Chapter 11, Problem 11.84QP

(a)

Interpretation Introduction

Interpretation: The direction of the solvent flow for each of the given pairs of aqueous solutions, which are separated by a semipermeable membrane, is to be stated.

Concept introduction: Semipermeable membrane is a thin film which is present almost in both living and nonliving things. This film comprises small pores through which solvent moves from one portion to another. Solvent always flows from lower concentration to higher concentration.

This process of solvent flow is known as osmosis. Now if another side external pressure is applied then this process reversed and this applied reverse pressure is known as osmotic pressure. Generally the concentration is expressed in terms of molarity and represents as M that is molar concentration. One of the concentration units is millimolar and in terms of molar it is expressed as, $1\text{mM}=1\times {10}^{-3}\text{M}$.

To determine: The direction of the solvent flow for the given pair of aqueous solution, which is separated by semipermeable membrane.

Answer to Problem 11.84QP

Solution

The direction of the solvent flow for the given pair is $\text{A}\to \text{B}$.

Explanation of Solution

Explanation

Given

The pair of aqueous solution is given as,

• A is $1.00\text{L}$ of $0.48\text{M}\text{NaCl}$ and B is $55.85\text{g}$ of $\text{NaCl}$ dissolved in $1.00\text{L}$ of solution.

Water is a solvent here. Solvent moves through semipermeable membrane. Solvent always flows from lower concentration to the higher concentration till the equilibrium is reached.

The given pair has different concentration. In the solution A the concentration is $0.48\text{M}$, that is in terms of molarity. While in solution B there is only amount of solute and solvent is given. Therefore, for the solution B the concentration in terms of molarity is calculated by the formula,

$M=\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solvent}\text{(L)}}$ (1)

Here, the solute is $\text{NaCl}$ and the molar mass of $\text{NaCl}$ is $58.5\text{g/mol}$. The given mass of $\text{NaCl}$ is $55.85\text{g}$. Therefore, the number of moles of solute is calculated by the formula,

$n=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}$ (2)

Where,

• $n$ is the number of moles of solute.

Substitute the values in above formula.

$\begin{array}{l}n=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}\\ n=\frac{55.85\text{g}}{58.5\text{g}/\text{mol}}\\ n=0.95\text{mol}\end{array}$

Now, substitute the value of given volume that is $1.00\text{L}$ and calculated number of moles in equation (1).

$\begin{array}{l}M=\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solvent}\text{(L)}}\\ M=\frac{0.95\text{mol}}{1.00\text{L}}\\ M=0.95\text{mol}/\text{L}\\ M=0.95\text{M}\end{array}$

The solution A has the concentration of $0.48\text{M}$ and the solution B has the concentration of $0.95\text{M}$. Therefore, the direction of flow of solvent is from lower to higher concentration that is solution $\text{A}\to \text{B}$.

(b)

Interpretation Introduction

To determine: The direction of the solvent flow for the given pair of aqueous solutions, which are separated by semipermeable membrane.

Answer to Problem 11.84QP

Solution

The direction of the solvent flow for the given pair is $\text{A}\to \text{B}$.

Explanation of Solution

Explanation

Given

The pair of aqueous solution is given as,

• A is $100\text{mL}$ of $0.982\text{M}{\text{CaCl}}_2$ and B is $16\text{g}$ of $\text{NaCl}$ dissolved in $100\text{mL}$ of solution

The given pair has different concentration. In the solution A the concentration is $0.982\text{M}$, that is in terms of molarity. While in solution B there is only amount of solute and solvent is given. Therefore, for the solution B the concentration in terms of molarity is calculated by the formula given in equation (1).

For the solution B, the solute is $\text{NaCl}$ and the molar mass of $\text{NaCl}$ is $58.5\text{g/mol}$. The given mass of $\text{NaCl}$ is $16\text{g}$. Therefore, the number of moles of solute is calculated by the formula given in equation (2).

Substitute the values in above formula that is equation (2).

$\begin{array}{l}n=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}\\ n=\frac{16\text{g}}{58.5\text{g}/\text{mol}}\\ n=0.273\text{mol}\end{array}$

The value of given volume is $100\text{mL}$. In the liter unit it is $0.100\text{L}$. Now, substitute the values in equation (1).

$\begin{array}{l}M=\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solvent}\text{(L)}}\\ M=\frac{0.273\text{mol}}{0.100\text{L}}\\ M=2.73\text{mol}/\text{L}\\ M=2.73\text{M}\end{array}$

The solution A has the concentration of $0.982\text{M}$ and the solution B has the concentration of $2.73\text{M}$. Therefore, the direction of flow of solvent is from lower to higher concentration that is solution $\text{A}\to \text{B}$.

(c)

Interpretation Introduction

To determine: The direction of the solvent flow for the given pair of aqueous solutions, which are separated by semipermeable membrane.

Answer to Problem 11.84QP

Solution

The direction of the solvent flow for the given pair is $\text{A}\to \text{B}$.

Explanation of Solution

Explanation

Given

The pair of aqueous solution is given as,

• A is $100\text{mL}$ of $6.65\text{mM}{\text{MgSO}}_4$ and B is $5.24\text{g}$ of ${\text{MgCl}}_2$ dissolved in $250\text{mL}$ of solution

The given pair has different concentration. In the solution A the concentration is $6.65\text{mM}$, that is in terms of molarity. While in solution B there is only amount of solute and solvent is given. Therefore, for the solution B the concentration in terms of molarity is calculated by the formula given in equation (1).

For the solution B, the solute is ${\text{MgCl}}_2$ and the molar mass of ${\text{MgCl}}_2$ is $95.21\text{g/mol}$. The given mass of ${\text{MgCl}}_2$ is $5.24\text{g}$. Therefore, the number of moles of solute is calculated by the formula given in equation (2).

Substitute the values in above formula that is equation (2).

$\begin{array}{l}n=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}\\ n=\frac{5.24\text{g}}{95.21\text{g}/\text{mol}}\\ n=0.055\text{mol}\end{array}$

The value of given volume is $250\text{mL}$. In the liter unit it is $0.250\text{L}$. Now, substitute the values in equation (1).

$\begin{array}{l}M=\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solvent}\text{(L)}}\\ M=\frac{0.055\text{mol}}{0.250\text{L}}\\ M=0.22\text{mol}/\text{L}\\ M=0.22\text{M}\end{array}$

The solution A has the concentration of $6.65\text{mM}$ that in millimolar unit. In terms of molar it is equal to $6.65\times {10}^{-3}\text{M}$ that is $0.00665\text{M}$ and the solution B has the concentration of $0.22\text{M}$. Therefore, the direction of flow of solvent is from lower to higher concentration that is solution $\text{A}\to \text{B}$.

Conclusion

1. a) The direction of the solvent flow for the given pair is $\text{A}\to \text{B}$.
2. b) The direction of the solvent flow for the given pair is $\text{A}\to \text{B}$.
3. c) The direction of the solvent flow for the given pair is $\text{A}\to \text{B}$.