Chapter 15, Problem 20A

Interpretation Introduction

Interpretation:

The given statement which says exactly 1 liter of water would not needed to prepare1 liter of 5 M NaCl solution has to be explained.

Concept Introduction:

Composition of a solution can be defined by expressing its concentration. The concentrations of solutions can be expressed in different ways, which are involved in the quantity of solute and the quantity of solution or solvent. Various methods are used to describe the concentration of the solution quantitatively. Some commonly used quantitative concentration terms are percent by mass, percent by volume, molarity, molality and mole fraction.

Molarity: Molarity is defined as the number of moles of solute present in one liter of the solution In expression, $\mathrm{Molarity}ofthesolution=\frac{Numberofmolesof the solute}{ Volume of the solution(inlitre)}$

Again $\mathrm{Number}ofmolesofsolute=\frac{Massofthesolute}{Molecularweightofthesolute}$

Answer to Problem 20A

292.2 gm of NaCl is dissolved in enough amount of water to make 1 liter of NaCl solution. So the final volume of NaCl solution will be 1 liter, thus less than 1 liter of water is needed to make 1 liter of 5 M NaCl solution.

Explanation of Solution

  $\mathrm{Molarity}ofthesolution=\frac{Numberofmolesof the solute}{ Volume of the solution(inlitre)}$

Data given: Molarity of NaClsolution = 5.0 M.

  $\begin{array}{c}MolarityofNaClsolution=\frac{Numberofmolesof NaCl}{ Volume of NaCl solution(inliter)}\\ Numberofmolesof NaCl=MolarityofNaClsolution\times Volume of NaCl solution(inliter)\\ Numberofmolesof NaCl=5.0mol/litre\times 1litre=5.0mole\end{array}$

  $\begin{array}{c}Numberofmolesof NaCl=\frac{MassofNaCl}{MolecularweightofNaCl}\\ MassofNaCl=Numberofmolesof NaCl\times MolecularweightofNaCl\\ MassofNaCl=5.0mole\times 58.44gm/mol\\ =292.2gm\end{array}$

292.2 gm of NaCl is dissolved in enough amount of water to make 1 liter of NaCl solution. So the final volume of NaCl solution will be 1 liter, thus less than 1 liter of water is needed to make 1 liter of 5 M NaCl solution.