Calculating Mole Fraction from Molality: Sodium Nitrate Solution Example

In summary, to find the mole fraction of sodium nitrate in an aqueous solution with a molality of 2.14 m, we can use the equation mole fraction of A = moles of A / total number of moles, with 2.14 moles of NaNO3 and 1000 grams of water (with a molar mass of 18 grams per mole) as our inputs. This yields a mole fraction of 0.0370. Using a more accurate molar mass of water may result in a slightly better result.
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Homework Statement



The molality of an aqueous sodium nitrate solution is 2.14 m. What is the mole fraction of sodium nitrate?

Homework Equations



Molality = moles of solute / kg of solvent.

Mole fraction of A = moles of A / total number of moles (in this case, moles of solute + moles of solution).

The Attempt at a Solution



Assuming we have 1 kg of solvent, we can assume we have 2.14 moles of NaNO3.

Mole fraction of NaNO3 is therefore 2.14 / [(1000/18) + 2.14] = 0.0370.

1000/18 because 1000 grams of water is present and there are 18 grams per mole of water. The grams cancel out and yield moles of water.
 
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  • #2
Looks OK. You will get slightly better result by using more accurate molar mass of water.
 
  • #3
I appreciate your consideration and helpfulness!
 

1. What is mole fraction and how is it calculated?

Mole fraction is a way to express the concentration of a solution, particularly in chemistry. It is calculated by dividing the number of moles of a specific component by the total number of moles in the solution.

2. What is molality and how does it relate to mole fraction?

Molality is another unit of concentration that is based on the number of moles of solute per kilogram of solvent. It is related to mole fraction through the formula molality = (moles of solute) / (kilograms of solvent).

3. How do you calculate mole fraction from molality for a specific solute?

To calculate the mole fraction from molality, you first need to convert the molality to moles of solute per mole of solvent. Then, divide the moles of solute by the total moles of solute and solvent in the solution to obtain the mole fraction.

4. Can you provide an example of calculating mole fraction from molality?

Sure, let's say we have a solution of sodium nitrate with a molality of 0.1 mol/kg. We first need to convert this to moles of solute per mole of solvent, which would be 0.1 mol/1 kg = 0.1 mol/mol. Then, we can calculate the mole fraction by dividing the moles of sodium nitrate (0.1 mol) by the total moles in the solution (0.1 mol + 1 mol = 1.1 mol). Therefore, the mole fraction of sodium nitrate in this solution would be 0.091 mol/mol.

5. Why is it important to know the mole fraction of a solution?

Mole fraction is important because it gives a more accurate representation of the concentration of a solution compared to other units, such as molarity or molality. It takes into account the total number of moles of both the solute and solvent, rather than just the solute or solvent alone. This is particularly useful in chemical reactions and in determining the properties of a solution.

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