Question

A solution is prepared by dissolving 23.7 g of cacl2 in 375 g of water. the density of the resulting solution is 1.05 g/ml. the mole fraction of cl- in this solution is ________.

Answer 1

The density of the solution =1.05 g/ml.
The total mass of the resulting solution is = 398.7 g (CaCl2 + water)

Find moles of CaCl2 and water.
Molar mass of CaCl2 = 110 (approx.)

Moles of CaCl2 = 23.7 / 110  = 0.22
so, moles of Cl- ion = 2 x 0.22 = 0.44  (because each molecule of CaCl2 will give two Cl- ions)
Moles of water = 375 / 18 = 20.83

Now, Mole fraction of CaCl2 =  (moles of CaCl2) / (total moles)

total moles = moles of Cl- ions + moles of Ca2+ ions + moles of water

                  = 0.44 + 0.22 + 20.83

=21.49


So, mole fraction = 0.44 / (21.49) = 0.02

Guess what !!! density is not used. No need

Answer 2

The mole fraction of ${\text{C}}{{\text{l}}^ - }$ in the given solution of ${\text{CaC}}{{\text{l}}_{\text{2}}}$ is $\boxed{{\text{0}}{\text{.0199}}}$.

Further Explanation:

The proportion of substance in the mixture is called concentration. The most commonly used concentration terms are as follows:

1. Molarity (M)

2. Molality (m)

3. Mole fraction (X)

4. Parts per million (ppm)

5. Mass percent ((w/w) %)

6. Volume percent ((v/v) %)

Mole fraction:

It is defined as the ratio of the number of moles of particular component to the total number of moles of all the components in the mixture. It is represented by X.

The expression for the mole fraction is as follows:

${\text{Mole}}\;{\text{fraction}}\left( {\text{X}} \right)=\dfrac{{{\text{Moles}}\;{\text{of}}\;{\text{component}}}}{{{\text{Total number of moles}}}}$                                            …… (1)

The formula to calculate the moles of substance is as follows:

${\text{Moles of substance}} = \dfrac{{{\text{Given mass of substance}}}}{{{\text{Molar mass of substance}}}}$        ...... (2)                              

Substitute 23.7 g for the given mass and 110.98 g/mol for the molar mass in equation (2) to calculate the moles of ${\text{CaC}}{{\text{l}}_{\text{2}}}$.

 $\begin{aligned}{\text{Moles of CaC}}{{\text{l}}_2}&= \left( {23.7{\text{ g}}} \right)\left( {\frac{{{\text{1 mol}}}}{{{\text{110}}{\text{.98 g}}}}} \right)\\&= 0.2136{\text{ mol}}\\\end{aligned}$

Substitute 375 g for the given mass and 18.02 g/mol for the molar mass in equation (2) to calculate the moles of ${{\text{H}}_{\text{2}}}{\text{O}}$.

$\begin{aligned}{\text{Moles of }}{{\text{H}}_2}{\text{O}} &= \left( {{\text{375 g}}} \right)\left( {\frac{{{\text{1 mol}}}}{{{\text{18}}{\text{.02 g}}}}} \right)\\&= 20.8102{\text{ mol}}\\\end{aligned}$

One mole of ${\text{CaC}}{{\text{l}}_{\text{2}}}$ produces two moles of chlorine ions and one mole of calcium ions so the number of moles of ${\text{C}}{{\text{a}}^{2 + }}$ is the same as that of ${\text{CaC}}{{\text{l}}_{\text{2}}}$. The moles of   can be calculated as follows:

 $\begin{aligned}{\text{Moles of C}}{{\text{l}}^ - }&= 2\left( {0.2136{\text{ mol}}} \right)\\&= 0.4272{\text{ mol}}\\\end{aligned}$

The formula to calculate the total number of moles in given solution is as follows:

${\text{Total moles}}={\text{Moles of C}}{{\text{a}}^{2 + }} + {\text{Moles of C}}{{\text{l}}^ - } + {\text{Moles of }}{{\text{H}}_2}{\text{O}}$  ...... (3)                            

Substitute 0.2136 mol for the moles of ${\text{C}}{{\text{a}}^{2 + }}$, 0.4272 mol for the moles of ${\text{C}}{{\text{l}}^ - }$ and 20.8102 mol for the moles of ${{\text{H}}_{\text{2}}}{\text{O}}$ in equation (3).

 $\begin{aligned}{\text{Total moles}}&= 0.2136{\text{ mol}} + 0.4272{\text{ mol}} + 20.8102{\text{ mol}}\\&= {\text{21}}{\text{.451 mol}}\\\end{aligned}$

Substitute 0.4272 mol for the moles of component and 21.451 mol for the total number of moles in equation (1) to calculate the mole fraction of ${\text{C}}{{\text{l}}^ - }$.

 $\begin{aligned}{\text{Mole fraction of C}}{{\text{l}}^ - }&= \frac{{0.4272{\text{ mol}}}}{{21.451{\text{ mol}}}}\\&= 0.0199\\\end{aligned}$

Learn more:

1. Calculation of volume of gas: brainly.com/question/3636135
2. Determine the moles of water produced: brainly.com/question/1405182

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Concentration terms

Keywords: mole fraction, Ca2+, Cl-, CaCl2, 0.0199, mole fraction of Cl-, moles of CaCl2, moles of H2O, moles of Cl-, 0.4272 mol, 21.451 mol, 0.2136 mol, 20.8102 mol, molar mass, 18.02 g/mol, 110.98 g/mol.