What is the molarity of a solution in which 58.44 g of NaCl are dissolved in 2.0 L of solution?

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What is molarity?

Molarity is the concentration of a solution in terms of the number of moles of the solute in 1 dm3 (1 liter) of the solution.

The units of molarity are M or mol/L. A 1 M solution is said to be “one molar”.

A mole is the quantity of anything that has the same number of particles as 12 g of carbon-12. This equates to roughly 6.02x1023, also referred to as Avogadro's Number. So, 1 mole of hydrogen gas (H2) contains 6.02x1023 molecules, and 1 mole of glucose (C6H12O6.) also contains 6.02x1023 molecules, but as H2 is a much simpler molecule, 1 mole of H2 will have a much smaller mass (the molar mass) than 1 mole of C6H12O6.

The molar mass is the mass in grams of 1 mole of a particular molecule.

One mole of sodium (Na) is 22.99 g, and 1 mole of chlorine is 35.45 g. For sodium chloride (NaCl) they are in a ratio of 1:1 so the molar mass of NaCl is 22.99 + 35.45 = 58.44 g/mol.
For a compound like water (H2O), 1 mole of hydrogen (H) is 1.008 g/mol and 1 mole of oxygen (O) is 15.9994 g/mol. So, the molar mass of H2O is (2 x 1.008) + 15.9994 = 18.0154 g/mol.

Two solutions that have the same molarity will have the same number of molecules of the chemical per liter but are likely to contain differing masses of that chemical per liter to achieve this. Whereas two solutions at the same concentration will have the same mass of the chemical per liter of solution but are therefore likely to have differing numbers of molecules of that chemical per liter. Provided some additional information is known, one value can be deduced from the other using the equations below.

To calculate molarity or to calculate related values (including volume, mass, molar mass and concentration) from molarity, the following equations are utilized.

Number of moles (mol) = Mass (g) / Molar Mass (g/mol) Concentration (g/L) = Mass (g) / Volume (L)

Molarity (M or mol/L) = Number of Moles (mol) / Volume (L)

The scenario in which most lab scientists will encounter this type of calculation is when making up solutions following a standard operating procedure (SOP) or a scientific paper. Here, the solution being used is typically defined by its molar concentration (M). For example;
You need to make a 0.5 M solution of NaCl, having decided you want 2 liters how much NaCl should you add?

1. First you must calculate the number of moles in this solution, by rearranging the equation
   No. Moles (mol) = Molarity (M) x Volume (L) = 0.5 x 2 = 1 mol
2. For NaCl, the molar mass is 58.44 g/mol Now we can use the rearranged equation Mass (g) = No. Moles (mol) x Molar Mass (g/mol) = 1 x 58.44 = 58.44 g

   So, to make 2 liters of a 0.5 M solution of NaCl, you would need to add 58.44 g of NaCl.

   
   

– mass of one atom of that element which typically reflects the mass of the nucleus (protons plus neutrons). For example, hydrogen is 1. This used to be measured in atomic mass units (AMU) but is now typically expressed in Daltons (Da).

- sum of the atomic weights of all atoms appearing in a given molecular formula. For example, glucose has a molecular formula of C6H12O6, the molecular weight of C is 12 Da, H is 1 Da and O is 16 Da. Therefore, the molecular mass of glucose is = (6 x 12) + (12 x 1) + (6 x 16)

– values for atomic and therefore molecular masses are normally obtained relative to the mass of the isotope 12C (carbon-12), however “relative” is generally omitted from the title. Written correctly, the relative values have no units.

- sum of the atomic weights of all atoms appearing in a given empirical formula. The empirical formula indicates the ratio of atoms of each element in a molecule rather than the actual number. For example, glucose (molecular formula C6H12O6) would therefore have the empirical formula CH2O, the molecular weight of C is 12 g, H is 1 g and O is 16 g. Therefore, the formula mass of glucose is

For molecules like H2O, where the formula is already in its simplest form, the formula mass and molecular mass are the same.

– similar to molarity, however calculation of normality uses the number of mole equivalents rather than the number of moles. Units are N or eq/L. Normality is generally only used when a substance has more than one sub-species that can participate in a specified reaction such as a proton for acid/base reactions, an electron for oxidation/reduction reactions, or in precipitation reactions. For example, sulfuric acid (H2SO4) has two ionizable protons (H+) which can participate in the neutralization of a base such as sodium hydroxide (NaOH)

– similar to molarity, however calculation of molality uses the mass rather than volume of the solvent used, making it temperature independent unlike molarity. Units are m or mol/kg.

As is clear from its name, molarity involves moles. ��The molarity of a solution is calculated by taking the moles of solute and dividing by the liters of solution.

This is probably easiest to explain with examples.

Example #1 - Suppose we had 1.00 mole of sucrose (it's about 342.3 grams) and proceeded to mix it into some water. It would dissolve and make sugar water. We keep adding water, dissolving and stirring until all the solid was gone. We then made sure that when everything was well-mixed, there was exactly 1.00 liter of solution.

What would be the molarity of this solution?

The answer is 1.00 mol/L. Notice that both the units of mol and L remain. Neither cancels.

A replacement for mol/L is often used. It is a capital M. So if you write 1.00 M for the answer, then that is correct.

And never forget this: replace the M with mol/L when you do calculations. The M is just shorthand for mol/L.

Example #2 - Suppose you had 2.00 moles of solute dissolved into 1.00 L of solution. What's the molarity?

The answer is 2.00 M.

Notice that no mention of a specific substance is mentioned at all. The molarity would be the same. It doesn't matter if it is sucrose, sodium chloride or any other substance. One mole of anything contains 6.022 x 1023 units.

Example #3 - What is the molarity when 0.75 mol is dissolved in 2.50 L of solution?

The answer is 0.300 M.

Now, let's change from using moles to grams. This is much more common. After all, chemists use balances to mass things and balances give grams, NOT moles.

Example #4 - Suppose you had 58.44 grams of NaCl and you dissolved it in exactly 2.00 L of solution. What would be the molarity of the solution?

The solution to this problem involves two steps which will eventually be merged into one equation.

Step One: convert grams to moles.

Step Two: divide moles by liters to get molarity.

In the above problem, 58.44 grams/mol is the molecular weight of NaCl. ��Dividing 58.44 grams by 58.44 grams/mol gives 1.00 mol.

Then, dividing 1.00 mol by 2.00 L gives 0.500 mol/L (or 0.500 M). Sometimes, a book will write out the word "molar," as in 0.500-molar.

Do examples #5 and #6:

5) Calculate the molarity of 25.0 grams of KBr dissolved in 750.0 mL.

6) 80.0 grams of glucose (C6H12O6, mol. wt = 180. g/mol) is dissolved in enough water to make 1.00 L of solution. What is its molarity?

Goto the example answers (Coming soon)

Practice Problems

1) Calcuate the molarity when 75.0 grams of MgCl2 is dissolved in 500.0 mL of solution.

2) 100.0 grams of sucrose (C12H22O11, mol. wt. = 342.3 g/mol) is dissolved in 1.50 L of solution. What is the molarity?

3) 49.8 grams of KI is dissolved in enough water to make 1.00 L of solution. What is the molarity?

Go to the problem answers (Coming soon)

Notice how the phrase "of solution" keeps showing up. The molarity definition is based on the volume of the solution, NOT the volume of pure water used. For example, to say this:

"A one molar solution is prepared by adding
one mole of solute to one liter of water"

is totally incorrect. It is "one liter of solution" not "one liter of water."

Be careful on this, especially when you get to molality.

Go to Molarity Worksheet

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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