Chapter 6, Problem 3MCP

(a)

Interpretation Introduction

Interpretation:

The boiling point of solution that contains $5gMgC{l}_2$ in $1kg$ of water has to be calculated.

Elevation in boiling point:

Boiling point is the temperature at which vapor pressure becomes equal to atmospheric pressure.  If a non volatile solute is added then the vapor pressure get lowered.  So, more temperature has to be provided for vaporizing.  Hence the boiling point increases.

    $\Delta T_b=k_b\left(mparticles\right)$

Where, $\Delta T_b$ difference in temperature of solution and pure solvent, $k_b$ is boiling point elevation constant.

$k_b$ for aqueous solution is $\frac{{0.52}^{o}C}{m}.$

Answer to Problem 3MCP

That is boiling point of magnesium chloride solution is $100.078^{o}C.$

Explanation of Solution

Molar mass of $MgC{l}_2$ is $95.211g/mol.$

Number of moles of $5gMgC{l}_2$ can be calculated as follows,

    $\begin{array}{c}numberofmoles=\frac{givenmass}{molarmass}\\ \\ =\frac{5g}{95.211g/mole}\\ \\ =0.05mole.\end{array}$

Molality of the solution can be calculated as follows,

    $\begin{array}{c}molality=\frac{molesofsolute}{kgofsolvent}\\ \\ =\frac{0.05mole}{1kg}\\ \\ =0.05m\end{array}$

Magnesium chloride dissolves in water and produces three ions in solution.  So total concentration of ions in solution will be $0.15m\left(0.05m\times 3\right).$

Therefore elevation in boiling point can be calculated as follows,

    $\begin{array}{c}\Delta T_b=k_b\left(mparticles\right)\\ \\ =\left(\frac{{0.52}^{o}C}{m}\right)\times 0.15m\\ \\ ={0.078}^{o}C\end{array}$

So the boiling point of the solution will be ${0.078}^{o}C$ more than the normal melting point of water.

That is, melting point of solution is $100.078^{o}C.$

(b)

Interpretation Introduction

Interpretation:

The melting point of solution that contains $5gMgC{l}_2$ in $1kg$ of water has to be calculated.

Depression in freezing point:

At freezing point solid phase of the solvent will be in equilibrium with liquid phase.  When solute molecule is added, it will interfere with the rate at which the liquid molecules associate to form solid state, hence lower the freezing point of the solution.

    $\Delta T_f=k_f\left(mparticles\right)$

Where, $\Delta T_f$ difference in temperature of pure solvent and solution, $k_f$ is freezing point depression constant.

$k_f$ for aqueous solution is $\frac{{1.86}^{o}C}{m}.$

Answer to Problem 3MCP

That is melting point of magnesium chloride solution is $-0.279^{o}C.$

Explanation of Solution

Molar mass of $MgC{l}_2$ is $95.211g/mol.$

Number of moles of $5gMgC{l}_2$ can be calculated as follows,

    $\begin{array}{c}numberofmoles=\frac{givenmass}{molarmass}\\ \\ =\frac{5g}{95.211g/mole}\\ \\ =0.05mole.\end{array}$

Molality of the solution can be calculated as follows,

    $\begin{array}{c}molality=\frac{molesofsolute}{kgofsolvent}\\ \\ =\frac{0.05mole}{1kg}\\ \\ =0.05m\end{array}$

Magnesium chloride dissolves in water and produces three ions in solution.  So total concentration of ions in solution will be $0.15m\left(0.05m\times 3\right).$

Therefore elevation in boiling point can be calculated as follows,

    $\begin{array}{c}\Delta T_f=k_f\left(mparticles\right)\\ \\ =\left(\frac{{1.86}^{o}C}{m}\right)\times 0.15m\\ \\ ={0.279}^{o}C\end{array}$

So the melting point of the solution will be ${0.279}^{o}C$ less than the normal melting point of water.

That is, melting point of solution is $-0.279^{o}C.$

(c)

Interpretation Introduction

Interpretation:

One practical application where a solute is used to alter the boiling point of a liquid has to be provided.

Explanation of Solution

During cooking salt is added before or while heating, in order to increase the boiling point so as to get higher temperature for food items.

(d)

Interpretation Introduction

Interpretation:

One practical application where a solute is used to alter the melting point of a liquid has to be provided.

Explanation of Solution

During winter season, salt is put on ices on road so that that it melts and easy passage for vehicles.

(e)

Interpretation Introduction

Interpretation:

Among the same concentrated solution of magnesium chloride and acetone, the one with higher melting point has to be determined.

Explanation of Solution

Magnesium chloride is an ionic compound, so it dissociate in solution and give three ions per mole but acetone is a covalent compound and will not dissociates.  Therefore total ion concentration for magnesium will be more.  Colligative properties depend on particle concentration.  Hence depression in freezing point will be more for magnesium chloride solution.  So, the melting point is more for acetone solution.

(f)

Interpretation Introduction

Interpretation:

Among the same concentrated solution of magnesium chloride and acetone, the one with higher boiling point has to be determined.

Explanation of Solution

Magnesium chloride is an ionic compound, so it dissociate in solution and give three ions per mole but acetone is a covalent compound and will not dissociates.  Therefore total ion concentration for magnesium will be more.  Colligative properties depend on particle concentration.  Hence elevation in boiling point will be more for magnesium chloride solution.  So, boiling point is more for magnesium chloride solution.

(g)

Interpretation Introduction

Interpretation:

Osmotic pressure of $5gMgC{l}_2$ in $1L$ solution has to be calculated.

Concept introduction:

Osmotic pressure ($\pi$) can be calculated as follows,

  $\pi =iMRT$

Where,

    $i$ is number of particles per mole of solute

    $M$ is molar concentration of the solute

    $R$ is universal gas constant

    $T$ is temperature in Kelvin scale.

Answer to Problem 3MCP

Osmotic pressure of $5gMgC{l}_2$ in $1L$ solution is $3.7atm.$

Explanation of Solution

Number of moles of magnesium chloride can be calculated as follows,

  $\begin{array}{c}NumberofmolesofMgC{l}_2=\frac{givenmass}{molarmass}\\ \\ =\frac{5g}{95.211g/mole}\\ \\ =0.05mole.\end{array}$

Therefore molarity of magnesium chloride solution is given below.

    $\begin{array}{c}Molarity=\frac{moleofsolute}{Volumeofsolution\left(L\right)}\\ \\ =\frac{0.05mole}{1L}\\ \\ =0.05M.\end{array}$

Molarity of magnesium chloride solution is $0.05M.$

Given temperature is ${25}^{o}C\left(298.15K\right).$

The value of universal gas constant is $0.0821L.atm/K.mole.$

There will be three ions per mole of the solution, because magnesium chloride dissociates to give one magnesium ion and two chloride ions.

Therefore osmotic pressure can be calculated as follows,

    $\begin{array}{c}\pi =iMRT\\ \\ =\left(3\right)\times \left(\text{0}\text{.05}\text{M}\right)\times \left(0.0821L.atm/K.mole.\right)\times \left(298.15K\right)\\ \\ =3.7atm.\end{array}$

Osmotic pressure is $3.7atm.$