physical chemistry lab

first file is data on matlab

Experiment Ideal Gas Law

1 Lessons to be learned

1. Equation of state for an ideal gas.

2. Gay-Lussac’s Law

3. Boyle–Mariotte law

4. Charles’ Law

5. Universal Gas constant

2 Objectives

Investigate the relationships of temperature, pressure and volume using air and determine the universal gas contstant.

3 Theory

Different gases show remarkably similar physical behavior regardless of their chemical make-up. Numerous observations made in the late 1600s showed that the physical properties of any gas can be defined by four variables, namely pressure (p), temperature (T), volume (V ) and the amount n, which is usually given in mol (n). These four state variables determine each other, i.e. if three are given then the fourth one can be determined. For a dilute gas this relation can be written in a simple equation, the ideal gas law:

pV = nRT

with R being the universal gas constant. The value for R is: (1)

R = 8.314Jmol-1 K-1 (2)

If the volume as well as the amount of an ideal gas is kept constant we can write instead of (1):

= constant (3)

According to this correlation, which is also known as Gay-Lussac’s law, after Joseph Gay-Lussac (1778-1850), a plot of the pressure p, as a function of the temperature T, results in linear relationship starting with an intercept at p = T = 0. Therefore for a known volume and number of gas molecules the ideal gas constant can be determined from the slope of such a p-T-diagram. The goal of this experiment is to verify the ideal gas law and to determine the universal gas constant by making use of this equation of state.

At a given pressure and temperature 1 mol of ideal gas will take up a specific volume, the Molar Volume.

Temperature in ?C Molar Volume in mol l

5 22.83

10 23.24

15 23.65

20 24.06

25 24.47

30 24.88

35 25.29

40 25.70

45 26.11

50 26.52

55 26.93

60 27.34

65 27.75

4 Equipment and Chemicals

1. Chemicals:

(a) air

(b) water

2. Equipment

(a) 100 ml Syringe

(b) Cylinder for coolant

(c) Pressure and temperature sensor with box

(d) Tubing with beaker for coolant overflow

(e) Labjack

(f) Heater

(g) Stand and clamp

5 Procedure

1. Setup Equipment (20 Minutes)

• Prepare an ice bath.

• Setup the equipment according to the picture.

• Lubricate the piston with vegetable oil.

• Set the piston to 30mL.

Figure 1: Setup without coolant overflow

• Close the rubber tubing at the tip and seal it with the sleeve.

• Don’t pour the coolant in yet.

2. Boyle–Mariotte law (Isothermic expansion) (10 Minutes)

• Meassure the pressure from 30mL to 100mL or as far as you can go in steps of 10mL at constant temperature.

• Observe how the temperature changes, when you pull the piston too fast. Does it go up or down? (adiabatic state change)

• Observe how the pressure changes when you keep the setup at low pressure for a moment.

• The volume from the experiment Vexp is not the actual volume being expanded. The sensor takes up some space, while the rubber tubing adds some volume V = Vexp - VD.

VD is called dead volume. Plot the pressure on the x-axis and the volume measured in the experiment on the y-axis, then fit . What are a1 and b1 ? What kind of function is that?

• We can linearize this plot by plotting the reciprocal pressure vs. the volume. What is the slope a2 and what is the y-axis intercept b2?

• How many mole n of air are in 30mL ? The molar volume of air at 25?C is Vm = 24.47Lmol-1.

• What is VD? What is the universal gas constant R?

3. Gay-Lussac’s law (Isochoric state change) (30 Minutes)

• Re-apply lubricant

• Add the plastic tubing to the overflow valve.

• Put the tubing in a container to catch the coolant overflow.

• Add water to the outer cooling cylinder

• Turn on the heater.

• Once you have reached about 65?C, remove the heater.

• Reset the starting Volume to 100mL and seal the syringe.

• Start flushing the outer cylinder with ice-water.

• Meassure the pressure in steps of 5?C down to 65?C at constant volume. Keep the pressure at about atmospheric pressure and set the

• Stop the cooling and your meassurements when the temperature is ˜ 5?C.

• Plot the temperature on the x-axis and the pressure on the y-axis. Fit p = a3 · T . What is a3? Calculate R.

4. Charles’ Law (Isobaric state change) (45 Minutes)

• Re-apply lubricant.

• At either 5?C or 10?C reset the starting volume to 80ml.

• Meassure the volume every 5?C until you reach 65?C at atmospheric pressure.

• Plot the temperature on the x-axis and the volume on the y-axis. Fit V = a4 · T. What is a4? Calculate R.

• Compare the R from the 3 experiments with each other and the literature value.

5. Clean up (15 Minutes)

• Remove the coolant from the cylinder.

• Remove the sensor from the syringe.

• Clean the lubricant from the piston and the inside of the syringe.

6 Data (Attach this page to your labreport!)

Estimate your measurement uncertainties:

u(p) = u(V ) = u(T) =

2. Boyle–Mariotte law (Isothermic expansion)

3. Gay-Lussac’s law (Isochoric state change)

4. Charles’ Law (Isobaric state change)

7 Results Page (Attach this page to your labreport!)

2. Boyle–Mariotte law (Isothermic expansion)

3. Boyle–Mariotte law (Isothermic expansion)

4. Boyle–Mariotte law (Isothermic expansion)

5. Plots

first file is data on matlab

Experiment Ideal Gas Law

1 Lessons to be learned

1. Equation of state for an ideal gas.

2. Gay-Lussac’s Law

3. Boyle–Mariotte law

4. Charles’ Law

5. Universal Gas constant

2 Objectives

Investigate the relationships of temperature, pressure and volume using air and determine the universal gas contstant.

3 Theory

Different gases show remarkably similar physical behavior regardless of their chemical make-up. Numerous observations made in the late 1600s showed that the physical properties of any gas can be defined by four variables, namely pressure (p), temperature (T), volume (V ) and the amount n, which is usually given in mol (n). These four state variables determine each other, i.e. if three are given then the fourth one can be determined. For a dilute gas this relation can be written in a simple equation, the ideal gas law:

pV = nRT

with R being the universal gas constant. The value for R is: (1)

R = 8.314Jmol-1 K-1 (2)

If the volume as well as the amount of an ideal gas is kept constant we can write instead of (1):

= constant (3)

According to this correlation, which is also known as Gay-Lussac’s law, after Joseph Gay-Lussac (1778-1850), a plot of the pressure p, as a function of the temperature T, results in linear relationship starting with an intercept at p = T = 0. Therefore for a known volume and number of gas molecules the ideal gas constant can be determined from the slope of such a p-T-diagram. The goal of this experiment is to verify the ideal gas law and to determine the universal gas constant by making use of this equation of state.

At a given pressure and temperature 1 mol of ideal gas will take up a specific volume, the Molar Volume.

Temperature in ?C Molar Volume in mol l

5 22.83

10 23.24

15 23.65

20 24.06

25 24.47

30 24.88

35 25.29

40 25.70

45 26.11

50 26.52

55 26.93

60 27.34

65 27.75

4 Equipment and Chemicals

1. Chemicals:

(a) air

(b) water

2. Equipment

(a) 100 ml Syringe

(b) Cylinder for coolant

(c) Pressure and temperature sensor with box

(d) Tubing with beaker for coolant overflow

(e) Labjack

(f) Heater

(g) Stand and clamp

5 Procedure

1. Setup Equipment (20 Minutes)

• Prepare an ice bath.

• Setup the equipment according to the picture.

• Lubricate the piston with vegetable oil.

• Set the piston to 30mL.

Figure 1: Setup without coolant overflow

• Close the rubber tubing at the tip and seal it with the sleeve.

• Don’t pour the coolant in yet.

2. Boyle–Mariotte law (Isothermic expansion) (10 Minutes)

• Meassure the pressure from 30mL to 100mL or as far as you can go in steps of 10mL at constant temperature.

• Observe how the temperature changes, when you pull the piston too fast. Does it go up or down? (adiabatic state change)

• Observe how the pressure changes when you keep the setup at low pressure for a moment.

• The volume from the experiment Vexp is not the actual volume being expanded. The sensor takes up some space, while the rubber tubing adds some volume V = Vexp - VD.

VD is called dead volume. Plot the pressure on the x-axis and the volume measured in the experiment on the y-axis, then fit . What are a1 and b1 ? What kind of function is that?

• We can linearize this plot by plotting the reciprocal pressure vs. the volume. What is the slope a2 and what is the y-axis intercept b2?

• How many mole n of air are in 30mL ? The molar volume of air at 25?C is Vm = 24.47Lmol-1.

• What is VD? What is the universal gas constant R?

3. Gay-Lussac’s law (Isochoric state change) (30 Minutes)

• Re-apply lubricant

• Add the plastic tubing to the overflow valve.

• Put the tubing in a container to catch the coolant overflow.

• Add water to the outer cooling cylinder

• Turn on the heater.

• Once you have reached about 65?C, remove the heater.

• Reset the starting Volume to 100mL and seal the syringe.

• Start flushing the outer cylinder with ice-water.

• Meassure the pressure in steps of 5?C down to 65?C at constant volume. Keep the pressure at about atmospheric pressure and set the

• Stop the cooling and your meassurements when the temperature is ˜ 5?C.

• Plot the temperature on the x-axis and the pressure on the y-axis. Fit p = a3 · T . What is a3? Calculate R.

4. Charles’ Law (Isobaric state change) (45 Minutes)

• Re-apply lubricant.

• At either 5?C or 10?C reset the starting volume to 80ml.

• Meassure the volume every 5?C until you reach 65?C at atmospheric pressure.

• Plot the temperature on the x-axis and the volume on the y-axis. Fit V = a4 · T. What is a4? Calculate R.

• Compare the R from the 3 experiments with each other and the literature value.

5. Clean up (15 Minutes)

• Remove the coolant from the cylinder.

• Remove the sensor from the syringe.

• Clean the lubricant from the piston and the inside of the syringe.

6 Data (Attach this page to your labreport!)

Estimate your measurement uncertainties:

u(p) = u(V ) = u(T) =

2. Boyle–Mariotte law (Isothermic expansion)

3. Gay-Lussac’s law (Isochoric state change)

4. Charles’ Law (Isobaric state change)

7 Results Page (Attach this page to your labreport!)

2. Boyle–Mariotte law (Isothermic expansion)

3. Boyle–Mariotte law (Isothermic expansion)

4. Boyle–Mariotte law (Isothermic expansion)

5. Plots

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