Under mass conversions, connections between **grams, moles **and **molecules** are established.

The **mole** is the chemical unit for the amount of a substance and serves as the bridge that connects grams to molecules, atoms, formula units and ions.

**Concept:** Avogadro’s Number, Moles, Molecules & Atoms

Before we begin, we should realize that mass conversions are going to play a very important and essential role in almost all the calculations we're going to do this semester.

We're going to start off by saying that the mole is the chemical unit for the amount of a substance. What exactly does this mean? Instead of a chemist ordering a hundred pounds of a particular element, a scientist could easily say 'I need 10.12 moles of carbon' or '100 moles of nitrogen'. It's basically a certain way that chemist communicate with each other to designate the amount, the weight they need of a particular element or compound.

We're going to say that one mole which you can write as this way, one mole contains 6.022x1023 entities. We're going to say that this special number has a name to it. This special number is known as Avogadro's number. When we say the word 'entities', entities means different things. When we say entities, entities can mean atoms, molecules or particles.

We're going to say we use atoms when we're dealing with a single or individual element. If I want 1,000 atoms of oxygen, I'm only talking about single oxygen. Remember oxygen can exists as a diatomic molecule, but here we're not talking about the molecule, we're talking about just the atom.

We're going to say we use molecules or particles when dealing with more than one element together or a compound, so just remember the difference. Atoms go with a single elements, molecules or particles goes with more than one element together or a compound. Compounds remember are just different elements combined together.

The words **atoms** and **ions** are used when talking about a single element and the words **molecules** and **formula units** are used when talking about more than one element together.

**Concept:** Atoms to Moles to Grams

How does this relate to our calculations we're going to do this semester?

Here we have two good examples of when do we use atoms versus when do we use molecules or particles. If we take a look, we say we have 6.022x1023 atoms of iron. Iron is there by itself, so that's why we're using the term atoms. Remember that's Avogadro's number. That number is always equal to one mole of whatever we're talking about. Since we have this many atoms of iron, that means we have one mole of iron.

We're going to say also that one mole of something is related to its weight. It's atomic mass which you'll find on your periodic table. If you look at your periodic table right now, look for iron, it's a transition metal. One mole of iron is equal to its atomic mass that you see on your periodic table. If you take a look, you'll see 55.85. That's representative of its atomic mass unit or we can say 55.85 grams per mole.

What we need to realize here, that there's a connection. We can go from atoms to moles to grams. I show you double arrows meaning we can go either way. So we can go from atoms to moles or moles to atoms. We can go from moles to gram or grams to moles. The arrows go both ways.

What we should realize here is that moles play the connection that's between atoms and grams. Remember you can’t go straight from atoms to grams without having first go through moles.

**Example:** Determine the mass (in grams) found in 7.28 x 10** ^{28}** nitrogen atoms.

**Concept:** Molecules to Moles to Grams

We've seen how atoms work. Now let's see how molecules work. We're going to start out again with Avogadro's number, but this time in terms of molecules of water. Remember that Avogadro's number is equal to one mole of whatever we're talking about, whether it be an atom, whether it be a molecule, whether it be particles, so that's equal to one mole of water.

One mole of any substance, whether it be an individual element or a compound, one mole of anything is equal to that objects molecular weight, its atomic mass. Here we have a mixture of different elements together, we have two hydrogens, we have one oxygen and water. To find out its total mass, we're going to add up each individual part.

We have two hydrogens, right? Because this little two here with the H, if you look on your periodic table, look for the atomic mass of hydrogen. When you look at it, you'll see that on your periodic table, its 1.008 grams and there are two hydrogens, so multiply that number times two. So that's 2.016 grams per mole.

Also, we have one oxygen which weighs 16 grams according to our periodic table, so that's 16 grams per mole. When you add those two numbers up together, that gives you the 18.016 grams per mole or 18.016 atomic mass units. That's where that number came from. We looked up each of the atomic masses of each individual element and then added them up together to get our answer.

Remember, Avogadro's number is always equal to one mole of whatever we're talking about. One mole of anything is just equal to the total mass of that object. If we take a look at this example, we're going to say it says, 'Determine how many molecules of carbon dioxide are found in 75 grams of carbon dioxide?'

Now, you should notice that this chart is similar to the one we just saw, except now instead of seeing atoms, we see molecules. You could also put particles in there too. Remember, there's a connection between molecules at moles, you can go from molecules to moles or moles to molecules and again there's a connection between moles and grams.

**Example:** Determine the how many molecules of carbon dioxide, CO_{2}, are found in 75.0 g CO_{2}.

**Problem:** If the density of water is 1.00 g/mL at 25^{o}C calculate the number of water molecules found in 1.50 x 10^3 µL of water.

**Problem:** Calculate the number of oxygen atoms found in 783.9 g in copper (II) sulfate pentahydrate, CuSO4 x 5 H2O.

**Problem:** The density of the sun is 1.41 g/cm3 and its volume is 1.41 x 10^27 m3. How many hydrogen molecules are in the sun if we assume all the mass is hydrogen gas?

**Problem:** A cylindrical copper wire is used for the fences around a house. The copper wire has a diameter of 0.0750 in. How many copper atoms are found in 5.160 cm piece? The density of copper is 8.96 g/cm3. ( V = pi x r^2 x h )

How many xenon atoms are contained in 2.36 moles of xenon?

Watch Solution

On the planet Tatooine, the unit of length is the zither which is defined by the relationship 7.50 cm = 1 zither. A distance of 100 meters would be _________ zithers.

a. 133

b. 266

c. 750

d. 1.33 X 10^{3}

e. 7.5 X 10^{4}

Watch Solution

What is the average mass in grams of one atom of iron?

a. 55.85 g

b. 6.02 x 10^{-23} g

c. 9.28 x 10^{-23} g

d. 1.66 x 10^{-24} g

e. 55.85 x 10^{-25} g

Watch Solution

Which of the following samples contains the largest number of atoms?

a. 1 g Li

b. 1 g F_{2}

c. 1 g C

d. 1 g P_{4}

e. 1 g N_{2}

Watch Solution

How many atoms of carbon are there in 0.80 moles of C _{6}H_{4}Cl_{2}?

a. 3.9 x 10^{24}

b. 3.6 x 10^{24}

c. 2.9 x 10^{24}

d. 6.0 x 10^{23}

e. 4.8 x 10^{23}

Watch Solution

How many sodium atoms are in 6.0 g of Na _{3}N?

a. 1.3 x 10^{23} atoms

b. 3.6 x 10^{24} atoms

c. 1.217 atoms

d. 4.6 x 10^{22} atoms

e. 0.072 atoms

Watch Solution

How many sulfur atoms are present in 256 mg of Al _{2}(S_{2}O_{3})_{3}?

a. 3.95 x 10^{22}

b. 6

c. 7.90 x 10^{22}

d. 0.393

e. 2.37 x 1021

Watch Solution

What is the molecular weight of glucose, C_{6}H_{12}O_{6}

Watch Solution

Suppose we have 100 g of each of the following substances. Which sample contains the largest number of moles?

1. MgCO_{3}, formula weight 84.3

2. AgCl, formula weight 143.3

3. Impossible to tell, unless we know what reaction will take place with the substance.

4. HCl, formula weight 36.5

5. H_{2 }O, formula weight 18.0

Watch Solution

Stearic acid (C_{18}H_{36}O_{2}) is a fatty acid found in beef and butter.

a) What is the molecular mass of stearic acid? Give your answer in units of g/mol.

b) How many oxygen atoms are present in 1.000 g of stearic acid?

Watch Solution

What is the identity of substance X if 0.380 mol of X weighs 17.5 g?

A) NO_{2 }

B) N_{2}O

C) N_{2}O_{4}

D) NO_{3}

Watch Solution

What is the molar mass of calcium permanganate?

A) 199 g/mol

B) 278 g/mol

C) 216 g/mol

D) 159 g/mol

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How many moles of C_{3}H_{8 }contain 4.95 × 10 ^{24 }hydrogen atoms?

A) 3.09 moles C_{3}H_{8}

B) 6.58 moles C_{3}H_{8}

C) 1.03 moles C_{3}H_{8}

D) 9.73 moles C_{3}H_{8}

E) 8.22 moles C_{3}H_{8}

Watch Solution

How many moles of N_{2}O_{3} contain 2.55 × 10^{24} oxygen atoms?

A) 7.87 moles N_{2}O_{3}

B) 1.41 moles N_{2}O_{3}

C) 4.23 moles N_{2}O_{3}

D) 12.7 moles N_{2}O_{3}

E) 2.82 moles N_{2}O_{3}

Watch Solution

What is the mass of 9.44 × 10 ^{24} molecules of NO_{2}? The molar mass of NO_{2} is 46.01 g/mol.

A) 294 g

B) 341 g

C) 205 g

D) 685 g

E) 721 g

Watch Solution

What is the mass (in kg) of 6.89 × 10 ^{25} molecules of CO_{2}? The molar mass of CO_{2} is 44.01 g/mol.

A) 5.04 kg

B) 3.85 kg

C) 3.03 kg

D) 2.60 kg

E) 6.39 kg

Watch Solution

How many C_{2}H_{4 } molecules are contained in 45.8 mg of C _{2}H_{4 }? The molar mass of C_{2}H_{4 } is 28.05 g/mol.

A) 2.71× 10 ^{20} C_{2}H_{4 }molecules

B) 9.83 × 10 ^{20} C_{2}H_{4 } molecules

C) 7.74 × 10^{ 26 } C_{2}H_{4 } molecules

D) 4.69 × 10^{ 23} C_{2}H_{4 }molecules

E) 3.69 × 10^{ 23} C_{2}H_{4 } molecules

Watch Solution

How many N_{2}O_{4 }molecules are contained in 76.3 g N _{2}O_{4}? The molar mass of N_{2}O_{4} is 92.02 g/mol.

A) 4.59 × 10 ^{25} N_{2}O_{4} molecules

B) 5.54 × 10 ^{25} N_{2}O_{4 }molecules

C) 7.26 × 10 ^{23} N_{2}O_{4} molecules

D) 1.38 × 10 ^{24 }N_{2}O_{4} molecules

E) 4.99 × 10 ^{23} N_{2}O_{4} molecules

Watch Solution

Calculate the molar mass for Mg(ClO_{4})_{2}.

A) 247.52 g/mol

B) 119.52 g/mol

C) 123.76 g/mol

D) 223.21 g/mol

E) 75.76 g/mol

Watch Solution

Calculate the mass (in kg) of 4.87 x 10 ^{25 }atoms of Zn.

A) 1.09 kg

B) 1.89 kg

C) 5.29 kg

D) 1.24 kg

E) 8.09 kg

Watch Solution

How many iron atoms are contained in 354 g of iron?

A) 9.50 × 10 ^{22} Fe atoms

B) 3.82 × 10 ^{24} Fe atoms

C) 2.13 × 10 ^{26} Fe atoms

D) 4.69 × 10 ^{24} Fe atoms

E) 2.62 × 10^{25} Fe atoms

Watch Solution

If 4.05 x 10^{23} molecules of a substance have a mass of 86.2 g, what is the molar mass of the substance?

A) 128 g/mol

B) 3.49 x 10^{25} g/mol

C) 2.13 x 10^{22} g/mol

D) 4.70 x 10^{21} g/mol

E) 58.0 g/mol

Watch Solution

How many formula units are in 0.25 mole of Na _{2}O?

A) 4.5 x 10^{23}

B) 0.75

C) 1.5 x 10^{23}

D) 4.2 x 10^{–25}

E) 0.25

Watch Solution

How many moles of PBr_{3} are contained in 3.68 × 10^{25} bromine atoms?

A) 61.1 moles PBr_{3}

B) 20.4 moles PBr_{3}

C) 16.4 moles PBr_{3}

D) 183 moles PBr_{3}

E) 49.1 moles PBr_{3}

Watch Solution

What is the mass (in kg) of 6.89 × 10 ^{25} molecules of CO_{2}? The molar mass of CO_{2} is 44.01 g/mol.

A) 3.85 kg

B) 5.04 kg

C) 2.60 kg

D) 3.03 kg

E) 6.39 kg

Watch Solution

A 20.0 g sample of an element contains 4.95 x 10^{23} atoms. Identify the element.

A) Cr

B) O

C) Mg

D) Fe

Watch Solution

What is the molar mass of aspartic acid, C _{4}O_{4}H_{7}N?

A) 43.03 g/mol

B) 70.02 g/mol

C) 86.91 g/mol

D) 133.11 g/mol

E) 197.98 g/mol

Watch Solution

The ebola virus is structured like a long filament that ranges from 974 to 1086 nm in length. If length of a virus filament is found to be 1046 nm, what would the the length be in cm?

a. 1.046 x 10^{10} cm

b. 1.046 x 10 ^{-4} cm

c. 1.046 x 10^{14} cm

d. 1.046 x 10 ^{-8} cm

e. 1.046 x 10^{-3} cm

Watch Solution

Amavadin is a vanadium-containing compound found in three species of toxic mushrooms. The chemical formula for amavadin is VC_{12}H_{16}N_{2}O_{10} and has molar mass 398.94 g•mol^{-1}. If a mushroom contains 2.00 mg of amavadin, how many molecules are present?

a. 1.20 x 10^{23}

b. 4.80 x 10^{23}

c. 3.02 x 10^{21}

d. 3.02 x 10^{18}

Watch Solution

What mass (in kg) does 0.0822 moles of lead (Pb) have?

a. 0.397 kg

b. 17.0 kg

c. 2.52 kg

d. 0.0170 kg

e. 0.632 kg

Watch Solution

In the chemical reaction N_{2} + 3 Mg → Mg _{3}N_{2 }if you begin with 1.35 moles of Mg, how many moles of N_{2} are required to react all of the Mg?

A. 0.45

B. 1.01

C. 1.35

D. 1.80

E. 4.05

Watch Solution

If 2.50 grams of an unknown compound contains 6.25 x 10 ^{19} molecules, what is its molecular mass?

Watch Solution

Which of the following amounts have the ** most** molecules?

a) 15.0 g N_{2}

b) 15.0 g Br_{2}

c) 15.0 g O_{2}

d) 15.0 g l_{2}

Watch Solution

Which of the following amounts would contain the ** least** atoms?

a) 10.0 g Sr

b) 10.0 g Br

c) 10.0 g Mg

d) 10.0 g Li

Watch Solution

How many atoms of oxygen are there in 53.2 g Al _{2}(SO_{4})_{3}?

a. 9.36 x 10^{22}

b. 3.75 x 10^{23}

c. 1.12 x 10^{24}

d. 2.81 x 10^{23}

Watch Solution

How many moles of sodium ions (Na ^{+}) are in 56.0 g of sodium phosphate (Na _{3}PO_{4})?

A. 0.342 mol Na^{+}

B. 1.03 mol Na^{+}

C. 0.114 mol Na^{+}

D. 3.06 x 10^{3} mol Na^{+}

Watch Solution

A 2.000 g sample of an unknown metal, M, was completely burned in excess O _{2} to yield 0.02224 mol of the metal oxide, M_{2}O_{3}. What is the metal?

A. Y

B. Ca

C. Al

D. Sc

Watch Solution

The number of atoms in 9.0 g of aluminum is the same as the number of atoms in _____.

A. 8.1 g of magnesium

B. 9.0 g of magnesium

C. 12.1 g of magnesium

D. 18.0 g of magnesium

Watch Solution

What mass of the compound CrO_{3} (M = 100.0) contains 4.5 x 10 ^{23} oxygen atoms?

a) 2.25 g

b) 12.0 g

c) 25.0 g

d) 75.0 g

Watch Solution

If the mass of 2.51 x 10 ^{-3} moles of compound A is 0.452 g, then what is the molar mass?

Watch Solution

How many sodium ions are contained in 99.6 mg of Na _{2}SO_{3} ?

a) 1.05 X 10^{21}

b) 1.52 X 10^{27}

c) 2.10 X 10^{21}

d) 9.52 X 10^{20}

Watch Solution

How many iron atoms are contained in 354 g of iron?

A) 2.62 × 10^{25} Fe atoms

B) 2.13 × 10^{26} Fe atoms

C) 4.69 × 10^{24} Fe atoms

D) 3.82 × 10^{24} Fe atoms

E) 9.50 × 10^{22} Fe atoms

Watch Solution

How many Li atoms are contained in 97.9 g of Li?

A) 5.90 × 10^{25} Li atoms

B) 7.09 × 10^{21} Li atoms

C) 8.49 × 10^{24} Li atoms

D) 4.27 × 10^{22} Li atoms

E) 4.18 × 10^{24} Li atoms

Watch Solution

How many argon atoms are contained in 7.66 x 10 ^{5} mol of argon?

A) 4.61 × 10^{29} Ar atoms

B) 1.84 × 10^{28} Ar atoms

C) 1.15 × 10^{28} Ar atoms

D) 7.86 × 10^{20} Ar atoms

E) 3.24 × 10^{26} Ar atoms

Watch Solution

How many cm^{3} are contained in 3.77 × 10^{4} mm^{3}?

A) 3.77 × 10^{4} cm^{3}

B) 3.77 × 10^{1} cm^{3}

C) 3.77 × 10^{-10} cm^{3}

D) 3.77 × 10^{20} cm^{3}

E) 3.77 × 10^{6} cm^{3}

Watch Solution

A 0.370 mol sample of a metal oxide (M _{2}O_{3}) weighs 55.4 g. How many grams of M are in the sample, and what element is represented by the symbol M?

a) 75.28 g/mol; Arsenic

b) 101.7 g; Ruthenium

c) 37.6 g; Vanadium

d) 17.8 g; Metalium

e) 41.3 g; Iron

Watch Solution

What mass of carbon is present in 0.500 mol of sucrose (C_{12}H_{22}O_{11})?

Molar mass: C_{12}H_{22}O_{11} = 342 g/mol

A. 60.0 g

B. 72.0 g

C. 90.0 g

D. 120 g

Watch Solution

A 1.000-g sample of a metal chloride, MCl _{2}, is dissolved in water and treated with excess aqueous silver nitrate. After drying, the silver chloride that formed weighed 1.286 g. Calculate the mass of M.

a) 222.8 g b) 76.00g c) 152.0 g d) 304.0 g e) none of these

Watch Solution

What is the atomic weight of an element, X, if 1.00g of X combines with 0.66 g of oxygen to form a compound XO_{3}?

A. 24

B. 67

C. 73

D. 100

E. 146

Watch Solution

What is A, if 64.0 g of A combines exactly with 142 g of Cl to give the compound ACl _{2}?

A. Br

B. Mg

C. Ca

D. S

E. Ba

Watch Solution

What is the mass of one molecule of C_{8}H_{18} (octane) in grams?

A. 114

B. 1.9 x 10^{-22}

C. 26

D. 6.9 x 10^{-21}

E. 3.8 x 10^{-22}

Watch Solution

A compound has a formula of Y_{2}O_{5}. If 2.8 g of Y combines with 8.0 g of oxygen, what is the atomic weight of Y?

A. 10

B. 12

C. 14

D. 16

E. 18

Watch Solution

Which of the following contains most hydrogen atoms in one gram of sample?

A. HClO_{4}

B. HClO_{3}

C. HClO_{2}

D. HClO

E. HCl

Watch Solution

Which contains the largest number of carbon atoms?

A. 0.10 mol of carbon atoms

B. 1.2 g carbon

C. 0.10 mol of CH_{4}

D. 1.6 g of CH_{4}

E. All are the same

Watch Solution

How many moles are in 25 mg of O _{2}? (Atomic mass of O = 16.00 g/mol)

A) 7.8 ×10^{−4}

B) 1.6 ×10^{−3 }

C) 0.40

D) 0.80

E) 800

Watch Solution

For a 90.0 g sample of glucose (C_{6}H_{12}O_{6)} and a 171.1 g sample of sucrose (C_{12}H_{22}O_{11}), which statement is true?

a. The sample of glucose has more moles than the sample of sucrose.

b. The sample of sucrose has more moles than the sample of glucose.

c. The samples have the same number of moles.

d. 1 mol of glucose has greater molecular mass than 1 mol of sucrose.

e. 1 mol of glucose has more C atoms in comparison to 1 mol of sucrose.

Watch Solution

We have a 1.3 x 10^{22} lead atoms and the same number of gold atoms. Which statement is true regarding the mass of these samples?

a. The mass of both of the samples is the same

b. The mass of the lead sample is greater than the mass of the gold sample.

c. The mass of the gold sample is greater than the mass of the lead sample.

d. The mass of the gold sample is 4.5 g.

e. The mass of the lead sample is 4.3 g.

Watch Solution

The definition of the mole gives the relationship between:

a. mass and the atomic number.

b. mass and number of atoms.

c. mass and weight.

d. the masses of the different isotopes of an atom.

e. the isotopes of an atom and the number of atoms.

Watch Solution

One molecule of a compound weighs 2.03 x 10 ^{-22} grams. Calculate the molar mass of this molecule.

a. 3.37 x 10^{-46} g/mol

b. 3.36 x 10^{-23} g/mol

c. 1.23 x 10^{-21} g/mol

d. 1.22 x 10 ^{2} g/mol

e. 1.21 x 10^{24} g/mol

Watch Solution

What is the molar mass of calcium phosphate, Ca _{3}(PO_{4})_{2}?

a. 87.05 g/mol

b. 215.21 g/mol

c. 278.18 g/mol

d. 279.21 g/mol

e. 310.18 g/mol

Watch Solution

How many moles of methanol are present in a 150.0 gram sample of methanol, CH_{3}OH?

a. 7.776 x 10 ^{-24 }moles

b. 4.681 moles

c. 5.172 moles

d. 4806 moles

e. 2.818 x 10 ^{24} moles

Watch Solution

What mass (in kg) does 5.84 moles of Titanium (Ti) have?

a. 0.352 kg

b. 0.122 kg

c. 0.820 kg

d. 0.280 kg

e. 0.632 kg

Watch Solution

If 2.50 grams of an unknown compound contains 6.25 x 10^{19} molecules, what is its molecular mass?

Watch Solution

Which of the following equals the number of hydrogen atoms in 40 grams of methane?

a. 1.5 x 10 ^{24}

b. 2.4 x 10 ^{24}

c. 6.0 x 10 ^{24}

d. 6.022 x 10 ^{23}

Watch Solution

A single atom of a certain element has a mass of 3.352 x 10 ^{-23 }g. The element is

a. Ne

b. Co

c. Al

d. Br

e. Ti

Watch Solution

What is the mass of 1.3 x 10 ^{13} moles of N_{2 }in pg?

a. 3.64 x 10^{14}

b. 1.82 x 10^{14}

c. 1.82 x 10^{26}

d. 3.64 x 10^{26}

e. none of the given answers is even close to being correct

Watch Solution

What is the weight of O in 742.0 g of citronella oil that has the chemical formula C_{10}H_{18}O?

a. 19.31

b. 18.52

c. 77.10

d. 115.5

e. 231.3

Watch Solution

How many oxygen atoms are in a 125 mg sample of aspirin? The molar mass of aspirin is 180.15 g/mol and its molecular formula is C_{9}H_{8}O_{4}.

a) 4.18 × 10^{23 }

b) 4.18 × 10^{20 }

c) 1.67 × 10^{21}

d) 1.36 × 10^{25}

e) 8.68 × 10^{23}

Watch Solution

A piece of metal was placed in a beaker, heated, and reacted with oxygen, thereby becoming a metal oxide. During this process, depending on reaction conditions, the metal’s oxidation state could become either M^{2+} or M^{3+}. Consider the mass of the metal oxide.

a) The mass of the metal oxide is the same as the mass of the initial metal

b) The mass of the metal oxide is greatest if the metal becomes M ^{3+}

c) The mass of the metal oxide is greatest if the metal becomes M ^{2+}

d) The mass of the metal oxide is greatest if O _{2}(g) is the limiting reactant.

Watch Solution

How many Cl^{–} ions are there in 15.6 g of MgCl _{2}?

Watch Solution

How many Cl atoms are there in 27.3 grams of magnesium chloride?

Watch Solution

Identify the correct statement regarding the mole.

a) A mole of oxygen gas contains 6.02 x 10 ^{23} atoms.

b) A mole of chlorine gas contains 2 x 6.02 x 10 ^{23} molecules.

c) A mole of carbon dioxide contains two moles of oxygen atoms.

d) A mole of ammonia gas (NH _{3}) has a mass of 34.0 g.

e) A mole consists of the number of particles in exactly 12 g of naturally occurring carbon.

Watch Solution

A 1.000-g sample of a metal chloride, MCl _{2}, is dissolved in water and treated with excess aqueous silver nitrate. After drying, the silver chloride that formed weighed 1.286 g. Calculate the atomic mass of M.

a) 222.8 g

b) 76.00 g

c) 152.0 g

d) 304.0 g

e) none of these

Watch Solution

How many Cl atoms are there in 27.3 grams of magnesium chloride?

Watch Solution