Question

An aqueous solution is 0.467 m in hcl. what is the molality of the solution if the density is 1.23 g/ml?

Answer 1

The molality of the given solution is $\boxed{0.385{\text{ mol/kg}}}$.

Further explanation:

Molarity:

The molarity of the solution can be defined as the concentration of the solution and is equal to the number of moles of the solute dissolved in 1 liter of the solution.

The expression of molarity (M), volume (V) and number of moles (n) is as follows:

${\text{M}}=\frac{{{\text{n}}\left({{\text{mol}}}\right)}}{{{\text{V}}\left({\text{L}}\right)}}$ …… (1)

Here, V is a volume of solution in liters and n is a number of moles of solute.

Molality:

The molality of the solution can be defined as the measure of the amount of solute dissolved in one kilogram of the solvent. The expression of molality is,

${\text{m}}=\frac{{{\text{n}}\left({{\text{mol}}}\right)}}{{{\text{mass of solvent}}\left({{\text{kg}}}\right)}}$ …… (2)

Here, m is a molality and n is a number of moles of solute.

The molarity of given aqueous solution of HCl is 0.467 M. This means 0.467 moles of HCl are dissolved in 1 liter of the solution.

Therefore, the mass of 0.467 moles of HCl can be calculated as follows:

$\begin{gathered}{\text{Mass of HCl}}=\left({{{\text{n}}_{{\text{HCl}}}}}\right)\times\left({{\text{molar mass of HCl}}}\right)\\=\left({0.467{\text{ mol}}}\right)\times\left({36.5{\text{ g/mol}}}\right)\\=17.0455{\text{ g}}\\\end{gathered}$

Since the density of the solution is 1.23 g/mL, it means that the mass of 1 mL solution is 1.23 g. Therefore, the mass of 1 liter solution is calculated as follows:

$\begin{gathered}{\text{Mass of solution}}=\left( {\frac{{1.23\;{\text{g}}}}{{1\;{\text{mL}}}}}\right)\left({\frac{{1000\;{\text{mL}}\;}}{{1\;{\text{L}}}}}\right)\\=1230\;{\text{g/L}}\\\end{gathered}$

The mass of solvent (water) is calculated as follows:

$\begin{gathered}{\text{Mass of solvent}}={\text{mass of solution}}\left({aq{\text{ HCl}}}\right)-{\text{mass of solute}}\left({{\text{HCl}}}\right)\\=1230{\text{ g}}-17.0455{\text{ g}}\\{\text{=1212}}{\text{.95 g}}\times\left({\frac{{1{\text{ kg}}}}{{1000\;{\text{g}}}}}\right)\\=1.21295{\text{ kg}}\\\end{gathered}$

Substitute 1.21295 kg for mass of solvent and 0.467 number of moles of solute (HCl) in equation (2).

$\begin{gathered}{\text{m}}=\frac{{{\text{n}}\left({{\text{mol}}} \right)}}{{{\text{mass of solvent}}\left({{\text{kg}}}\right)}}\\=\frac{{0.467{\text{ mol}}}}{{1.21295{\text{ kg}}}}\\=0.385{\text{ mol/kg}}\\\end{gathered}$

Therefore, molality of the given solution is ${\mathbf{0}}{\mathbf{.385 mol/kg}}$.

Learn more:

1. Determine the number of moles of chlorine in 8 moles of carbon tetrachloride: brainly.com/question/3064603

2. Determine how many moles of water produce: brainly.com/question/1405182

Answer details:

Grade: Senior school

Subject: Chemistry

Chapter: Solutions

Keywords: Molecules, elements, atom, solution, molarity, molality, hydrogen, chlorine, 0.385, 0.467 mol/L, number of moles.

Answer 2

Answer:
molarity = 0.385 moles/kg

Explanation:
Assume that the volume of the aqueous solution given is 1 liter = 1000 ml
Now, density can be calculated using the following rule:
density = mass / volume
Therefore:
mass = density * volume = 1.23 * 1000 = 1230 grams
Now, 0.467 m/L * 1L = 0.467 moles of HCl
We will get the mass of the 0.467 moles of HCl as follows:
mass = molar mass * number of moles = (1+35.5)*0.467 = 17.0455 grams
Now, we have the mass of the solution (water + HCl) calculated as 1230 grams and the mass of the HCl calculated as 17.0455 grams. We can use this information to get the mass of water as follows:
mass of water = 1230 - 17.0455 = 1212.9545 grams
Finally, we will get the molarity as follows:
molarity = number of moles of solute / kg of solution
molarity = (0.467) / (1212.9594*10^-3)
molarity = 0.385 mole/kg 

Hope this helps :)