1.8: Diluciones en Serie y Curva Estándar

Objetivos de aprendizaje

Objetivos:

• Preparar soluciones comenzando con un sólido.
• Realizar una dilución en serie.
• Utilice el espectrofotómetro para medir la absorbancia de las soluciones.
• Genere una curva estándar y utilice la curva estándar para determinar la concentración de una solución.

Resultados de aprendizaje de los estudiantes:

Al finalizar este laboratorio, los estudiantes serán capaces de:

• Determinar la masa de soluto necesaria para elaborar en% (p/v) solución.
• Hacer un tampón de la concentración apropiada.
• Hacer una solución madre de la concentración apropiada.
• Crear una serie de soluciones de concentraciones decrecientes mediante diluciones en serie.
• Utilice el espectrofotómetro para medir la absorbancia de una solución.
• Usa excel y haz una curva estándar y usa el valor R2 para evaluar la calidad de la curva estándar.
• Utilice la curva estándar para calcular la concentración de una solución.

Introducción

Una dilución en serie es una serie de diluciones, permaneciendo el factor de dilución igual para cada paso. El factor de concentración es el volumen inicial dividido por el volumen final de la solución. El factor de dilución es el inverso del factor de concentración. Por ejemplo, si tomas 1 parte de una muestra y agregas 9 partes de agua (solvente), entonces has hecho una dilución 1:10; esto tiene una concentración de 1/10th (0.1) del original y un factor de dilución de 10. Estas diluciones se utilizan a menudo para determinar la concentración aproximada de una enzima (o molécula) a cuantificar en un ensayo. Las diluciones en serie permiten diluir pequeñas alícuotas en lugar de desperdiciar grandes cantidades de materiales, son rentables y son fáciles de preparar.

Ecuación 1.

\[concentration factor= \frac{volume_{initial}}{volume_{final}}\nonumber\]

\[dilution factor= \frac{1}{concentration factor}\nonumber\]

Figura 1. Una dilución en serie de diez veces, que también se puede llamar dilución 1:10, o una serie con factor de dilución de 10. Para determinar la concentración en cada paso de la serie, se divide la concentración previa por el factor de dilución.
*Los tubos de dilución comienzan con 9 mL. Se agrega 1 mL y se mezcla, luego se transfiere 1 mL al siguiente tubo. El volumen final en el último tubo sería de 10 ml

Consideraciones clave a la hora de elaborar soluciones:

• Asegúrese de investigar siempre las precauciones a usar cuando trabaje con productos químicos específicos.
• Asegúrese de que está utilizando la forma correcta del químico para los cálculos. Algunos químicos vienen como hidratos, lo que significa que esos compuestos contienen agua unida químicamente. Otros vienen como “anhidros” lo que significa que no hay agua ligada. Asegúrate de prestar atención a cuál estás usando. Por ejemplo, el CaCl ₂ anhidro tiene un MW de 111.0 g, mientras que la forma deshidratada, CaCl ₂ ● 2 H ₂ O tiene un MW de 147.0 gramos (110.0 g + el peso de dos aguas, 18.0 gramos cada una).
• Siempre use un cilindro graduado para medir la cantidad de agua para una solución, use el tamaño más pequeño de cilindro graduado que acomodará toda la solución. Por ejemplo, si necesitas hacer 50 mL de una solución, es preferible usar un cilindro graduado de 50 mL, pero se puede usar un cilindro de 100 mL si es necesario.
• Si usa una barra agitadora magnética, asegúrese de que esté limpia. No manipule la barra agitadora magnética con sus propias manos. Es posible que desee lavar la barra agitadora con detergente para lavavajillas, seguido de un enjuague completo en agua desionizada para asegurarse de que la barra de mezcla esté limpia.
• Para una solución de 500 mL, comience disolviendo los sólidos en aproximadamente 400 mL de agua desionizada (generalmente aproximadamente 75% del volumen final) en un vaso de precipitados que tenga una barra de agitacion magnetica. Luego transferir la solución a un cilindro graduado de 500 mL y llevar el volumen a 500 mL
• El término “llevar al volumen” (btv) o “cantidad suficiente” (qs) significa agregar agua a una solución que esté preparando hasta que alcance el volumen total deseado
• Si necesita pH la solución, hágalo ANTES de subir el volumen al volumen final. Si el pH de la solución es inferior al pH deseado, entonces se agrega una base fuerte (a menudo NaOH) para elevar el pH. Si el pH está por encima del pH deseado, entonces se agrega un ácido fuerte (a menudo HCl) para bajar el pH. Si tu pH está muy lejos del pH deseado, usa ácidos o base de mayor molaridad. Por el contrario, si estás cerca del pH deseado, usa ácidos o bases de baja molaridad (como HCl 0.5M). Se mostrará en clase una demostración de cómo usar y calibrar el medidor de pH.
• Etiquete la botella con la solución con la siguiente información:
  • Tus iniciales
  • El nombre de la solución (incluir concentraciones)
  • La fecha de preparación
  • Temperatura de almacenamiento (si sabe)
  • Etiquetar peligros (si hay alguno)

Matemáticas de laboratorio: hacer soluciones porcentuales

Ecuación 2.

Fórmula para porcentaje en peso (p/v):

\[ \dfrac{\text{Mass of solute (g)}}{\text{Volume of solution (mL)}} \times 100 \nonumber \]

Example

Make 500 mL of a 5% (w/v) sucrose solution, given dry sucrose.

1. Write a fraction for the concentration \[5\:\%\: ( \frac{w}{v} )\: =\: \dfrac{5\: g\: sucrose}{100\: mL\: solution} \nonumber\]
2. Set up a proportion \[\dfrac{5\: g\: sucrose}{100\: mL\: solution} \:=\: \dfrac{?\: g\: sucrose}{500\: mL\: solution} \nonumber\]
3. Solve for g sucrose \[\dfrac{5\: g\: sucrose}{100\: mL\: solution} \: \times \: 500 \: mL \: solution \: = \: 25 \: g \: sucrose \nonumber\]
4. Add 25-g dry NaCl into a 500 ml graduated cylinder with enough DI water to dissolve the NaCl, then transfer to a graduated cylinder and fill up to 500 mL total solution.

Activity 1: Calculating the Amount of Solute and Solvent

Calculate the amount (include units) of solute and solvent needed to make each solution.

A. Solutions with Soluble Solute and water as the solvent

1. How many grams of dry NaCl should be used to make 100 mL of 15% (W/V) NaCl solution?
2. How many grams of dry NaCl should be used to make 300 mL of 6% (W/V) NaCl solution?
3. How many grams of dry NaCl should be used to make 2L of 12% (W/V) NaCl solution?
4. How many grams of dry NaCl should be used to make 300 mL of 25% (W/V) NaCl solution?
5. How many grams of dry NaCl should be used to make 250 mL of 14% (W/V) NaCl solution?

B. Solutions with Insoluble Solutes in Cold Water

1. Calculate how to prepare 200 mL 1.2% (w/v) agarose in 1X SB buffer, given dry agarose and SB buffer.
2. Calculate how to prepare 300 mL 2.5 % (w/v) agarose in 1X SB buffer, given dry agarose and SB buffer.
3. Calculate how to prepare 50 mL 1.5 % (w/v) agarose in 1X SB buffer, given dry agarose and SB buffer.
4. Calculate how to prepare 60 mL 0.8 % (w/v) agarose in 1X SB buffer, given dry agarose and SB buffer.
5. Calculate how to prepare 150 mL 1.8 % (w/v) agarose in 1X SB buffer, given dry agarose and SB buffer.

Note

For dry chemicals that cannot dissolve in cold water (such as agarose and gelatin), pour the dry solute directly into an Erlenmeyer flask, measure the total volume of solvent in a graduated cylinder, then add the total volume of solvent into flask. Microwave the solution as recommended until solute is dissolved.

Part I: Solution Prep of 30-mLs of 13.6% Sodium Acetate

Sodium Acetate Buffer solutions are inexpensive and ideal to practice your skills. Your accuracy can be verified by taking a pH reading.

MATERIALS

Reagents

• Sodium Acetate (Trihydrate) solid
• DI H2O
• Stock bottle of verified 1 Molar Acetic Acid solution

Equipment

• pH meter
• Stir plate
• Electronic balance and weigh boats
• 50-mL graduated cylinder
• 50-mL conical tubes (Falcon tubes)
• P-1000 Micropipettes with disposable tips (or 5 mL Serological pipettes with pumps)

Calculations

• Calculate the amount of sodium acetate needed to make 30 mL of 13.6% sodium acetate solution.

Procedure

1. Make sure to wear goggles and gloves.
2. Measure _______ g of solid sodium acetate in a weigh boat on an electronic balance.
3. Transfer the sodium acetate into a 50 mL conical tube.
4. Add about 20 mL of DI water into the conical tube.
5. Secure the cap on the tube and invert to mix the contents until the solute is completely dissolved.
6. Pour out all of the solution into a 50 mL graduated cylinder.
7. Add DI water to bring the total volume to 30.0 mL.
8. Transfer all of the solution back into your 50 mL conical tube and secure the cap.
9. Invert the tube several times to thoroughly mix the contents.
10. Label the tube with contents (13.6% Sodium Acetate), initial, and date.

Verify your work by creating a buffer solution

1. Pipette exactly 5.0 mL of your sodium acetate solution into a clean 15 mL conical tube (or 25 mL glass test tube).
2. Pipette exactly 5.0 mL of 1M acetic acid solution into your conical tube (or 25 mL glass test tube).
3. Secure the cap on the conical tube (or a piece of parafilm over the test tube opening).
4. Invert several times to thoroughly mix the 10 mL of solution into an acetate buffer.
5. Measure the pH of the test buffer solution using a calibrated pH meter.
6. If you were accurate in all of your work, the test buffer should have a pH of 4.75 (+/- 0.06).
7. Check in with your instructor and report the pH of your test buffer.
8. If your test buffer pH is within the expected range, then congratulations! You have verified that the sodium acetate solution you made earlier has a concentration of 13.6%. Give your 50 mL tube of remaining sodium acetate solution to your instructor to save for use in a future lab.
9. If your test buffer pH is far outside of the expected range then something went wrong during the preparation of your sodium acetate solution and you should mark the tube with an “X” and give it your instructor to set aside.

Part II: Preparation of a Standard Curve

In this part of the lab, we will be preparing solutions of known concentrations. These then will be used to create a standard curve. Standard curves (also known as calibration curves) represent the relationship between two quantities. The standard curve will be used in part 3 of the lab to determine the concentrations of unknown solutions of methylene blue.

Materials

Reagents

• Stock 1% (w/v) methylene blue solution – (500 microliter (µL) aliquots in 1.5 mL microcentrifuge tubes)
• DI H₂O

Equipment

• P-20 Micropipettes and disposable tips
• P-1000 Micropipettes and disposable tips
• Spectrophotometer

Glassware

• 10 mL serological pipettes and pumps
• 1.5 mL microcentrifuge tubes
• 15 mL plastic conical tubes with screw-top caps
• 50 mL plastic conical tubes with screw-top caps

Calculations

1. Calculate the volume of stock 1% methylene blue solution needed to make 40 mL of 0.0005 % methylene blue solution.
2. This new percentage concentration is equivalent to 5.0 micrograms per milliliter (µg/mL) and will be the concentration of our working solution for the next 2 parts of the lab exercise.

Procedure

Prepare Stock Solution of Methylene Blue

Prepare 40 mL of 5.0 µg/mL Methylene Blue Working Solution

1. Make sure to wear goggles and gloves.
2. Very accurately pipette 40.0 mL of DI water into a 50 mL conical tube.
3. Very accurately micropipette ________ µL of 1% stock methylene blue into the DI water in your tube.
4. Secure the cap on the tube and invert repeatedly to thoroughly mix the solution.
5. Label your tube as “5.0 µg/mL Methylene Blue”, your name, and date.

Prepare Known Concentrations of Methylene Blue Working Solution via Dilution

Prepare 80% Methylene Blue Working Solution

1. Pipette 8.0 mL of 5.0 µg/mL methylene blue working solution into a 15 mL conical tube.
2. Pipette 2.0 mL DI H2O into the tube to make 10.0 mL of total solution.
3. Seal the tube and invert repeatedly to mix.
4. What is the concentration of your new solution? Label the tube _______ µg/mL methylene blue.

Prepare 60% Methylene Blue Working Solution

1. Pipette 6.0 mL of 5.0 µg/mL methylene blue working solution into a 15 mL conical tube.
2. Pipette 4.0 mL DI H2O into the tube to make 10.0 mL of total solution.
3. Seal the tube and invert repeatedly to mix.
4. What is the concentration of your new solution? Label the tube _______ µg/mL methylene blue.

Prepare 40% Methylene Blue Working Solution

1. Pipette 4.0 mL of 5.0 µg/mL methylene blue working solution into a 15 mL conical tube.
2. Pipette 6.0 mL DI H2O into the tube to make 10.0 mL of total solution.
3. Seal the tube and invert repeatedly to mix.
4. What is the concentration of your new solution? Label the tube _______ µg/mL methylene blue.

Prepare 20% Methylene Blue Working Solution

1. Pipette 2.0 mL of 5.0 µg/mL methylene blue working solution into a 15 mL conical tube.
2. Pipette 8.0 mL DI H2O into the tube to make 10.0 mL of total solution.
3. Seal the tube and invert repeatedly to mix.
4. What is the concentration of your new solution? Label the tube _______ µg/mL methylene blue.

Measuring Absorbance of Methylene Blue Working Solutions

1. Turn on the spectrophotometer and let it warm up for at least 10 minutes.
2. Place 1 mL of DI water into a clean cuvette. This is your blank.
3. Place 1 mL of your methylene blue solutions into clean cuvettes. These are your samples.
4. Set the wavelength of the spectrophotometer to 664 nm.
5. Place the blank into the spectrophotometer.
6. Press the “Zero” button and wait for the Absorbance to read “0.00”
7. Take out the blank and set aside.
8. Place your first sample into spec and record the absorbance reading. Do not press any buttons.
9. Repeat with each sample and record into lab notebook

Results

Complete Data Table 1. based on your results. Put in your notebook

Figure 1. Completing the excel table

Table 1. Absorbances of Methylene Blue at Various Concentrations

Percentage of Working Solution Conc.	Methylene Blue Concentration (µg/mL)	Absorbance @ 664 nm
100%	5.0
80%
60%
40%
20%

Making a Standard Curve

1. Enter the data into Excel in adjacent columns.
2. Select the data values with your mouse. On the Insert tab, click on the Scatter icon and select Scatter with Straight Lines and Markers from its drop-down menu to generate the standard curve.

Figure 2. An example of a standard curve

1. To add a trendline to the graph, right-click on the standard curve line in the chart to display a pop-up menu of plot-related actions. Choose Add Trendline from this menu. Select “display equation on chart” and “display R-squared value on chart”. Ideally, the R2 value should be greater than 0.99.
2. Use the equation to determine the concentration of the sample solution by entering the absorbance for y and solving for x.
3. Print the standard curve and add to your notebook.

Part III: Determining Concentrations

Serial dilutions are quick way of making a set of solutions of decreasing concentrations. In this part of the lab we will make a series of dilutions starting with the Methylene Blue solution prepared in part 2 of this lab. Then, we will us the spectrophotometer to determine the absorbance of each solution. Once we know the absorbance, we will use the equation from your standard curve prepared in part 2, to determine the actual concentrations of each of your solutions.

Materials

Reagents

• 5.0 µg/mL Methylene Blue Working Solution
• DI H2O

Equipment

• P-20 Micropipettes and disposable tips
• P-1000 Micropipettes and disposable tips
• Spectrophotometer
• 5 mL serological pipettes and pumps
• 15 mL plastic conical tubes with screw-top caps

Preparation of Methylene Blue Solutions

Using the remainder of your 5.0 µg/mL methylene blue working solution from part 2, perform a set of 1:2 serial dilutions to make the following concentrations of the solution (50.0 %, 25.0 %, 12.5 %, 6.25 %, 3.125 %, and 1.5625 %).

Diagram of 1:2 Serial Dilutions

In your notebook, draw a diagram showing the serial dilutions for the 6 methylene blue solutions you are preparing. In the diagram, indicate the volume being withdrawn from the concentrated solution, the volume of water added, the concentration of the new solution, and the total volume.

Procedure

Preparation of Methylene Blue Concentrations via Serial Dilutions

Making 1:2 dilutions

• Pipette 5.0 mL of the 5.0 µg/mL methylene blue working solution into a 15 mL conical tube.
• Pipette 5.0 mL of DI water into the tube for a total of 10 mL of solution.
• Cap and mix well.
• Label this tube “50.0% MB”

Making 1:4 dilution

• Pipette 5.0 mL of the 50.0% MB solution into a new 15 mL conical tube.
• Pipette 5.0 mL of DI water into the tube for a total of 10 mL of solution.
• Cap and mix well.
• Label this tube “25.0% MB”

Making 1:8 dilution

• Pipette 5.0 mL of the 25.0% MB solution into a new 15 mL conical tube.
• Pipette 5.0 mL of DI water into the tube for a total of 10 mL of solution.
• Cap and mix well.
• Label this tube “12.5% MB”

Continue with this process to make the 1:16, 1:32, and 1:64 serial dilutions.

Write the procedures you used to make the solutions in your lab notebook.

Measuring absorbance

1. Follow the procedures in part 2 to prepare the spectrophotometer
2. Measure the absorbance values of the diluted solutions
3. Record the absorbance values and concentrations in your lab notebook in a table as shown below.

Data Table 2

Dilution Factor	% of Working Solution Concentration	Absorbance @ 664 nm	Methylene Blue Conc. (µg/mL)
1:2	50.0%
1:4	25.0%
1:8	12.5%
1:16	6.25%
1:32	3.125%
1:64	1.5625 %

Calculations

Use the equation from your standard curve in part 2 and the absorbance values of your solutions from Part 3, to determine the actual concentration of your solutions.

Study Questions

1. Describe how you would prepare 50.0-mL a 0.10% NaOH solution. In your description, include a calculation and step by step procedures including glassware.

2. It is common for solutions that are used often in a lab (or which are time consuming to prepare) to be intentionally prepared to be many times more concentrated than needed. For example, if a 1.36% sodium acetate is often used in the lab, then the 13.6% sodium acetate solution prepared in part 1 can be labeled as “10X” sodium acetate solution because the concentration is 10 times greater than needed. This way, you can save on storage space for the solution and you can quickly and easily dilute any desired amount of this to the correct concentration right before use.
3. Describe how you would prepare 100.0 mL of 10X sodium acetate solution. In your description, include a calculation and step by step procedures including glassware. Make sure to include steps to verify your solution by checking the pH.
4. Describe how you would prepare 100.0 mL of 1X sodium acetate solution from the 10x sodium acetate solution prepared in the questions above. In your description, include a calculation and step by step procedures including glassware.
5. Using a serial dilution, describe how you would prepare 10 mL of a 1%, 0.1% and 0.01% solution of NaOH. The stock solution of NaOH is 10%. Draw diagram as part of your description.
6. Using the standard curve below, calculate the concentration of an unknown solution if its absorbance is 0.55.

   

   Figure 3. A standard absorbance curve of Copper II

7. Evaluate the quality of the standard curve above by using the R2 value.