the solution is as follows.

Number of atoms of Na added to the solution in 9 gm = 9.27×1019atoms Na/mL

Number of atoms of Cl added to the solution in 9 gm = 9.27×1019atoms Cl/mL

Number of atoms of H in 1 millilitre of water = 6.69×1022atoms H/mL

Number of atoms of O in 1 millilitre of water = 3.34×1022atoms O/mL

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