# What is the Molality of a solution in which 50g of AlCl3 is added to 500.0g of water?

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AlCl3 is the solute and H2O (Water) is the solution. For calculating Molality, we need moles of the solute (mol) and mass of solvent (kg).

Let us calculate the molar mass of AlCl3

Al = 26.981 g/mol

Cl = 35.453 g/mol

molar mass of AlCl3= (Al x 1) + (Cl x 3) = (26.981 x 1) + (35.453 x 3) = 26.981 + 106.359 = 133.34 g/mol

Moles of solute (AlCl3)= 50(g)/133.34(g/mol)= 0.375 moles

Mass of solvent= 500.0g or 500/1000=0.5kg

Molality (m) = moles of solute (mol)/mass of solvent (kg)

Molality of AlCl3 = 0.375 mol/0.5kg=0.75 m

Molarity and molality are two ways of expressing the concentration of a substance dissolved in a solvent. Molarity is the number of moles of the solute per liter of the solution whereas molality refers to the number of moles of the solute in a kilogram of the solvent.

Here, 50 g of `AlCl_3` is added to 500.0 g of water. The molar mass of `AlCl_3` is 133.33. 50 g of `AlCl_3` is equivalent to 50/133.33 moles. As this is dissolved in 500 g of water, the molality of the resulting solution is:

`(50/133.33)/(.500)` = 0.75 mole/kg

When solving for molality, the equation you use is

molality = moles of solute / mass of solvent in kilograms`<br>`

Identify which is the solute and which is the solvent. Water is the solvent and AlCl3 is the solute. Remember, the one with the greater amount is the solvent. You have 50 g of AlCl3 and 500.0 g of water.

To plug your values in the equation above, you need to convert the 50 g of AlCl3 to moles. So get the molar mass of AlCl3 and let's solve.

50 g AlCl3 x (1 mol / 133.33 g) = 0.375 mol AlCl3

Great, you have your numerator!

But now you need to convert your grams of water into kilograms so you can solve the equation. Remember, 1 kg = 1,000 g.

500.0 g H2O x (1 kg / 1000 g) = 0.5 kg water

Now plug in your values into the molality equation.

m = .375 mol / 0.5 kg = 0.75

m = 0.75

Now, if this problem requires sig figs, look at the question and look at the value with the smallest number of sig figs. You have 50 and 500.0. 50 has 1. 500.0 has 4. Thus, you should set your answer to 1 sig fig.

Then your molality would be 0.8!

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The equation for molality is:

`m = ("moles" "of" "solute")/("kilograms" "of" "solvent")`

Make sure the units match. If not, be sure to use stoichiometry!

`50 "g" = (1 "mol")/(133.28 "g") = 0.375 "mol"`

`500 "g" = (1 "kg")/(1000"g") = 0.5 "kg"`

Now, all you need to do is plug in your known variables!

`m = (0.375 "mol")/(0.5 "kg")`

`m = 0.75`

Make sure your sig figs are correct too! Since 50 has only one sig fig, the answer can be rounded to 0.8 m.