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QuestionWhat is the new molarity of a 0.455M0.455 \mathrm{M} sodium chloride solution after adding 1.88L1.88 \mathrm{L} of water to 375 mL375 \mathrm{~mL}?

Studdy Solution

STEP 1

Assumptions1. The initial volume of the sodium chloride solution is375 mL. The initial concentration of the sodium chloride solution is0.455 M3. The volume of water added to the solution is1.88 L4. The dilution does not cause any chemical reactions, meaning the number of moles of sodium chloride remains constant before and after dilution

STEP 2

First, we need to convert all volumes to the same unit. Here, we will convert milliliters (m) to liters () since the volume of water is given in liters.1 L =1000 mLSo, we can convert the initial volume of the sodium chloride solution to liters as followsInitial volume=375 mL=375/1000 LInitial\, volume =375\, mL =375/1000\, L

STEP 3

Now, plug in the given value for the initial volume to calculate the initial volume in liters.
Initial volume=375/1000 L=0.375 LInitial\, volume =375/1000\, L =0.375\, L

STEP 4

We can calculate the total volume of the solution after dilution by adding the initial volume of the sodium chloride solution and the volume of water added.
Total volume=Initial volume+Volume of water addedTotal\, volume = Initial\, volume + Volume\, of\, water\, added

STEP 5

Now, plug in the values for the initial volume and the volume of water to calculate the total volume.
Total volume=0.375 L+1.88 LTotal\, volume =0.375\, L +1.88\, L

STEP 6

Calculate the total volume of the solution after dilution.
Total volume=0.375 L+1.88 L=2.255 LTotal\, volume =0.375\, L +1.88\, L =2.255\, L

STEP 7

The number of moles of sodium chloride before and after dilution remains the same. Therefore, we can calculate the new concentration (molarity) after dilution by dividing the number of moles of sodium chloride by the total volume of the solution.The number of moles of sodium chloride can be calculated by multiplying the initial volume by the initial concentration.
Number of moles=Initial volumetimesInitial concentrationNumber\, of\, moles = Initial\, volume \\times Initial\, concentration

STEP 8

Now, plug in the values for the initial volume and initial concentration to calculate the number of moles.
Number of moles=0.375 Ltimes0.455 MNumber\, of\, moles =0.375\, L \\times0.455\, M

STEP 9

Calculate the number of moles of sodium chloride.
Number of moles=.375 Ltimes.455 M=.170625 molNumber\, of\, moles =.375\, L \\times.455\, M =.170625\, mol

STEP 10

Now, we can calculate the new concentration after dilution by dividing the number of moles of sodium chloride by the total volume of the solution.
New concentration=Number of moles/Total volumeNew\, concentration = Number\, of\, moles / Total\, volume

STEP 11

Plug in the values for the number of moles and the total volume to calculate the new concentration.
New concentration=0.170625 mol/.255 LNew\, concentration =0.170625\, mol /.255\, L

STEP 12

Calculate the new concentration in molarity.
New concentration=0.170625 mol/2.255 L=0.0757 MNew\, concentration =0.170625\, mol /2.255\, L =0.0757\, MThe new concentration of the sodium chloride solution after dilution is0.0757 M NaCl.

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