What is the mole fraction of sugar if 2.00 moles of it are dissolved in 400.0 grams of water

With this molality calculator, you can quickly calculate the molality – one way of measuring the concentration of a solute in a solution (not to be confused with molarity). Simply type the number of moles of your solute substance and the mass of the solvent, and the tool will calculate the morality.

If you don't know how many moles of a substrate you have, use the calculator's advanced mode to calculate it with the use of the mass and molar mass of the compound. Are you still unsure what's the molality definition, its units, and its formula – or simply how to calculate molality step by step? Keep reading, and you'll find the answer!

If you were looking for a tool to calculate molarity – head over to molarity calculator.

Molality, also called molal concentration, is defined as the amount of substance of solute divided by the mass of the solvent msolvent:

Molality = nsolute / msolvent = msolute / (Wsolute × msolvent),

where:

• nsolute – Amount of the solute (in moles);
• msolvent – Mass of the solvent (in kg);
• msolute – Mass of the solute (in g); and
• Wsolute – Molar mass of the solute (in g/mol).

The molality unit from the SI system is mol/kg; sometimes, the name molal is used (though it's considered obsolete).

Molality plays a significant role in calculating the ionic strength of a solution. Learn more in the ionic strength calculator.

Molarity and molality are similar concepts – both are measures of the concentration of a solution. However, there is one main difference between those terms: molarity is expressed as the amount of substance per unit volume of solution, whereas molality defines the concentration as the amount of substance per unit mass of the solvent.

We've put all the most important differences between those two terms into a short molarity vs. molality table:

To change between molarity and molality, you can use the following relation:

M = m × d / (1 + m × W),

where:

• M – Molarity;
• m – Molality;
• W – The molar mass of the solute; and
• d – Mass density of the solution.

Let's show you an example of how to calculate molality:

1. Choose your substance. Let's assume it's table salt – sodium chloride (NaCl).

2. Calculate its molar mass. For sodium chloride, it's equal to 58.44 g/mol (as Na = 22.99 g/mol and Cl = 35.45 g/mol).

3. Convert grams to moles. Use the formula moles = mass of solute / molar mass. Assume we want to dissolve 70.128 grams of salt in 1.5 kg of water. So: moles of NaCl = 70.128 g / (58.44 g/mol) = 1.2 mol.

4. Plug the number of moles and the mass of the solvent into the molality formula. Divide 1.2 mol by 1.5 kg, and you'll find out that the molality of the NaCl solution is 0.8 molal (in standard molality units: 0.8 mol/kg).

5. Or save yourself some time and use our molality calculator (choose advanced mode to enter also the molar mass and solute mass).

To compute the molality of a solute, you need to:

1. Divide the amount of the solute (in moles) by the mass of the solvent (in grams).

2. Alternatively, if the amount of the solute is unknown, multiply the mass of the solvent (in g) and its molar mass (in g/mol).

3. Then divide the mass of the solute (in g) by the result from Step 2.

4. That's it! You've just determined the molality.

5. Remember to include the units in your answer: it's mol/kg or molal.

The answer is 6 mol/kg. To see how this result is derived, recall that the formula for molality reads:

molality = moles of solute / mass of solvent (kg).

Plugging in moles of solute = 3 and mass of solvent = 0.5 kg, we obtain molality = 3 / 0.5 = 6 mol/kg.

The formula that allows us to convert molarity to molality is the following:

m = M/( d - M × W),

where:

• M – Molarity;
• m – Molality;
• W – The molar mass of the solute; and
• d – Mass density of the solution.

The problem gives you all the information you need in order to solve for the molality and mole fraction of the solution. In order to determine its molarity, you're going to need the solution's volume.

To get the volume, you have to know what the density of the solution is. Determine the percent concentration by mass of the solution first

#"%w/w" = m_"solute"/m_"solution" * 100#

In your case, the mass of the solution will be

#m_"solution" = m_"glucose" + m_"water"#

#m_"solution" = 20 + 150 = "170 g"#

This means that you get

#"%w/w" = (20cancel("g"))/(170cancel("g")) * 100 = "11.8%"#

The density of this solution will thus be

http://us.mt.com/us/en/home/supportive_content/application_editorials/D_Glucose_de_e.html

#rho = "1.045 g/mL"#

Use glucose's molar mass to determine how many moles you have

#20cancel("g") * "1 mole glucose"/(180.16cancel("g")) = "0.111 moles glucose"#

The solution's volume will be

#170cancel("g") * "1 mL"/(1.045cancel("g")) = "162.7 mL"#

This means that its molarity is - do not forget to convert the volume to liters!

#C = n/V = "0.111 moles"/(162.7 * 10^(-3)"L") = color(green)("0.68 M")#

A solution's molality is defined as the number of moles of solute divided by the mass of the solvent - in kilograms! This means that you have

#b = n/m_"water" = "0.111 moles"/(150 * 10^(-3)"kg") = color(green)("0.74 molal")#

To get the mole fraction of sucrose, you need to know how many moles of water you have present. Once again, use water's molar mass

#150cancel("g") * "1 mole water"/(18.02cancel("g")) = "8.24 moles water"#

The total number of moles the solution contains is

#n_"total" = n_"glucose" + n_"water"#

#n_"total" = 0.111 + 8.24 = "8.351 moles"#

This means that the mole fraction of sucrose, which is defined as the number of moles of sucrose divided by the total number of moles in the solution, will be

#chi_"sucrose" = n_"sucrose"/n_"total" = (0.111cancel("moles"))/(8.351cancel("moles")) = color(green)("0.013")#

SIDE NOTE I've left the values rounded to two sig figs, despite the fact that you only gave one sig fig for the mass of glucose.

Definitions

Solute-the substance being dissolved

Solvent-the substance doing the dissolving (the larger amount)

Solution- a homogeneous mixture of the solute and the solvent

Solution= solvent + solute

Aqueous (aq)= water solution

Tincture= alcohol solution

Amalgam= Mercury solution

Molarity (M)- is the molar concentration of a solution measured in moles of solute per liter of solution.

The molarity definition is based on the volume of the solution, NOT the volume of water.

Vocab. Lesson

 Incorrect= The solution is 5.0 Molarity.

Correct= The solution is 5.0 Molar.

 Example Problems

Level 1- Given moles and liters

Determine the molarity when 3.0 moles of sucrose are dissolved to make 2.0 liters of solution.

Level 2- Given Molarity and liters of solution

 Determine the number of moles of salt dissolved in 5.0 liters of a 0.50M solution of salt water.

cross multiply, X= 2.5 mols

Level 3- Given grams (instead of moles) and liters of solution

Determine the molarity when 117g of NaCl are dissolved to make 0.500 liters of solution.

   1st convert to moles, 2nd plug into the molarity equation

117g NaCl( 1mol/58.5g)= 2.00mol NaCl

Level 4-Given grams (instead of moles) and milliliters of solution (instead of liters)

Determine the molarity when 55.5g of CaCl2 are dissolved to make 250.mL of solution.

1st convert to moles, 2nd convert to liters, 3rd plug into the molarity equation

55.5g CaCl2( 1mol/111g)= 0.500mol CaCl2

250.ml( 1L/1000mL) =0.250L

Past Regents Questions-Follow link to check the answers

Jan 2003-44 What is the molarity of a solution of NaOH if 2 liters of the solution contains 4 moles of NaOH?

(1) 0.5 M     (3) 8 M
(2) 2 M       (4) 80 M

Jan. 04-41 What is the molarity of a solution containing 20 grams of NaOH in 500 milliliters of solution?

(1) 1 M (2) 2 M (3) 0.04 M (4) 0.5 M

Jan 2002-42 What is the molarity of a solution that contains 0.50 mole of NaOH in 0.50 liter of solution?

(1) 1.0 M      (3) 0.25 M
(2) 2.0 M      (4) 0.50 M

Aug. 2006-42 How many total moles of KNO3 must be dissolved in water to make 1.5 liters of a 2.0 M solution?

     (1) 0.50 mol     (2) 2.0 mol     (3) 3.0 mol     (4) 1.3 mol

Aug 2005-

41 What is the total number of moles of NaCl(s) needed to make 3.0 liters of a 2.0 M NaCl solution?(1) 1.0 mol      (3) 6.0 mol

(2) 0.70 mol    (4) 8.0 mol

June 2006-

16 Molarity is defined as the(1) moles of solute per kilogram of solvent(2) moles of solute per liter of solution(3) mass of a solution

(4) volume of a solvent

Aug 2008-

15 Which phrase describes the molarity of a solution?(1) liters of solute per mole of solution(2) liters of solution per mole of solution(3) moles of solute per liter of solution

(4) moles of solution per liter of solution

June 2009-46 Which sample of HCl(aq) contains the greatest number of moles of solute particles?
(1) 1.0 L of 2.0 M HCl(aq)
(2) 2.0 L of 2.0 M HCl(aq)
(3) 3.0 L of 0.50 M HCl(aq)
(4) 4.0 L of 0.50 M HCl(aq)

June 2007-

13 A 3.0 M HCl(aq) solution contains a total of(1) 3.0 grams of HCl per liter of water(2) 3.0 grams of HCl per mole of solution(3) 3.0 moles of HCl per liter of solution

(4) 3.0 moles of HCl per mole of water

June 2010-14 The molarity of an aqueous solution of NaCl is defined as the(1) grams of NaCl per liter of water(2) grams of NaCl per liter of solution(3) moles of NaCl per liter of water

(4) moles of NaCl per liter of solution

Jan 2008-

15 Which unit can be used to express solution concentration?(1) J/mol     (3) mol/L

(2) L/mol    (4) mol/s

Jan 04-41 What is the Molarity of a solution containing 20 grams of NaOH in 500 milliliters of solution?(1) 1 M      (3) 0.04 M

(2) 2 M      (4) 0.5 M

Jan 2010-40 What is the molarity of 1.5 liters of an aqueous solution that contains 52 grams of lithium fluoride, LiF, (gram-formula mass =26 grams/mole)?(1) 1.3 M    (3) 3.0 M

(2) 2.0 M    (4) 0.75 M

on to ppm or Molality

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