How to find liters from molarity and moles

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Molarity is a unit of concentration, measuring the number of moles of a solute per liter of solution. The strategy for solving molarity problems is fairly simple. This outlines a straightforward method to calculate the molarity of a solution.

The key to calculating molarity is to remember the units of molarity (M): moles per liter. Find the molarity by calculating the number of moles of the solute dissolved in liters of a solution.

Sample Molarity Calculation

• Calculate the molarity of a solution prepared by dissolving 23.7 grams of KMnO4 into enough water to make 750 mL of solution.

This example has neither the moles nor liters needed to find molarity, so you must find the number of moles of the solute first.

To convert grams to moles, the molar mass of the solute is needed, which can be found on certain periodic tables.​

• Molar mass of K = 39.1 g
• Molar mass of Mn = 54.9 g
• Molar mass of O = 16.0 g
• Molar mass of KMnO4 = 39.1 g + 54.9 g + (16.0 g x 4)
• Molar mass of KMnO4 = 158.0 g

Use this number to convert grams to moles.

• moles of KMnO4 = 23.7 g KMnO4 x (1 mol KMnO4/158 grams KMnO4)
• moles of KMnO4 = 0.15 moles KMnO4

Now the liters of solution is needed. Keep in mind, this is the total volume of the solution, not the volume of solvent used to dissolve the solute. This example is prepared with "enough water" to make 750 mL of solution.

Convert 750 mL to liters.

• Liters of solution = mL of solution x (1 L/1000 mL)
• Liters of solution = 750 mL x (1 L/1000 mL)
• Liters of solution = 0.75 L

This is enough to calculate the molarity.

• Molarity = moles solute/Liter solution
• Molarity = 0.15 moles of KMnO4/0.75 L of solution
• Molarity = 0.20 M

The molarity of this solution is 0.20 M (moles per liter).

Quick Review of Calculating Molarity

To calculate molarity:

• Find the number of moles of solute dissolved in solution,
• Find the volume of solution in liters, and
• Divide moles solute by liters solution.

Make certain to use the correct number of significant figures when reporting your answer. One easy way to track the number of significant digits is to write all your numbers in scientific notation.

Cite this Article

Format

Your Citation

Helmenstine, Todd. "How to Calculate Molarity of a Solution." ThoughtCo. https://www.thoughtco.com/calculate-molarity-of-a-solution-606823 (accessed December 27, 2022).

Molarity is the number of moles of a substance in one litre of solution. The official symbol for molarity is “c” (concentration), but many people use the old symbol “M”.

#M = n/V#, where#n#is the number of moles and#V#is the volume in litres.

We can rearrange this equation to get the number of moles:

#n = M × V#

Example
:
How many moles of#"NaCl"#are contained in 0.300 L of 0.400 mol/L#"NaCl"#solution?

Solution:

#n = 0.300 color(red)(cancel(color(black)("L soln"))) × "0.400 mol NaCl"/(1 color(red)(cancel(color(black)("L soln")))) = "0.120 mol NaCl"#

Molarity is used to measure the concentration of a solution. It is used to calculate the volume of solvent or the amount of solute. Molarity is the concentration of a solution or substance in solution, measured as the number of moles of solute per liter of solution. It is denoted by the upper case letter “M.” The smallest particle of matter which can take part in a chemical reaction is called the atom. Molecule is formed by two or more atoms tightly bound together. Mole is a fundamental SI unit. It is used to measure the amount of substance. A mole of any substance (atom, molecule, etc.) is 6.022 × 1023 molecules. Molecular mass is defined as the sum of atomic masses of all atoms in a molecule of a substance. It is expressed in the atomic mass unit (u). For example,

2H+ + O2 ⇢ H2O = 1×2 +16 = 18u

Dilution is the process by which a solution is made by the addition of more solvent to make it less concentrated. The concentration of a solution is the amount of solute in a solution. There is a difference between molarity and molar mass, molarity is the number of moles of solute per liter of solution, whereas molar mass is the number of grams per mole of some substance.

Calculating Molarity

Molarity is defined as the number of moles of solute that is dissolved in one liter of solution. It is also known as molar concentration and is denoted by the letter “M.”

Molarity Formula

M = n/v

Where,

• M denotes the molar concentration
• n denotes the number of moles
• v denotes the total volume of solution in liters

To calculate the molarity of a solution by using the above formula,

1. To find the molarity of a solution, we divide the number of moles of solute by the total volume of liters of solution. 
2. When the amount of solute is given in grams, then we must first find or calculate the number of moles of solute.
3. To find the number of moles of solute, we can calculate by dividing by the solute molecular mass. So, when it is divided by total volume, the answer is molarity.
4. The volume of specific mass in given grams of solution can also be calculated by the process by finding the number of moles of solute as above. Then divided with molarity given to find the total volume of the solution.

Sample Problems

Problem 1: What is the molarity of a solution by dissolving 42.5g of H2SO4 in 1 liter of the solution?

Solution: 

Given mass = 42.5g, volume of solution = 1L 

By using the formula,

M = n/v

But, we must find number of moles,

n = mass given/molecular mass

n = 42.5g/98.076 g mol-1

n = 0.43 moles

Now divide the no. of moles with a total volume of solution.

M = 0.43 moles/1L

M = 0.43

The molarity of H2SO4 is 0.43M.

Problem 2: If seawater contains 40g of sodium chloride per 500ml, then what is the molarity of a solution?

Solution: 

Given mass = 40g, volume of solution = 500mL

By using the formula,

M = n/v

but, we must find number of moles

n = mass given/molecular mass

n = 40g/58.443 g mol-1

n = 0.68 moles

Now divide the no. of moles with the total volume of solution,

Convert ml to L

M = 0.68g/0.500L

M = 1.36

The molarity of NaCl is 1.36M.

Problem 3: How many moles of Na2CO3 are present in 15L of a 2M solution?

Solution: 

Given M = 2, v = 15L and n = ?

By using the formula

M = n/v

2M = n/15L

n = 2M × 15L

n = 30 moles

There are 30 moles of Na2CO3 present in 15L of a 2M solution.

Problem 4: In a 20.0ml HCL of  2.0 M solution, how many moles are present?

Solution: 

Given: M = 2.0, v = 20.0ml and n = ?

Convert milliliter to liter 

By using the formula

M = n/v

2.0M = n/0.0200L

n = 2.0M × 0.0200L

n = 0.040 moles.

There are 0.040 moles in 20.0ml HCl of  2.0 M solution.

Problem 5: How many grams of H2SO4 in weight are required to make 950ml of 0.500 M solution?

Solution: 

Given: M = 0.500, v = 950ml

M = n/v

To find mass (grams),

Mv = n

Where n = mass/molecular mass

Mv = mass/molecular mass

0.500M × 0.950L = x/98.0768 g mol-1

x = 0.500M × 0.950L × 98.0768 g mol-1

x = 46.6g

46.6 grams of H2SO4 in weight required to make 950ml of 0.500 M solution.

Problem 6: How many grams of Ca(OH)2 are needed to make 250 ml of 0.350M solution?

Solution: 

Given M = 0.350, v = 250ml

M = n/v

To find mass (grams),

Mv = n

n = mass/molecular mass

n = x/74.0918 g mol-1

Mv = x/74.0918 g mol-1

x = 0.350M × 0.250L × 74.0918 g mol-1

x = 6.48g

6.48g of Ca(OH)2 are needed to make 250 ml of 0.350M solution.

Problem 7: What is the total volume in ml of 10.0M HCl is needed to contain 5.00 moles of HCl solution?

Solution: 

Given M = 10.0, n = 5.00 moles and v = ?

By using the formula,

M = n/v

v = n/M

v = 5.00 moles/10.00M

v = 0.500L

Convert liters to milliliters,

v = 500ml

Therefore, 500ml of volume is needed to make 10.0M HCl contain 5.00 moles of HCl solution.

Problem 8: What is the molarity of 25g of NaCl solution, which is dissolved in water to produce 2L of the solution?

How do you calculate liters in molarity?

How do you turn moles into liters?