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Chapter 12: Problem 159

How would you prepare \(250.0 \mathrm{~mL}\) of a \(0.350 \mathrm{M}\) \(\mathrm{NaOH}\) solution from a \(6.00 \mathrm{M} \mathrm{NaOH}\) stock solution?

Short Answer

Expert verified
To prepare \(250.0 \mathrm{~mL}\) of a \(0.350 \mathrm{M}\) NaOH solution from a \(6.00 \mathrm{M}\) NaOH stock solution, we need to mix \(14.6 \mathrm{~mL}\) of the stock solution with an appropriate volume of water (250.0 mL - 14.6 mL).

Step by step solution

01

List the Information and Formulate the Equation

The concentration and volume of the final NaOH solution are given as \(0.350 \mathrm{M}\) and \(250.0 \mathrm{~mL}\) respectively. The concentration of the stock NaOH solution is given as \(6.00 \mathrm{M}\). We denote the stock solution concentration as \(C_1\), its volume as \(V_1\), the final solution concentration as \(C_2\), and its volume as \(V_2\). We will use the dilution formula to determine the required volume of the stock solution: \(C_1V_1 = C_2V_2\)
02

Substitute the Known Values into the Equation

Now, substitute the values of \(C_1\), \(C_2\), and \(V_2\) into the equation: \((6.00 \mathrm{M})(V_1) = (0.350 \mathrm{M})(250.0 \mathrm{~mL})\)
03

Solve for the Volume of the Stock Solution, \(V_1\)

Now, we need to adjust the above equation to solve for \(V_1\): \(V_1 = \frac{C_2V_2}{C_1}\) Next, we can plug the known values for \(C_1\), \(C_2\), and \(V_2\) back into the equation: \(V_1 = \frac{(0.350 \mathrm{M})(250.0 \mathrm{~mL})}{6.00 \mathrm{M}}\)
04

Calculate the Volume of the Stock Solution, \(V_1\)

Now, perform the calculations to find out the required volume of the stock solution: \(V_1 = \frac{(0.350)(250.0)}{6.00}\) \(V_1 = 14.5833 \mathrm{~mL}\)
05

Round and Present the Final Answer

Round the final volume to an acceptable number of significant figures based on the information given: \(V_1 \approx 14.6 \mathrm{~mL}\) Thus, to prepare \(250.0 \mathrm{~mL}\) of a \(0.350 \mathrm{M}\) NaOH solution, we need to mix \(14.6 \mathrm{~mL}\) of the \(6.00 \mathrm{M}\) NaOH stock solution with an appropriate volume of water (250.0 mL - 14.6 mL).

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