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.

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**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?

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.

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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

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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

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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

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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

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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

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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

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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

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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

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

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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.

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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

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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

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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

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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

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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

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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

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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?

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

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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.

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

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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

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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.

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

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

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

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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

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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

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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

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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

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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

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Muriatic acid, a commercial-grade hydrochloric acid used for cleaning masonry surfaces, is typically around 10 percent HCl by mass and has a density of 1.2 g/cm^{3}. Assuming 2 sig figs in all numbers, calculate the molarity of muriatic acid.

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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

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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

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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