To what volume must a solution of 83.1 g H2SO4 in 505.3 mL of solution be diluted to give a 0.28 M solution?

Question

To what volume must a solution of 83.1 g H2SO4 in 505.3 mL of solution be diluted to give a 0.28 M solution?

I do not understand this problem. Also as a hint the professor said to use M1V1= M2V2.

Answer 1

Figure the moles in the H2SO4

moles= mass/molmassH2SO4

That is Molarity1

M1*V1=M2*V2

solve for V2

Answer 2

Figure the moles in the H2SO4

moles= mass/molmassH2SO4

That is Molarity1

M1*V1=M2*V2=molesabove

solve for V2

Answer 3

To solve this problem, we'll use the formula M1V1 = M2V2, also known as the dilution equation. This formula relates the initial concentration (M1) and volume (V1) of a solution to its final concentration (M2) and volume (V2) after dilution.

Let's start by identifying the given values:
M1 = initial concentration = unknown
V1 = initial volume = 505.3 mL
M2 = final concentration = 0.28 M
V2 = final volume = unknown

We need to find the final volume, V2. From the problem statement, we know that the initial volume, V1, is 505.3 mL. Therefore, we can rewrite the equation as:
M1 * V1 = M2 * V2
M1 * 505.3 mL = 0.28 M * V2

Next, we need to find the initial concentration, M1. To do this, we'll convert the given mass of H2SO4 (83.1 g) to moles using its molar mass.

The molar mass of H2SO4 is:
(2 * atomic mass of H) + atomic mass of S + (4 * atomic mass of O)
= (2 * 1.008 g/mol) + 32.06 g/mol + (4 * 16.00 g/mol)
= 98.09 g/mol

Now, let's calculate the number of moles of H2SO4:
Moles of H2SO4 = Mass of H2SO4 / Molar mass of H2SO4
= 83.1 g / 98.09 g/mol
≈ 0.8472 moles

Since moles = Molarity * Volume (in liters), we can rearrange the equation to solve for M1:
M1 = Moles / V1
M1 = 0.8472 moles / 0.5053 L (since 505.3 mL = 0.5053 L)
≈ 1.676 M

Now that we know the initial concentration, M1, we can substitute all the values into the dilution equation:
(1.676 M) * (0.5053 L) = (0.28 M) * V2

Simplifying the equation gives us:
V2 = (1.676 M * 0.5053 L) / 0.28 M
V2 ≈ 3.017 L

Therefore, the solution needs to be diluted to approximately 3.017 liters to obtain a final concentration of 0.28 M. Remember to always pay attention to the unit conversions (from mL to L) to ensure accurate calculations.