 # Determination of the Molar Mass of an Unknown Metal

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Determination of the Molar Mass of an Unknown Metal
The Chemical Reaction and its Mass-Mole Relationships
To determine the molar mass of an unknown metal, which we will represent generically as “M”. we will react it with hydrochloric acid to produce hydrogen gas as shown in this reaction equation:
M(s) + 2 HCl(aq) ---> MCl2(aq) + H2(g)
We will measure the properties of the hydrogen gas produced and with the Ideal Gas Law calculate the number of moles of gas formed. Since the balanced reaction equation has a 1:1 ratio of M to H2 the moles of hydrogen are numerically equal to the moles of metal used in the reaction. Since we can calculate the moles of metal used this way, all that is needed is the weight of the sample of metal to calculate the molar mass of the unknown by dividing the mass (g) of the metal by the moles of metal. Since this reaction equation is balanced only for metals that form MCl2 when they react with acid, our unknown will be limited to those metals that form +2 cations. Once we have calculated the molar mass, a quick scan of the atomic masses of the elements on the periodic table will allow us to identify the metal.
The Ideal Gas Law
In the reaction shown above the H2 gas produced obeys the Ideal Gas Law. In, fact at everyday temperatures and pressures, all gases obey the Ideal Gas Law. This gas law combines together all the major properties of a gas: pressure, volume, temperature and amount (moles) of gas. The algebraic expression for this law is:
PV = nRT
where P is the pressure of the gas in atmospheres (atm), V is the volume in liters (L), n is the moles of gas, R is the Ideal Gas Constant and has a value of 0.0821 atm-L/mole-K and T is the temperature of the gas in degrees Kelvin (K). With this algebraic equation and the measurement of any three properties of a gas, the fourth property can be calculated. For example, if P, V and T are measured, then the moles of gas can be found by substituting these measured values into the Ideal Gas Law equation, along with the value for R and solving for the moles of gas.
In most laboratories the properties of P, V and T are often measured in units different from those used in the Ideal Gas Law. In the lab, pressure is typically measured in mm Hg or torr, volume is typically measured in milliliters (mL) and temperature is typically measured in degrees Celsius (°C). Properties of a gas measured with the these units must be converted to those in the Ideal Gas Constant before being used in the Ideal Gas Law. To do this you can use the following conversion factors: 760 torr (or mm Hg) = 1 atm, 1 L = 1000 mL and K = 273 + °C.
Procedure
Part I: Formation of Groups

Work in groups of two or three. You will be assigned one of the unknown metal by your instructor and you should do three or four trials.

Part II: Determination of the Amount of Gas Produced

To determine the amount of gas produced in this reaction, the pressure of gas produced at constant volume can be measured or the volume of the gas at constant pressure can be measured. In this experiment, you will measure the pressure of the gas produced at constant volume. In either case, the temperature of the gas (which should be the same as the temperature in the room) must be also be measured and the mass of each sample of metal.

Measuring the Change in Pressure at Constant Volume using Vernier LabPro and Pressure Sensor
1. Obtain a 125 mL Erlenmeyer flask that you will use for the experiment. Determine and record the available volume of the flask that the hydrogen gas will occupy as it is produced from the reaction of the solid metal and the hydrochloric acid solution. Account for the following items when you determine the volume of your flask:

• A 125 mL flask does not have a volume of precisely 125 mL.

• During the experiment, you will seal the flask with a rubber stopper and the stopper will occupy some of the volume of the flask.

• You will add 5 mL of solution (6M HCl solution) to the flask.

2. The remaining equipment set-up is shown in Figure 1 below: Figure 1: Experimental Set-up for Collecting Pressure Data

Note: Use a wet flask. This eliminates the need to do a calculation to correct for water vapor pressure in the flask as it will be a constant.

3. Obtain a piece of metal of the size or mass indicated by your instructor. Measure and record its mass. Place the metal in a clean but wet 125 mL Erlenmeyer flask.
4. Prepare a room temperature water bath in a large beaker. The bath should be deep enough to completely cover the gas level in the Erlenmeyer flask.
5. Connect a Gas Pressure Sensor to Channel 1 of the Vernier computer interface. Connect a Temperature Probe into Channel 2 of the interface. Connect the interface to the computer with the proper cable
6. Use the clear tubing to connect the white rubber stopper to the Gas Pressure Sensor. (About one-half turn of the fittings will secure the tubing tightly.) Twist the white stopper snugly into the neck of the Erlenmeyer flask to avoid losing any of the hydrogen gas that will be produced in the reaction (see Figure 1). Important: Close the valve on the white stopper by turning the white handle so it is perpendicular with the valve stem.
7. Obtain a small amount of 6.0 M hydrochloric acid. CAUTION: Handle the hydrochloric acid with care. It can cause painful burns if it comes in contact with the skin. Draw 5.0 mL of HCl solution into the 20 mL syringe. Thread the syringe onto the two-way valve on the white stopper (see Figure 1). Submerge the Erlenmeyer flask into the water bath. Position the Temperature Probe in the water bath so that the tip of the probe is not touching the beaker.
8. Start the Logger Pro program on your computer by opening the file “Molar Mass of a Metal”. (Look on the desktop)
9. With the flask still submerged in the water bath, click to begin data collection. After about 20 seconds, open the two-way valve directly below the syringe, press the plunger to add all of the 5 mL of HCl solution to the flask, and close the two-way valve.
10. Gently swirl the flask, while keeping it immersed in the water bath, as the reaction proceeds. Data collection will stop after 5 minutes. You may click to end data collection before 5 minutes have elapsed if the pressure has reached its peak and leveled off.
11. Carefully remove the white stopper from the flask to relieve the pressure in the flask. Important: Do not open the two-way valve to release the pressure in the flask.
12. Examine the pressure data to determine the change in pressure, ∆P, during the reaction. In addition, determine the mean temperature of the water bath during the reaction. Record these values in your data table.
13. Rinse the flask for a second trial. Obtain a new piece metal, determine its mass and place it in the flask. Repeat the necessary steps to conduct the second trial.
14. Follow the same procedure to conduct a third and fourth trial (if time permits).

Report Tutorial for Gas Laws: Molar Mass Determination of a Metal

(Palko 10-28-05)

In your report, use all the headings that appear below in BOLD. Bulleted and italicized notes in this tutorial are guidelines to help you complete the report
Purpose: To identify an unknown metal from its calculated the molar mass by measuring the mass of a metal sample and then the volume, temperature and pressure of the gas produced when the metal reacts completely with hydrochloric acid.
Procedure:

• Make a list of the students in your group and describe the major roles they played in the experiment.

• Indicate the unknown number or letter of the metal you were assigned if this information was provided. In some cases, only one metal is used.

Table of Data For Part II (reproduce this table in your lab notebook and turn in a copy of your notebook entry with the report)
 Trial Number Mass of Metal Sample (g) Temperature of Gas (°C) Initial Pressure of Gas (torr) Final Pressure of Gas (torr) Net Pressure of Gas (torr) Volume of Flask (mL)

• Create the following results table:

 Trial Number Moles of Gas = Moles of Metal (moles of M) n = PV/RT (R = 0.08206 L*atm/K*mol) Molar Mass of Metal MM = g of M / moles of M

Calculations: (include)

• Example calculation of the moles of gas (and metal), the molar mass of the metal.

Conclusions

1. Calculate the average value for the molar mass for the class. This may be done for you on the class data summary spreadsheet.

2. Use this average value as the accepted value and calculate a percent error for each of your trials.

3. How large is the range of molar mass values?. What was mesured during the lab? Does it appear that the variation in the molar masses is due to measurement uncertainties? If yes, what measurement seems to have the greatest uncertainty? If no, what other source(s) of error could explain any discrepancies in your results?

4. Use your average value for the molar mass to identify the metal.

5. Compare the experimental molar mass of the metal with the actual molar mass of the metal you’ve identified as the unkown. Be specific. Do not answer simply “They are close” without explanation or evidence to support your statement. Does your selection of metal make sense? For example, it is unlikely that sodium would be the unknown metal due to discrepancies in the appearance of the unknown and sodium.

6. How would using a sample of metal that had a larger molar mass but mass equal to the one you used affect the data collected? (Answer in terms of the pressure change that results and the mole relationships in the reaction equation)

7. Create a list of metals that could NOT be identified in this manner since they will not react with

HCl. (Hint: Check the activity series).
An alternative method to determine the molar mass of the metal reacted would be to collect the gas using water displacement. Use the sample data below to determine the molar mass and identity of the metal reacted:
0.056 g of a metal is reacted with excess HCl to produce 22.8 ml of hydrogen collected by water displacement at 25 C and a room pressure of 725 torr. The vapor pressure of water at this temperature is 24 torr.

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