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Chapter 6: Problem 9

You need to make \(150.0 \mathrm{mL}\) of a \(0.10-M\) NaCl solution. You have solid NaCl, and your lab partner has a \(2.5-M\) NaCl solution. Explain how you each make the 0.10-M NaCl solution.

Short Answer

Expert verified
To make a $0.10 \, \text{M}$ NaCl solution using solid NaCl, dissolve \(mass = (0.10 \,\text{M})(0.150 \,\text{L})(58.44 \,\text{g/mol})\) of solid NaCl in enough water to make a total volume of $150.0 \, \text{mL}$. To make the same solution using the $2.5 \, \text{M}$ NaCl solution, take an initial volume \(V1 = \frac{(0.10\,\text{M})(0.150 \,\text{L})}{2.5 \, \text{M}}\) and dilute it to a total volume of $150.0 \, \text{mL}$ with water.

Step by step solution

01

Calculate the moles of NaCl needed for the 0.10-M NaCl solution

Firstly, we need to find out the number of moles of NaCl required for creating a 0.10-M NaCl solution with a volume of 150.0 mL. To do this, we will use the molarity formula: Molarity (M) = moles of solute (n) / volume of solution (L) Rearrange the formula to solve for the moles of NaCl: moles of solute (n) = Molarity (M) × volume of solution (L) Since the volume is given in mL, it needs to be converted to L: Volume in L = 150.0 mL × (1 L / 1000 mL) = 0.150 L Now, calculate the moles of NaCl: \(n = (0.10 \,\text{M}) \times (0.150 \,\text{L})\)
02

Calculate the mass of solid NaCl needed

Now that we have the moles of NaCl required, we can calculate the mass of the solid NaCl needed. The molecular weight of NaCl is 58.44 g/mol. To find the mass of NaCl, multiply the moles of NaCl by its molecular weight: Mass of NaCl (g) = moles of NaCl × molecular weight of NaCl \(mass = (n) \times (58.44 \,\text{g/mol})\)
03

Making the 0.10-M NaCl solution with the solid NaCl

To make the 0.10-M NaCl solution, simply dissolve the calculated mass of solid NaCl in enough water to make a total volume of 150.0 mL.
04

Diluting the 2.5-M NaCl solution to make the 0.10-M NaCl solution

To dilute the 2.5-M NaCl solution to create the 0.10-M NaCl solution, use the dilution formula: C1V1 = C2V2 Here, C1 is the initial concentration of the solution (2.5-M), V1 is the initial volume of the solution we want to find, C2 is the final concentration of the solution (0.10-M), and V2 is the final volume of the solution (150.0 mL). Rearrange the formula to find the initial volume (V1): V1 = (C2V2) / C1 Convert the volume in mL to L: V2 in L = 150.0 mL × (1 L / 1000 mL) = 0.150 L Now, calculate the volume V1: \(V1 = \frac{(0.10 \,\text{M})(0.150 \,\text{L})}{2.5 \,\text{M}}\)
05

Making the 0.10-M NaCl solution by diluting the 2.5-M NaCl solution

To make the 0.10-M NaCl solution from the 2.5-M NaCl solution, measure the calculated volume (V1) and dilute it to a total volume of 150.0 mL with water.

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