Sample Problems on Molarity

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?

Solution: 

Given mass = 25g, v = 2L and M = ?

First, we must convert grams into moles by dividing with molecular weight NaCl 58.4 g/mole.

M = n/v

n = mass given/molecular mass

n = 25g/58.4 g mol^-1

n  = 0.42 moles.

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

M = 0.42 moles/2L

M = 0.2

The molarity of NaCl is 0.2M.

The molarity of a solution can be calculated by finding the ratio of several moles of solute dissolved in the solution with the volume of the solution in litres. Molarity is the measure of concentration of a solute present in a solution. In this article, we will learn what molarity is, how to calculate molarity and some sample problems on the molarity concept.