In this article we are going to analyze how to find molar mass from molarity.

**There are many ways to find molar mass from molarity, but we are going to work with one equation from which on rearranging it we can obtain the required product. For this we should know the other quantities other than the one of our interest.**

**To understand how to find molar mass from molarity we must first understand the relationship between the two terms.**

** The below equation is of our interest:**

**M = w/( mv ) … equation 1**

Where in,

**M = molarity ( in moles/L )**

w = the weight of the solute ( in grams )

m =molar mass of solute ( g/mole)

V = volume of the final solution once the complete dissolution is done ( in litres ).

We can find molar mass from molarity by rearranging the equation 1

**m = w/ Mv … equation 2**

So we can find the three quantities the weight of the solute ( w ), Molarity ( M ), and Volume of the solution ( V ).

**Finding molarity:**

There are many ways in which we can find or calculate molarity but the very basic one that we use nowadays is:

**Molarity = moles of solute / Liters of solution or Volume of solution.**

By using the above relation we can calculate molarity.

**Finding Volume:**

The provided Volume make sure before substituting it should be in liters.

**After knowing the three quantities, we can substitute them in equation 2 and obtain molar mass. So in this way by using the above relationship we can find out molar mass from molarity.**

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**How to find molarity from molar mass and density?**

In order to find molarity from molar mass and density, we should have a relation between the three terms.

**What I am referring to is if we know the two terms we can find out the third one. We can understand molarity in simple words as the amount of any substance present in a given volume of solution ( the one being considered). Another term used to describe molarity is the molar concentration ( of given solution). **

The notation used to denote molarity is M and its standard unit is mol m^{-3}. Density, which is also referred to as specific mass is the mass per unit volume, and the notation used to denote it is rho ( a Greek letter). Its standard unit is kg/m^{3}. A quantity like the pressure is directly proportional to density meaning as the pressure is increased ( keeping the temperature constant ) the density will increase.

Temperature is inversely proportional to density meaning as the temperature is increased ( keeping the pressure constant) the density will decrease. The Molar mass of a compound ( chemical) is the mass of the compound ( in consideration) divided by the substance ( amount) in the sample of the compound being referred.

It’s sometimes also referred to as molecular weight. The standard unit used to describe molar mass is kg/mol. So now we know the perfect meaning of the three terms. So the relation can be given as

**Molarity = density/molar mass × 1000**

**So, if we know density and molar mass of a substance we can easily calculate its molarity.**

**How to find moles from molar mass ?**

**We know that 1 mole is equivalent to 6.022 × 10 ^{23}. We can find moles from the molar mass by**

**using the formula given below:**

**n = m/M **

n = number of moles

m = given mass

M= molar mass

For better understanding let’s see some examples:

**Find out the number of moles in 70g of CH4.**

**Solution**

First, we should calculate molar mass ( by simply adding the weight of the atoms in CH4 formula) and we are provided with mass = **70g (m)**

Molar mass = CH4 = 12 + 4 = **16g/mol.**

**n = m/M = 70/16 = 4.36 mol**

2. **Find out number of moles in 10g of NaOH**.

Molar mass (M) = NaOH = 23 + 16 + 1 = **40g/mol**

m = **10g**

**n = m/M = 10/40 = 0.25 mol**

3.**Find out number of moles in 35g of glucose**

Molar mass (M) = C6H6O12 = 6×12 + 12×1 + 6×16 = **180g/mol**

m = **35g**

**n = m/M = 35/180 = 0.194 mol**

4.**Find out number of moles in 96g of NaCl**

Molar mass = NaCl = 23 + 35 = **58g/mol**

m =** 96g**

**n = m/M = 96/58 = 1.65 mol**

**Read more about: How To Find Molar Mass From Volume: Detailed Explanations**

**How to find mole fraction from molarity?**

**Let us now see what is the relation between mole fraction and molarity.**

Consider,

**XA = mole fraction of solvent**

**XB = mole fraction of solute**

**MA = Molecular mass of solvent**

**MB = Molecular mass of solute**

**nA = number of moles of solvent**

**nB = number of moles of solute**

**WA = mass of solvent**

**WB = mass of mass of solute**

So the mole fraction of the solvent:

**XB = nA / nA + nB … equation 1**

And the mole fraction of the solvent :

**XA = nA / nA + nB … equation 2**

After dividing equation 1 by equation 2 we get

**XB × 1000 / XA × MA = WB × 1000 / WA × MB = m = Molarity**

**Therefore Molarity = XB × 1000 / ( 1- XB ) × MA**

**By rearranging the above equation in an order of our requirements we can calculate mole fraction.**

**Read more about: Is Hydrogen Bond Stronger Than Covalent: Why, How and Detailed Facts**

**How to find the mass of a mole fraction?**

We can understand the interconversion of the two quantities from the following example:

**mass → mole**

36 C

16 H

20 O

28 N

**Assume a basis 100g**

**Change mass to moles**

36g C / 12g / mole = 3 moles

16g H / 1g / mole = 16 moles

20g O / 16g / mole = 1.25 moles

28g N / 14g / mole = 2 moles

**Add all the moles together = 22.25 moles**

**Find the mole** **fraction: moles / total moles**

**So the mole fraction will be**

C : 3 / 22.25 = 0.135

H : 16 / 22.25 = 0.719

O : 1.25 / 22.25 = 0.056

N : 2 / 22.25 = 0.090

**The total of mole fraction comes up to be 1.0.**

**Mole to mass fraction**

36 C

16 H

20 O

28 N

**Assume a basis of 100 moles**

**Change moles to mass**

C : 36 moles × 12g / mole = 432g

H : 16 moles × 1g / mole = 16g

O : 20 moles × 16g mole = 320g

N : 28 moles × 14g / mole = 392g

**On addition of all the masses we get 1160g**

**Find mass fraction: mass / total mass**

C : 432 / 1160 = 0.372

H : 16 / 1160 = 0.014

O : 320 / 1160 = 0.276

N : 392 / 1160 = 0.338

**So, in this way we can find the mass of a mole fraction.**

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**How to calculate molar mass example?**

**Calculating molar mass is very simple just have to add the weights of the atoms, let’s understand through the below example:**

**1.Calculate the molar mass of sodium carbonate**

**Solution :**

We know that the chemical formula of sodium carbonate is Na2CO3

Na (sodium) : 23×2 =** 46**

C : 12×1 = 12

O : 16×3 = 48

**After adding all the masses :**

46+12+48 = **106g/mol**

**So the molar mass of sodium bicarbonate is 106g/mol.**