M1V1=M2V2 - Examples, Calculator, Uses, formula for dilution in chemistry?

Dilution: It is a process in which the concentration of a solute in the solution is decreased by adding more solvent to the solution. In the dilution process, the concentration of the solution decreases while the volume of the whole solution increased.

The amount of dilute remains constant in the dilution process. (the number of moles is the same before and after dilution).

Why is the (M₁V₁=M₂V₂) formula used in the dilution problem, explain?

To understand this equation, we have to focus on the definition of Molarity. “Molarity is defined as the moles of a solute per liters of a solution”.

∴ Molarity = Moles of solute/liters of solution

We can also write it as –

⇒ Moles of solute = (Molarity) × (Liters of solution)

∴ Moles of solute = M × V      [∴ M represents molarity and V represents Volume]

In dilution process, the number of moles is the same before and after dilution. That means (M×V) remains same before and after concentration change.

So, according to this, we can write the initial and final conditions as –

⇒ M₁V₁=M₂V₂

The above equation represents the dilution equation.

Does M₁V₁=M₂V₂ have to be in liters?

The short answer is, It doesn’t matter whether the volumes in the M₁V₁=M₂V₂ equation are in liters or not, but it is important to be consistent with the units used. Here’s what you need to consider:

What really matters is –

• The initial and final concentrations must have the same units.
• If your initial concentration is in moles per liter and final concentration should also have the same unit(moles per liter).
• Also, if the concentration is in moles per liter, then, it doesn’t necessary that the volume should also be in liters. But the thing is, the initial volume and final volume must have the same unit.
• Let’s say if V₁ is in milliliters then V₂ should also be in milliliters, and vice versa, if the given volume is in liters then another volume should also be in liters.

Maintaining consistency in the units used for both concentration and volume will ensure the equation works correctly for solving dilution problems.

How to solve dilution problems using (M₁V₁=M₂V₂)?

It’s really easy, all you have to do is rearrange the formula(M₁V₁=M₂V₂) according to the question needs and find the value of the unknown one.

In most of the dilution problems, you have to ask to find either the concentration or volume in either the initial side or the final side of the equation.

For example, If in a given problem, the value of M1 is x, for M2, it is y, and for V2, it is z. Now find the value of V1 =?

∴ We have, M₁V₁=M₂V₂

Put the given values in the above equation-

⇒ xV₁ = yz

∴ V₁ = yz/x       Answer

That’s how simple it is to solve the problem of dilution using the equation M₁V₁=M₂V₂.

Examples of dilution problems using (M₁V₁=M₂V₂)?

Let’s take some examples to understand the process of solving dilution problems using the equation (M₁V₁=M₂V₂).

Q1. A solution having a molarity of 6 M and a volume of 4 liters, after the dilution, the volume of the solution becomes 8 liters, then, calculate the molarity of the dilute solution?

Answer – In the given problem, the initial molarity is 6 M, and the initial volume is 4 liters. So, we have, M1 = 6 and V1 = 4 Also, it is given, that after the dilution, the volume of the solution becomes 8 liters. So, V2 = 8 Now we have to find the molarity of the dilute solution which means M2 =? Use the equation, M1V1=M2V2 ∴ M2 = M1V1/V2 = (6 × 4)/8 = 3 ∴ So, the molarity of dilute solution (M2) is 3. Or use the M1V1=M2V2 calculator to solve this problem –

Q2. A solution having a molarity of 8 M and a volume of 4 liters. If 2 liters of solvent are added to the solution, calculate the molarity of the final solution?

Answer = Given, M1 = 8, V1 = 4 “If 2 liters of solvent are added to the solution” ∴ V2 = V1 + 2 = 4 + 2 V2 = 6 liters Now we have to find M2. Use the equation, M1V1=M2V2 ∴ M2 = M1V1/V2 = (8 × 4)/6 = 16/3 ∴ M2 = 5.33  Or use the M1V1=M2V2 calculator to solve this problem –

Q3. How many mL of a 2.50 M NaOH solution are required to make 525 mL of a 0.150 M NaOH solution?

Answer – In given problem, we have given, M1 = 2.50, M2 = 0.150, V2 = 525 We have to find, V1 =? Use the equation, M1V1=M2V2 ∴ V1 = M2V2/M1 = (0.150 × 525)/2.50 = 31.5 ∴ V1 = 31.5 mL Or use the M1V1=M2V2 calculator to solve this problem –

Q4. If 45.0 mL of a 6.00 M HCl solution is diluted to a final volume of 0.250 L, what is the final concentration?

Answer – Given, M1 = 6, V1 = 45 mL Also, the final volume (V2) is 0.250 L, we have to find, M2 =? We have one problem here, in the given question, V1 is in milliliters and V2 is in Liters, so, both have different units. According to the dilution equation concept – The initial and final volume must have same units. For example – If V1 is in liter then V2 must also be in liters. So, what we have to do is convert the milliliter unit to a liter. V1 = 45 mL = 0.045 Liter Now put these values in the dilution equation- ⇒ M1V1=M2V2 ∴ M2 = M1V1/V2 = (6 × 0.045)/0.250 = 1.08 ∴ M2 = 1.08 M Or use the M1V1 = M2V2 calculator to solve this problem –

Complex problem on (M₁V₁=M₂V₂)?

Determine the mass (g) of calcium nitrate in each milliliter of a solution prepared by diluting 56.0 mL of 0.705 M calcium nitrate to a final volume of 0.100 L.

1) use M1V1 = M2V2: ⇒ (0.705 mol/L) (0.0560 L) = (x) (0.100 L) ∴ x = 0.3948 M 2) moles of Ca(NO3)2 in 1 mL: ∴ 0.3948 mol/L = 0.3948 mol / 1000 mL = 0.0003948 mol/mL 3) Convert moles to grams: ∴ 0.0003948 mol/mL times 164.086 g/mol = 0.0648 g/mL You can check more complex problem on M1V1 = M2V2 here,  Dilution problem (chemteam.info)

FAQ

What does M1V1=M2V2 equation in chemistry represent?

We know, that M1V1=M2V2 represents the dilution equation, that M1 represents initial molarity, M2 represents final molarity, V1 represents initial volume and V2 denotes final volume.

How can you find initial molarity (M1), initial volume (V1), final molarity (M2), and final volume (V2) using the M1V1=M2V2 equation?

The given equation is- M1V1=M2V2 Now to find the initial molarity (M1), initial volume (V1), final molarity (M2), and final volume (V2) use the formulas given below- ⇒ ⇒ ⇒ ⇒