Hi, I have this question related to Molarity and hoping you can help?

The question says:
50.0 gram sample of NaCl is added to water to create a 0.50 L solution. What volume of this solution is needed to create a 1.30 L solution that is 0.100 M NaCl?

It says also "Choose the closest answer". so it won't be in the choices but here are the choices:

a) 152 mL
b) 255 mL
c) 87.6 mL
d) 412 mL
e) 10.1 mL
Thank you for your help.

mols NaCl = grams/molar mass

M NaCl = mols NaCl/L solution = approx 1.5 M but that's an estimate to use in the next part.
Then mL1 x M1 = mL2 x M2
mL1 x approx 1.5 = 1300 x 0.1M
mL1 = ?

To solve this problem, we need to use the concept of molarity, which is defined as the number of moles of solute divided by the volume of the solution in liters.

Let's start by calculating the number of moles of NaCl in the 50.0 gram sample.

The molar mass of NaCl is 58.44 g/mol, so to find the number of moles, we divide the mass by the molar mass:

Number of moles = Mass / Molar mass
= 50.0 g / 58.44 g/mol
= 0.856 moles

Next, we need to find the volume of the 0.100 M NaCl solution. We know the solution concentration (0.100 M) and the desired number of moles of NaCl (0.856 moles). The equation to use here is:

Molarity = Moles / Volume

Rearranging the equation to solve for volume:
Volume = Moles / Molarity
= 0.856 moles / 0.100 M
= 8.56 L

But our initial solution is only 0.50 L, so we can't directly get 8.56 L from it. We need to dilute it by adding more solvent (water) to reach the desired volume of 1.30 L.

Using the dilution formula:
M1V1 = M2V2

Where:
M1 = initial molarity
V1 = initial volume
M2 = final molarity
V2 = final volume

Rearranging the formula to solve for V1:
V1 = (M2 * V2) / M1
= (0.100 M * 1.30 L) / 0.50 L
= 0.260 L

To find the volume needed to make the 1.30 L solution, we subtract the initial volume (0.50 L) from V1:
Volume needed = V1 - initial volume
= 0.260 L - 0.50 L
= -0.240 L

However, a negative volume does not make sense in this context. It suggests that the initial solution is already larger than the final volume, which is not possible.

Therefore, there may be an error or inconsistency in the information or formulation of the problem. As a result, none of the given options (a, b, c, d, or e) are correct.

To resolve this issue, you may need to double-check the information or consult with your instructor or textbook for clarification.