- Ch.1 - Intro to General Chemistry
- Ch.2 - Atoms & Elements
- Ch.3 - Chemical Reactions
- BONUS: Lab Techniques and Procedures
- BONUS: Mathematical Operations and Functions
- Ch.4 - Chemical Quantities & Aqueous Reactions
- Ch.5 - Gases
- Ch.6 - Thermochemistry
- Ch.7 - Quantum Mechanics
- Ch.8 - Periodic Properties of the Elements
- Ch.9 - Bonding & Molecular Structure
- Ch.10 - Molecular Shapes & Valence Bond Theory
- Ch.11 - Liquids, Solids & Intermolecular Forces
- Ch.12 - Solutions
- Ch.13 - Chemical Kinetics
- Ch.14 - Chemical Equilibrium
- Ch.15 - Acid and Base Equilibrium
- Ch.16 - Aqueous Equilibrium
- Ch. 17 - Chemical Thermodynamics
- Ch.18 - Electrochemistry
- Ch.19 - Nuclear Chemistry
- Ch.20 - Organic Chemistry
- Ch.22 - Chemistry of the Nonmetals
- Ch.23 - Transition Metals and Coordination Compounds

Ever wonder how a mass amount such as moles can be converted into the volume amount of liters? Well, molarity serves as the bridge between moles and liters.

**Concept:** Definition of Molarity

We're going to say the molarity serves as a connection that allows us to interconvert between moles and liters. Basically, if I have molarity, I can go from moles to liters or liters to moles.

We're going to say, for example, we have 5.8, capital M means molarity, so that really means 5.8 molar, 5.8 molar NaCl solution really means, we have a 5.8 moles of NaCl per 1 liter of solution. So, just remember, whatever your molarity is, it's that number in moles over 1 liter. Now, the formula simply for molarity is molarity equals moles of solute over liters of solution.

Now, the terms of solute and solution, we really haven't talked about until now. What we should realize is that we talked about mixture before. We said that mixtures could be heterogeneous or homogenous and we're going to say that a typical mixture consists of basically two parts.

We have a smaller amount of one substance, which is called the solute and it's dissolved in a larger amount of another substance called the solvent. So, the smaller solute gets dissolved by the larger solvent. We're going to say together, solute plus solvent give us the solution.

Anytime that you hear the term **molarity **used, just think that we are talking about how many moles of a **solute** are in a liter of **solution**.

Forgot what's the difference between a solute and a solution? Here's a reminder:

**Concept:** The difference between a solute and solvent

Here we have an image. Here we're going to say that this represents pure water. Pure water is known as the universal solvent. That just means that it's able to dissolve tons of different types of compounds. Now, if you take some table salt or maybe even some sugar and you just sprinkle some in there, it's going to dissolve in there. So we're going to have little specs of sugar or salt mixed in there. Those little specs of sugar or salt will represent your solute. They're the solute because they're so much smaller than the total volume of the liquid. So, the little bits of sugar or salt that you pour in there are your solute, the water is the solvent and it dissolves it, together they formed a solution. This is our pure solvent. We say we throw in some salt or sugar. The solvent dissolves it and together they form our solution. So, these are the terms that we need to be aware of. And when we get to calculation on Molarity, it's going become essential that you guys remember, whatever your Molarity is, it's that number in moles over 1 liter.

In a **homogeneous mixture**, the smaller amount is the **solute**, and the larger amount is the **solvent**. When dissolving a solute into a solvent they make a solution.

**Example:** 2.64 grams of an unknown compound was dissolved in water to yield 150 mL of solution. The concentration of the solution was 0.075 M. What was the molecular weight of the substance?

A **concentrated solution** can become a **diluted solution** with the addition of water.

**Example:** A solution is prepared by dissolving 0.1408 mol calcium nitrate, Ca(NO_{3})_{2}, in enough water to make 100.0 mL of stock solution. If 20.0 mL of this solution is then mixed with an additional 90 mL of deionized water, calculate the concentration of the calcium nitrate solution.

We know how to calculate the molarity of a compound, but what do we do when we need the *molarity of ions *within the compound? Let's see.

**Problem:** What is the molarity of calcium ions of a 650 mL solution containing 42.7 g of calcium phosphate?

A

0.0657 M

B

0.636 M

C

0.000212 M

D

0.318 M

% of students got this right

Now let's try connecting molarity with an equation from the past, density.

**Problem:** A solution with a final volume of 750.0 mL was prepared by dissolving 30.00 mL of benzene (C6H6, density = 0.8787 g/mL ) in dichloromethane. Calculate the molarity of benzene in the solution.

A

0.4499 M

B

0.8998 M

C

0.2250 M

D

0.150 M

% of students got this right

What is the molarity of ZnCl2 that forms when 30.0 g of zinc completely reacts with CuCl2 according to the following reaction? Assume a final volume of 285 mL

Zn(s) + CuCl2 (aq) ---> ZnCl2(aq) + Cu(s)

Watch Solution

When solutions of silver nitrate and potassium chloride are mixed, silver chloride precipitates out of solution according to the equation

AgNO3(aq) + KCl(aq) --> AgCl(s) + KNO3(aq)

What mass of silver chloride can be produced from 1.97 L of a 0.232 M solution of silver nitrate? Express your answer with the appropriate units.

The reaction described in Part A required 3.65 L of potassium chloride. What is the concentration of this potassium chloride solution? Express your answer with the appropriate units.

Watch Solution

What is the concentration of nitrate ions in a 0.125 M Mg(NO _{3})_{2} solution?

a. 0.0625 M

b. 0.160 M

c. 0.250 M

d. 0.125 M

e. 0.375 M

Watch Solution

A chemist wants to make 5.0 L of a 0.260 M CaCl_{2} solution. What mass of CaCl_{2} (in g) should the chemist use?

Watch Solution

What is the molarity of Cl^{−} in each solution?

A) 0.170 M NaCl.

B) 0.150 M SrCl_{2}.

Watch Solution

Zinc reacts with hydrochloric acid according to the reaction equation:

Zn + 2HCl → ZnCl_{2} + H_{2}

How many milliliters of 5.50 M HCl(aq) are required to react with 3.65 g of an ore containing 33.0% Zn(s) by mass?

Watch Solution

Zinc reacts with hydrochloric acid according to the reaction equation

Zn(s) + 2HCl(aq) = ZnCl_{2}(aq) + H_{2}(g)

How many milliliters of 6.00 M HCl(aq) are required to react with 5.65 g of Zn(s)?

Watch Solution

The concentration of distilled white vinegar is written as 5% (w/v) of acetic acid (CH_{3}COOH). Convert the concentration in the unit of molarity. Express your answer in four significant figures.

Watch Solution

The molecular weight of ethanol (C_{2}H_{5}OH) is 46.1 and the density of absolute (100%) ethanol = 0.79 g/mL

The legal limit for a driver’s blood alcohol is 50 mg of ethanol per 100 mL of blood (referred to as a blood alcohol content (BAC) of 0.05%). What is the molarity of ethanol (in blood) in a person at this legal limit?

Watch Solution

1) What is the concentration of K ^{+} in 0.15 M of K _{2}S?

2) If CaCl_{2} is dissolved in water, what can be said about the concentration of the Ca ^{2+} ion?

a. It has the same concentration as the Cl ^{−} ion.

b. Its concentration is half that of the Cl ^{−} ion.

c. Its concentration is twice that of the Cl ^{−} ion.

d. Its concentration is one-third that of the Cl ^{−} ion.

Watch Solution

The molecular weight of ethanol (C_{2}H_{5}OH) is 46.1 and the density of absolute (100%) ethanol = 0.79 g/mL

a) Calculate the molarity of absolute ethanol (100% ethanol).

b) Calculate the molarity of ethanol in a bottle of wine that is 14.0% ethanol by volume.

Watch Solution

When solutions of silver nitrate and magnesium chloride are mixed, silver chloride precipitates out of solution according to the equation.

2AgNO_{3}(aq)+MgCl_{2}(aq) → 2AgCl(s) + Mg(NO_{3})_{2}(aq)

a) What mass of silver chloride can be producd from 1.49L of a 0.254M solution of silver nitrate?

b) The reaction described in Part A required 4.00L of magnesium chloride. What is the concentration of this magnesium chloride solution?

Watch Solution

How many grams of phosphoric acid are there in 175 mL of a 3.5 M solution of phosphoric acid (MW 98.00 g/mol)?

a) 0.61 g

b) 60 g

c) 21 g

d) 4.9 g

e) 610 g

Watch Solution

How many grams of KOH are required to prepare a 250.0 mL solution of 0.50 M KOH? (K = 39.10 amu, O = 16.00 amu, H = 1.008 amu)

a. 16 g

b. 13 g

c. 11 g

d. 9.0 g

e. 7.0 g

Watch Solution

An aqueous solution that is 42.0% of C _{2}H_{6} by mass has a density of 1.78 g/mL. What is the molarity of this solution?

a. 24.9 M

b. 0.0249 M

c. 1.40 M

d. 43.0 M

e. 0.052 M

Watch Solution

How many grams of KMnO _{4} are required to prepare 750.0 mL of a 0.125 M solution?

A. 11.4

B. 14.8

C. 15.2

D. 17.5

E. 27.5

Watch Solution

What is the molarity of formaldehyde in a solution containing 0.300 g of formaldehyde (CH_{2}O) per mL?

(A) 0.0000100 M

(B) 0.0100 M

(C) 0.100 M

(D) 1.00 M

(E) 10.0 M

Watch Solution

What is the molarity of formaldehyde in a solution containing 0.30 g of formaldehyde (CH_{2}O) per mL?

(A) 0.3 M

(B) 1 M

(C) 3 M

(D) 10 M

(E) 30 M

Watch Solution

Hydrochloric acid is widely used as a laboratory reagent, in refining ore for the production of tin and tantalum, and as a catalyst in organic reactions. Calculate the number of moles of HCl in 62.50 mL of 0.500 M hydrochloric acid.

(A) 0.03125 mol

(B) 0.125 mol

(C) 8 mol

(D) 31.25 mol

(E) 125 mol

Watch Solution

How many liters of a 0.0550 M NaOH solution contain 0.163 moles of NaOH?

a) 3.37 L

b) 1.48 L

c) 8.97 L

d) 2.96 L

e) 1.12 L

Watch Solution

Calculate the number of moles HCl in 62.85mL of 0.453 M hydrochloric acid.

Watch Solution

A solution has 25.65 g of calcium perchlorate (*MW* = 238.98 g/mol) in 1.23 L. What is the concentration of perchlorate ions in M? Enter your answer with 3 decimal places and no units.

Watch Solution

What is the total concentration of ions in a 1.1 M solution of ammonium sulfate?

A. 1.1 M

B. 2.2 M

C. 3.3 M

D. 4.4 M

E. 18.7 M

Watch Solution

What would be the molarity of NaOH in a solution made by dissolving 57.2 g of NaOH in enough water to make a final volume of exactly 500 mL? The molar mass of NaOH is 40.01 g/mol?

A. 6.99 M

B. 14.3 M

C. 2.86 M

D. 5.71 M

E. 0.1092 M

Watch Solution

What is the mass of potassium iodide (molar mass = 166.0 g/mol) in 50.0 mL of 5.75 x 10^{–2} M KI (aq)?

a. 288 g

b. 0.191 g

c. 0.00288 g

d. 0.477 g

e. 191 g

Watch Solution

If 5.15 g Fe(NO_{3})_{3} (molar mass = 241.9 g/mol) is dissolved in enough water to make exactly 150.0 mL of solution, what is the molar concentration of nitrate ion?

a. 0.0473 M

b. 0.0212 M

c. 0.142 M

d. 0.318 M

e. 0.426 M

Watch Solution

If 4.49 g NaNO_{3} (molar mass = 85.0 g/mol) is dissolved in enough water to make 250.0 mL of solution, what is the molarity of the sodium nitrate solution?

a. 0.0180 M

b. 0.0528 M

c. 0.211 M

d. 0.0132 M

e. 18.0 M

Watch Solution

How many moles of Nal are in 23.0 mL of a 0.250 M solution?

A. 0.250 moles Nal

B. 5.75 moles Nal

C. 0.00575 moles Nal

D. 0.0920 moles Nal

E. 10.9 moles Nal

Watch Solution

Given the precipitation of AgCl from a NaCl solution using silver nitrate:

AgNO_{3} + NaCl(aq) → AgCl(s) + NaNO_{3}(aq)

If a solution of AgNO_{3} of unknown molarity is added to a flask containing 132ml of NaCl solution also of unknown molarity. At the endpoint 42.15 ml of the AgNO_{3} solution have been added and 8.42 g of AgCl are recovered as a precipitate from the reaction:

a) What is the molarity of the NaCl solution?

b) What is the molarity of AgNO_{3} solution?

Watch Solution

What is the molarity of an NaOH solution which contains 24.0g of NaOH dissolved in 200mL of solution?

Watch Solution

A 46.2-mL, 0.568 M calcium nitrate [Ca(NO_{3})_{2}] solution is mixed with 80.5 mL of 1.396 M calcium nitrate solution. Calculate the concentration of the final solution.

Watch Solution

What volume, in liters, of a 2.00 M KCl solution contains 2.5 g of KCl? (Molar mass KCl = 74.55 g/mole)

Watch Solution

Calculate the molarity of bromide ions in a solution if you mixed 12.86 g calcium bromide, CaBr_{2}, in enough water to make 305.0 mL of solution

Watch Solution

Which of the following solutions will have the highest concentration of bromide ions?

a) 0.10 M NaBr

b) 0.10 M CaBr_{2}

c) 0.10 M AlBr_{3}

d) 0.05 M MnBr_{4}

e) All of these solutions have the same concentration of bromide ions.

Watch Solution

How many moles of Ca** ^{2+}** ions are in 0.100 L of a 0.450 M solution of Ca

Watch Solution

What volume (in µL) of 0.100 M HBr contains 0.170 moles of HBr?

Watch Solution

How many milligrams of NaCN are required to prepare 712 mL of 0.250 M NaCN?

Watch Solution

A 4.691 g sample of MgCl_{2} is dissolved in enough water to give 750 mL of solution. What is the magnesium ion concentration in this solution?

A) 3.70 x 10^{–2} M

B) 1.05 x 10^{–2} M

C) 6.57 x 10^{–2} M

D) 4.93 x 10^{–2} M

E) 0.131 M

Watch Solution

How many liters of a 0.0550 M KCl solution contain 0.163 moles of KCl?

A) 1.12 L

B) 3.37 L

C) 8.97 L

D) 2.96 L

E) 1.48 L

Watch Solution

Determine the molarity of a solution formed by dissolving 468 mg of MgI _{2} in enough water to yield 50.0 mL of solution.

A) 0.0297 M

B) 0.0337 M

C) 0.0936 M

D) 0.0107 M

E) 0.0651 M

Watch Solution

Determine the molarity of a solution formed by dissolving 97.7 g LiBr in enough water to yield 750.0 mL of solution.

A) 1.50 M

B) 1.18 M

C) 0.130 M

D) 0.768 M

E) 2.30 M

Watch Solution

What mass of KBr is needed to make a 6.54 M solution in 25.00 mL ?

A. 19.5 g

B. 1.37 g

C. 0.151 g

D. 1.95 x 10^{4} g

Watch Solution

To prepare 100.0 mL of a 0.100 M copper(II) chloride solution from 0.500 M copper(II) chloride, pipet into a volumetric flask

(A) 10.0 mL of the 0.500 M solution and then add water until the total volume is 100.0 mL.

(B) 20.0 mL of the 0.500 M solution and then add water until the total volume is 100.0 mL.

(C) 20.0 mL of the 0.500 M solution into 80.0 mL of water.

(D) 40.0 mL of the 0.500 M solution into 60.0 mL of water.

Watch Solution

What is the molarity of a solution made by dissolving 8.56 g of sodium in acetate water and diluting to 750.0 mL?

(A) 5.30 M

(B) 0.139 M

(C) 0.104 M

(D) 0.0783 M

Watch Solution

Which diagram represents the most concentrated solution?

Watch Solution

How many moles of sodium ions are in 35.0 ml of a 0.750 M NaCl(aq) solution?

A. 0.0263 moles

B. 0.750 moles

C. 0.0523 moles

D. 0.375 moles

E. 0.131 moles

Watch Solution

Commercial grade HCl solutions are typically 39.0% (by mass) HCl in water. Determine the molarity of the HCl, if the solution has a density of 1.20 g/mL.

A) 13.9 M

B) 12.8 M

C) 10.7 M

D) 9.35 M

E) 7.79 M

Watch Solution

Determine the mass (g) of solute required to form 25 mL of a 0.1881 M H _{2}O_{2} solution.

a) 0.031

b) 160

c) 0.31

d) 0.022

e) 0.16

Watch Solution

How many chloride ions are present in 65.5 mL of 0.210 M AlCl_{3} solution?

a. 4.02 x 10^{23} chloride ions

b. 5.79 x 10^{24} chloride ions

c. 2.49 x 10^{22} chloride ions

d. 8.28 x 10^{21} chloride ions

e. 1.21 x 10^{22} chloride ions

Watch Solution

3.25 g of acetone (CH _{3}COCH_{3}, 58.08 g/mol) are dissolved in water to make 125.00 mL of a solution. What is the molarity of the acetone?

a. 0.0560 M

b. 0.448 M

c. 0.560 M

d. 0.000448 M

e. Cannot be calculated from the information given.

Watch Solution

How many milliliters of a 0.184 M NaNO _{3} solution contain 0.113 moles of NaNO_{3}?

a. 885 mL

b. 614 mL

c. 326 mL

d. 163 mL

e. 20.8 mL

Watch Solution

When making up a solution of accurately known volume, one has to allow the solution to reach room temperature before bringing the volume up to the mark because:

a) the same mass of a liquid will occupy different volumes at different temperatures

b) heat may be evolved when a liquid is added to a solid in a flask

c) heat may be evolved when two liquids are added together in a flask

d) none of the above is true

e) all of the above is true

Watch Solution

How many moles of PO_{4}^{3}^{–} ions are in 2.00 L of a 0.600 M solution of a Ca _{3}(PO_{4})_{2}?

a) 0.600

b) 1.000

c) 1.200

d) 2.400

e) 3.600

Watch Solution

Patrick Star took 33.0 mL of a 1.50 M solution of KI and diluted it to 400.0 mL. What was the resulting molarity of his solution?

a) 8.08

b) 1.32 x 10^{4}

c) 7.58 x 10^{-5}

d) 18.18

e) 0.124

Watch Solution

Spongebob Squarepants dissolved 4.96 g HNO_{3} on enough water to make 269 mL of solution.

What was the molarity of his solution?

a) 3.41

b) 0.293

c) 0.0242

d) 18.43

e) 0.0184

Watch Solution

Determine the molarity of a solution formed by dissolving 0.468 g of MgI _{2} in enough water to yield 50.0 mL of solution.

A. 0.0287 M

B. 0.0107 M

C. 0.0936 M

D. 0.0337 M

E. 0.0651 M

Watch Solution

Which one of the following solutions will have the greatest concentration of hydroxide ions?

a) 0.100 M hydrochloric acid

b) 0.100 M magnesium hydroxide

c) 0.100 M ammonia

d) 0.300 M rubidium hydroxide

e) 0.250 M calcium hydroxide

Watch Solution

In a solution, the solute is the smaller portion that is being dissolved by the solvent, the larger portion usually in the form of H_{2}O. Molarity is the term used to describe the solubility of the solute within the solvent.

**Molarity Formula **

Molarity serves as the bridge between moles and volume. It is the concentration of a solution represented as moles of solute per liter of solution:

This would mean a solution that is 0.10 M NaCl:

Although moles per liter are the traditional units for molarity, you can also use mg/mL because it is proportionally equivalent.

**Molarity Calculations**

From the molarity formula, you can calculate volume, grams or the moles of solute.

To calculate molarity from mass (in grams, milligrams, etc.) and volume (milliliters, liters, microliters, etc.):

To calculate the mass from volume and concentration:

To calculate the volume from mass and concentration:

**Osmolarity**

Ionic molarity or osmolarity represents the molarity of dissolved ions in a solution. For example, if you were asked how to calculate the osmolarity of 0.200 M KNO_{3}.

** STEP 1**: Break the ionic compound into ions.

** STEP 2**: Now calculate the osmolarity of the solution with its equation.

**Dilutions**

Another common idea related to molarity deals with the dilution of stock solutions. In a dilution a concentrated solution is made more diluted by adding water.

**After Molarity **

Eventually you will do calculations that connect molarity to problems with density, molarity vs molality, mole fraction, mass fraction or percent.

Beyond these calculations that deal directly with the molarity formula you can bring in stoichiometry. This brings in more complex problems dealing with solution chemistry, acid base titration, pH and pOH.

Join **thousands** of students and gain free access to **46 hours** of Chemistry videos that follow the topics **your textbook** covers.