Brass is a substitutional alloy consisting of a solution of copper and zinc. A particular sample of red brass consisting of 79.0% Cu and 21.0% Zn by mass has a density of 8740 kg/m3.What is the molality and molarity of Zn in the solid solution?

Solute is the substance which is present in smaller proportion in a mixture and solvent is the substance which is present in larger proportion in a mixture.

We are given:

(m/m) % of Cu = 79 %

This means that 79 g of copper is present in 100 grams of alloy.

(m/m) % of Zn = 21 %

This means that 21 g of zinc is present in 100 grams of alloy.

As, zinc is present in smaller proportion. So, it is solute and copper is the solvent.

Calculating molality of zinc:

To calculate molality of the zinc, we use the equation:

[tex]Molality=\frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ in grams}}[/tex]

where,

[tex]m_{solute}[/tex] = Given mass of solute (Zinc ) = 21 g

[tex]M_{solute}[/tex] = Molar mass of solute (Zinc) = 65.3 g/mol

[tex]W_{solvent}[/tex] = Mass of solvent (copper) = 79 g

Putting values in above equation, we get:

[tex]\text{Molality of Zinc}=\frac{21\times 1000}{65.3\times 79}\\\\\text{Molality of zinc}=4.07m[/tex]

Calculating molarity of zinc:

To calculate volume of a substance, we use the equation:

[tex]\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}[/tex]

Density of solution = [tex]8740kg/m^3=\frac{8740kg\frac{1000g}{1kg}}{1m^3\times \frac{10^6cm^3}{1m^3}}=\frac{8740g}{1000cm^3}=8.740g/cm^3[/tex]

(Conversion factors used are: 1 kg = 1000 g & [tex]1m^3=10^6cm^3[/tex] )

Mass of solution = 100 g

Putting values in above equation, we get:

[tex]8.740g/cm^3=\frac{100.0g}{\text{Volume of zinc}}\\\\\text{Volume of zinc}=11.44cm^3[/tex]

To calculate the molarity of solution, we use the equation:

[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}[/tex]

We are given:

Molar mass of zinc = 65.3 g/mol

Volume of solution = [tex]11.44cm^3=11.44mL[/tex] (Conversion factor: [tex]1cm^3=1mL[/tex] )

Mass of zinc = 21.0 g

Putting values in above equation, we get:

[tex]\text{Molarity of zinc}=\frac{21\times 1000}{65.3\times 11.44}=28.11M[/tex]

Hence, the molality and molarity of zinc in the solution is 4.07 m and 28.11 M respectively.

aliasger2709 aliasger2709 · Answer 2 · 2022-02-25T11:26:17+01:00

A substitutional alloy of zinc and copper solution is called brass. The molality of zinc in the solution is 4.07 m and the molarity of zinc is 28.11 M.

What are molarity and molality?

Molarity is the concentration of the substances given by the moles of the substance dissolved in the volume in litres, while molality is the number of moles of solute present in the kilogram of the solvent.

Given,

Mass of copper in alloy = 79 gm
Mass of zinc in alloy = 21 gm

Calculation of molality of zinc in the alloy by the formula:

[tex]\rm molality = \dfrac {\text{mass of solute} \times 1000}{\text{molar mass of solute}\times \text{mass of solvent}}[/tex]

Here,

Mass of solute (Zinc ) = 21 g
Molar mass of solute (Zinc) = 65.3 g/mol
Mass of solvent (copper) = 79 g

Substituting values in the above equation:

[tex]\begin{aligned}\rm molality &= \dfrac{21 \times 1000}{65.3 \times 79}\\\\&= 4.07 \;\rm m\end{aligned}[/tex]

Calculation of molarity of zinc in the alloy can be done as:

Calculate the volume of the zinc:

[tex]\begin{aligned}\text{Volume of zinc} &= \rm \dfrac{mass}{density}\\\\&= \dfrac{100}{8.740}\\\\&= 11.44\;\rm cm^{3}\end{aligned}[/tex]

Calculate the molarity as:

[tex]\begin{aligned} \rm Molarity &= \dfrac {\text{mass of solute} \times 1000}{\text{Molar mass of solute} \times \text{Volume of solution}}\\\\&= \dfrac{21 \times 1000}{65.3 \times 11.44}\\\\&= 28.11 \;\rm m\end{aligned}[/tex]

Therefore, molality is 4.07 m and molarity is 28.11 M.

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