# Mass-Mole Calculations (n m

# Mass-Mole Calculations (n=m/M) Chemistry Tutorial

## Key Concepts

1 mole of a pure substance has a mass equal to its molecular mass (1) expressed in grams.

This is known as the molar mass, M, and has the units g mol -1 (grams per mole of substance)

The relationship between molar mass, mass and moles can be expressed as a mathematical equation as shown below:

g mol -1 = g ÷ mol

molar mass = mass ÷ moles

where:

M = molar mass of the pure substance (measured in g mol -1 )

m = mass of the pure substance (measured in grams, g)

n = amount of the pure substance (measured in moles, mol)

This mathematical equation can be rearranged to give the following:

n = m ÷ M

moles = mass ÷ molar mass

m = n × M

mass = moles × molar mass

To calculate the moles of pure substance: n = m ÷ M

To calculate mass of pure substance: m = n × M

To calculate molar mass of pure substance: M = m ÷ n

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## Calculating the Mass of a Pure Substance (m=nM)

1 mole of a pure substance is defined as having a mass in grams equal to its relative molecular mass.

This quantity is known as the molar mass (symbol M).

So, mass of 1 mole of a pure substance = relative molecular mass in grams

And, mass of 1 mole of a pure substance = molar mass of the pure substance (g mol -1 )

Or, mass of 1 mole = M (g mol -1 )

The table below gives the mass of 1 mole of a number of common pure substances:

name | molecular formula | relative molecular mass | molar mass (g mol -1 ) | mass of 1 mole (g) |
---|---|---|---|---|

helium gas | He | 4.003 | 4.003 g mol -1 | 4.003 g |

oxygen gas | O_{2} | 2 × 16.00 = 32.00 | 32.00 g mol -1 | 32.00 g |

carbon dioxide gas | CO_{2} | 12.01 + (2 × 16.00) = 44.01 | 44.01 g mol -1 | 44.01 g |

liquid water | H_{2}O | (2 × 1.008) + 16.00 = 18.016 | 18.016 g mol -1 | 18.016 g |

From the table we see that 1 mole of water has a mass of 18.016 grams, which isn’t very much (about the mass of water in a couple of small ice-cubes you’d make in your family freezer).

But what if you had 10 moles of water? What would be the mass of 10 moles of water?

If 1 mole of water has a mass of 18.016 g, then 10 moles of water must have ten times more mass:

mass of 10 moles of water = 10 × mass of 1 mole of water

mass of 10 moles of water = 10 × 18.016 = 180.16 g (about the mass of water you could put in a small glass)

So, if we only had ½ mole of water, what mass of water would we have?

If 1 mole of water has a mass of 18.016 g, then ½ mole of water must have ½ the mass:

mass of ½ mole of water = ½ × mass of 1 mole of water

mass of ½ mole of water = ½ × 18.016 = 9.008 g

In both of the examples above, we can calculate the mass of water in grams by multiplying the moles of water by the mass of 1 mole of water in grams:

mass water = moles of water × mass of 1 mole water

because the mass of 1 mole of water in grams is known as its molar mass, we can write:

mass water = moles of water × molar mass of water

The table below compares the mass of different amounts of water in moles and the data is graphed on the right:

| ||||||||||||||||||||||||||||||||||||

From the data in the table we can generalise and say that for any pure substance the mass of substance in grams is equal to the moles of substance multiplied by the mass of 1 mole of the substance:
mass = moles × mass of 1 mole and since mass of 1 mole of a substance (in grams) = molar mass (in grams per mole) mass (g) = moles × molar mass (g mol -1 ) | The graph above shows a straight line that passes through the origin (0,0) so the equation for the line is: y = slope × x where y is mass of water (g) and x is moles of water (mol) and slope (gradient) of the line = vertical rise ÷ horizontal run =270.24g÷15mol=18.016 g mol -1 = molar mass of water (g mol -1 ) So the equation for this line is: mass (H _{2}O) = molar mass (H_{2}O) × moles (H_{2}O) In general: mass (g) = molar mass (g mol -1 ) × moles (mol) |

Follow these steps to calculate the mass of a pure substance given the amount of substance in moles:

Extract the data from the question:

mass = m = ? (units are grams)

moles = n = write down what you are told in the question

molar mass = M = write down what you are told in the question (units are g mol -1 )

(you may need to calculate this using the molecular formula of the pure substance and a Periodic Table)

Check the units for consistency and convert if necessary:

The amount of substance must be in moles (mol) !

If amount is given in millimoles (mmol), divide it by 1,000 to give the amount in moles (mol).

If amount is given in micromoles (μmol), divide it by 1,000,000 to give an amount in moles (mol).

If amount is given in kilomoles (kmol), multiply it by 1,000 to give an amount in moles (mol).

Write the mathematical equation (mathematical formula):

Substitute in the values and solve the equation to find the value of mass, m, in grams (g).

Do you know this?

Play the game now!

## Calculating the Moles of a Pure Substance (n=m/M)

In the discussion above, we discovered that we could calculate the mass of a pure substance using the moles and molar mass of the substance:

mass (g) = moles (mol) × molar mass (g mol -1 )

How would we calculate the moles of pure substance if we knew the mass of the substance?

(a) We could use some algebra: divide both sides of the equation by the molar mass:

mass | = | moles × molar mass |

molar mass | molar mass |

moles = mass ÷ molar mass

(b) We could use some logic:

we know the mass with units of | grams (g) |

we know the molar mass with units of | grams per mole (g mol -1 ) |

we need to find moles with units of | mole (mol) |

By inspection of units we see that dividing molar mass by mass will give us a quantitiy in units of “mol -1 “

molar mass/mass = g mol -1 / g = mol -1

If we turn this upside down (in mathematical terms, take the reciprocal) we get a quantity with units of “mol” which is what we want:

mass/molar mass = g / g mol -1 = mol

moles = mass ÷ molar mass

Follow these steps to calculate the amount of pure substance in moles given the mass of substance:

Extract the data from the question:

mass = m = write down what you are told in the question

moles = n = ? (units are mol)

molar mass = M = write down what you are told in the question (units are g mol -1 )

(you may need to calculate this using the molecular formula of the pure substance and a Periodic Table)

Check the units for consistency and convert if necessary:

Mass must be in grams !

If mass is given in milligrams (mg), divide it by 1,000 to give the mass in grams (g).

If mass is given in micrograms (μg), divide it by 1,000,000 to give a mass in grams (g).

If mass is given in kilograms (kg), multiply it by 1,000 to give a mass in grams (g).

Write the mathematical equation (mathematical formula):

Substitute in the values and solve the equation to find moles of substances (mol).

Do you understand this?

Take the test now!

## Calculating the Molar Mass of a Pure Substance (M=m/n)

What if you knew the amount of a pure substance in moles and its mass?

Could you calculate its molar mass?

Recall that mass = moles × molar mass or m = n × M

(a) We could use some algebra: divide both sides of the equation by the moles:

mass | = | moles × molar mass |

moles | moles |

molar mass = mass ÷ moles

(b) We could use some logic:

By inspection of units we see that dividing the mass in grams by the amount in moles we arrive at a quantity with the units grams per mole (g mol -1 ) which are the units for molar mass.

Therefore, molar mass (g mol -1 ) = mass (g) ÷ moles (mol)

or you can write

Follow these steps to calculate the molar mass of a pure substance given the amount of substance in moles and the mass of substance:

Extract the data from the question:

mass = m = write down what you are told in the question

moles = n = write down what you are told in the question

molar mass = M = ? (units are g mol -1 )

Check the units for consistency and convert if necessary:

Mass must be in grams (g)!

Amount, moles, must be in moles (mol)!

Write the mathematical equation (mathematical formula):

Substitute in the values and solve the equation to find the molar mass of the substance in grams per mole.

Can you apply this?

Take the exam now!

## Worked Examples of Calculating Mass, Moles, Molar Mass

### Worked Example: mass = moles × molar mass (m=n×M)

Calculate the mass of 0.25 moles of water, H_{2}O.

Extract the data from the question:

moles = n = 0.25 mol

molar mass = M = (2 × 1.008) + 16.00 = 18.016 g mol -1 (Calculated using the periodic table)

mass = m = ? g

Check the data for consistency:

Is the amount of water in moles (mol)? Yes.

We do not need to convert this.

Write the mathematical equation (mathematical formula):

Substitute the values into the equation and solve for mass (g):

### Worked Example: moles = mass &div > Calculate the amount of oxygen gas, O_{2}, in moles present in 124.5 g of oxygen gas.

Extract the data from the question:

mass = m = 124.5 g

molar mass = M = 2 × 16.00 =32.00 g mol -1 (Calculated using the periodic table)

moles = n = ? mol

Check the data for consistency:

Is the mass of oxygen gas in grams (g)? Yes.

We do not need to convert this.

Write the mathematical equation (mathematical formula):

Substitute the values into the equation and solve to find moles of oxygen gas:

### Worked Example: molar mass = mass ÷ moles (M=m/n)

Calculate the molar mass of a pure substance if 1.75 moles of the substance has a mass of 29.79 g.

Extract the data from the question:

mass = m = 29.79 g

moles = n = 1.75 mol

Check the data for consistency:

Is the mass of in grams (g)? Yes. We do not need to convert this.

Is the amount of substance in moles (mol)? Yes. We do not need to convert this.

Write the equation:

Substitute the values into the equation and solve for molar mass:

molar mass = M = 29.79 ÷ 1.75 = 17.02 g mol -1

Can you apply this?

Do the drill now!

## Problem Solving Using Moles, Mass, and Molar Mass

The Problem: Calcium carbonate, CaCO_{3}, is an important industrial chemical. Chris the Chemist has an impure sample of calcium carbonate. The mass of the impure sample is 0.1250 kg and it is composed of 87.00% (by mass) calcium carbonate. Before Chris can use this calcium carbonate in a chemical reaction, Chris needs to know the amount, in moles, of calcium carbonate present in this sample.

Calculate the amount of calcium carbonate in moles present in this impure sample of calcium carbonate.

Solving the Problem using the StoPGoPS model for problem solving:

Calculate the amount of calcium carbonate in moles

n(CaCO_{3}) = moles of calcium carbonate = ? mol

PAUSE! What chemical principle will you need to apply?

Apply stoichoimetry (n = m ÷ M)

What information (data) have you been given?

mass of sample = m(sample) = 0.1250 kg

Step 1: Write the mathematical equation to calculate moles of calcium carbonate:

Step 2: Calculate the mass of calcium carbonate in the sample in kilograms (kg).

mass of calcium carbonate (kg) = 87.00% of mass of sample (kg)

m(CaCO_{3}) = ( 87.00/100) × m(sample)

Step 3: Convert the mass of calcium carbonate in kilograms (kg) to mass in grams (g)

Step 4: Calculate the molar mass of calcium carbonate (use Periodic Table to find molar mass of each element):

Step 5: Substitute the values for m(CaCO_{3}) in grams and M(CaCO_{3}) in g mol -1 into the mathematical equation and solve for n (mol)

GO! Step 1: Write the mathematical equation to calculate moles of calcium carbonate:

Step 2: Calculate the mass of calcium carbonate in the sample in kilograms (kg).

mass of calcium carbonate (kg) = 87.00% of mass of sample (kg)

m(CaCO_{3}) = ( 87.00/100) × m(sample)

m(CaCO_{3}) = ( 87.00/100) × 0.1250 kg = 0.10875 kg

Step 3: Convert the mass of calcium carbonate in kilograms (kg) to mass in grams (g)

m(CaCO

_{3}) in grams = m(CaCO_{3}) in kg × 1000 g/kg

m(CaCO_{3}) in grams = 0.10875 kg × 1000 g/kg 108.75 g

Step 4: Calculate the molar mass of calcium carbonate (use Periodic Table to find molar mass of each element):

molar mass = M(CaCO

_{3}) = M(Ca) + M(C) + [3 × M(O)]

M(CaCO_{3}) = 40.08 + 12.01 + [3 × 16.00] = 40.08 + 12.01 + 48.00 = 100.09 g mol -1

Step 5: Substitute the values for m(CaCO_{3}) in grams and M(CaCO_{3}) in g mol -1 into the mathematical equation and solve for n (mol)

PAUSE! Have you answered the question that was asked?

Yes, we have calculated the moles of calcium carbonate in the sample.

Is your solution to the question reasonable?

Let’s work backwards to see if the moles of calcium carbonate we have calculated will give us the correct mass for the sample.

Roughly calculate mass of CaCO_{3}in 1.087 mol (≈ 1 mol):

m(CaCO_{3}) = n × M = 1 × (40 + 12 + 3 × 16) = 100 g

Roughly calculate the mass of sample if 87% of its mass is due to CaCO_{3}:

m(CaCO_{3}) = 87/100 × m(sample)

m(sample) = 100/87 × m(CaCO_{3}) = 100/87 × 100 = 115 g = 0.115 kg

Since this approximate value for the mass of the sample is about the same as the mass of sample given in the question, we are reasonably confident that our answer is correct.

STOP! How many moles of calcium carbonate are present in the sample?

(1) Molecular mass is also known as molecular weight, formula weight or formula mass

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## Mole Calculator

Want to know how to calculate moles? Need a grams to moles calculator, or even a moles to grams calculator? Well then you’ve come to the right place. With our moles to grams converter, you can seamlessly convert between mass, molecular weight and moles. Chemistry just became that little bit easier! Impress your friends with your astounding ability to find how many moles of a substance you have at a kilogram, ounce, or even tonne scale! (Also useful for any serious industrial applications, for all you chemical engineers out there.)

While we’re on the topic of chemistry, we have a number of other calculators what you might find useful. Why not check out our molarity calculator or our percent yield calculator.

## What is a mole?

A mole is small, subterranean mammal belonging to the family Talpidae. Just kidding. A mole is how chemists define an amount of substance, useful when dealing with many different molecules reacting at once (i.e. any reaction). The official International System of Units definition is that a mole is the amount of a chemical substance that contains exactly 6.02214076×10 23 (Avogadro’s constant) atoms, molecules, ions or electrons (constitutive particles), as of 20 th May 2019. Prior to that, a mole was defined as the number of atoms in 12 grams of carbon-12 (an isotope of carbon). Turns out that memorising that definition for my GCSE chemistry exam was pointless. Shame.

So why do chemists use moles, and why do you need a mole calculator? Well, as we said above, it provides a useful metric when dealing with reactions. Maybe an example would explain it best. Lets say you want to neutralise 10 g of hydrochloric acid (HCl in water) with some sodium hydroxide (NaOH). Now, you want the resulting solution to be perfectly neutral, so you don’t want to add too much or to little NaOH, making it too basic or acidic respectively. It is therefore useful to find out exactly how many molecules of HCl are in the solution. This is where moles come in handy. To know how to calculate moles, the equation is:

mole = mass / molecular weight

If you wanted to find the concentration of the hydrochloric acid, you could use our concentration calculator.

## How to calculate moles – moles to grams converter

Let’s do a quick example to help explain how to convert from moles to grams, or grams to moles. We know we have 10 g of HCl, and it has a molecular weight of 36.5 g / mol. Lets plug these numbers into the above equation:

mole = 10 / 36.5 = 0.27 moles = 1.626×10^23 molecules of HCl

We can work out the number of molecules by timesing the moles by Avogadro’s constant above. Now we know the amount of molecules of HCl we have, and, since the reaction is 1:1, we need the exact same number of molecules of NaOH to neutralise it. As we need to find the mass of NaOH to add, lets quickly rearrange the equation:

mole = molecular weight / mass (mulitply both sides by mass)

mole * mass = molecular weight (divide both sides by mole)

mass = molecular weight / mole

As 1.626×10 23 molecules of NaOH is also equal to 0.27 moles, and we know that the molecular weight of NaOH is 40, we can use these numbers to get:

mass = 40 / 0.27 = 10.8 g

So we now know we need 10.8 g of NaOH to exactly neutralise our amount of hydrochloric acid.

We hope this grams to moles calculator (or moles to grams calculator) will help you with your chemical calculations! You may also find our titration calculator of use to you.

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## Mole Calculation

In these lessons, we will learn

- how to calculate the mass of a substance when we are given the number of moles (mole to mass conversion).
- how to calculate the number of moles of a substance when we are given the mass (mass to mole conversion).

The following diagram shows the conversion between Mole and Mass. Scroll down the page for more examples and solutions.

mass = number of moles × molar mass

where mass is in grams and the molar mass is in grams per mole.

**Moles to Mass Calculation**

We can use the above equation to find the mass of a substance when we are given the number of moles of the substance.

*Example:*

Calculate the mass of (a) 2 moles and (b) 0.25 moles of iron. (Relative atomic mass: Fe = 56)

*Solution:*

a) mass of 2 moles of iron

= number of moles × molar mass

= 2 × 56

= 112 g

b) mass of 0.25 mole of iron

= number of moles × molar mass

= 0.25 × 56

= 14 g

*Example:*

Calculate the mass of (a) 3 moles and (b) 0.2 moles of carbon diox >

*Solution:*

a) mass of 1 mole of CO_{2 }= (1 × 12) + (2 × 16)

= 44 g

mass of 3 moles of CO_{2 }= 3 × 44

= 132g

b) mass of 0.2 mole of CO_{2 }= 0.2 × 44

= 8.8 g

If we are given the mass of a substance and we are asked to find the number of moles of the substance, we can rewrite the above equation as

*Example:*

Calculate the number of moles of aluminum present in (a) 108 g and (b) 13.5 g of the element. (Relative atomic mass: Al = 27)

*Solution:*

*Example:*

Calculate the number of moles of magnesium ox >

*Solution:*

a) Mass of 1 mole of MgO

b)

**Examples of mass to mole calculation**

Example:

How many moles of acetic ac data-tab-content>

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## Mole Conversion Tips for Chemistry

## Chemistry Workbook For Dummies, 2nd Edition

In a general chemistry class, you usually end up having to perform a lot of conversions involving moles (mol). Whether you’re converting from moles to grams, moles to volume, or moles to particles (atoms or molecules), use this quick guide to remind you of how to do each type of mole conversion:

**Converting from mass (grams) to moles:** Divide your initial mass by the molar mass of the compound as determined by the periodic table.

**Converting from moles to mass (grams):** Multiply your initial mole value by the molar mass of the compound as determined by the periodic table.

**Converting from volume (liters) to moles:** Divide your initial volume by the molar volume constant, 22.4 L.

**Converting from moles to volume (liters):** Multiply your mole value by the molar volume constant, 22.4L.

**Converting from particles (atoms, molecules, or formula units) to moles:** Divide your particle value by Avogadro’s number, 6.02×10 23 . Remember to use parentheses on your calculator!

**Converting from moles to particles (atoms, molecules, or formula units):** Multiply your mole value by Avogadro’s number, 6.02×10 23 .

**Mole-to-mole conversions:** Use the coefficients from your balanced equation to determine your conversion factor. Be sure your units cancel out so you end up with the correct mole value.

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