Question

(verification of ideal gas equation of state experiment)

1. State and discuss TWO applications that depend on the theory of verification of ideal gas equation of state

experiment.

2. Compare between a needle value and at least TWO other valve types

3. Explain why the thermistor temperature probe is placed at that location.

4. Compare between a thermistor and at least TWO other temperature sensors.

5. Discuss another experiment that can be conducted to verify the ideal gas equation.

Answer 1

Q.5| Experimental verification of Ideal gas equation of state:

Introduction:

In this experiment, we verified the Ideal Gas Law and also determined Absolute Zero and the Universal Gas Constant. The Ideal Gas Law is an equation of a hypothetical gas that models the behavior of 'real' gasses under different conditions. It also describes the relationship between each condition.

pv = nRT -----------------------[1]

Equation [1] shows the equation of the Ideal Gas Law;

p is pressure in Pascal (Pa), V is volume in m³, n is the # moles of gas, R is the ideal gas constant in J/mol K, and T is temperature in Kelvin (K).

This ideal gas model refers to 'ideal' gasses that have sufficiently low densities, exert no long range forces on each other and only interact during collisions (elastic).

In this experiment, we are verifying the Ideal Gas Law using the relationship between pressure and volume. By rearranging the ideal gas law equation,

p = (1/V)*nRT -----[2]

pV = constant (At constant moles and Temperature)

Equation [2] shows us that Pressure is inversely proportional to Volume as long as nRT is kept constant. Theoretically, when volume increases, pressure will decrease exponentially as in Figure [1]. Therefore, you can validate the ideal gas law by experimentally increasing the volume and observing the effect on pressure.

In the next part of this lab. we calculated the Absolute Zero temperature and the Ideal Gas Constant. Absolute Zero is the theoretical temperature where there is no longer kinetic or thermal energy. It is the lowest possible temperature; no substance can be colder. Absolute Zero is defined as 0 on the Kelvin scale and -273.15" on the Celsius scale. Scientists have yet to fuliy reach absolute zero.

Absoiute Zero canbe calculated using the relationship between pressure and temperature.

p = (nR/V)*T -----[3]

Equation [3 ] shows that wh en nR/V is kept constant, pressure is directly proportional to temp. and will yield a linear graph as in Figure [2]. On this pressure vs. temperature graph, Absolute Zero will be the corresponding temperature at 0 pressure.

In order to calculate the Ideal Gas Constant R, we use the slope of the curve. Equation [4] illustrates that R can be calculate by dividing the slope with n/V and instead of calculating n/V, we can use the density (p) and molar mass (M) of air - Equation [5].

nR/V = Slope =>

----------------------[4]

-------------------------[5]

Equipment:

• Data Studio
• Quick-release coupling
• Absolute Pressure Sensor
• Metal canister with stopper
• Temperature Sensor
• Tubing-to-stopper connector
• Syringe
• Tubing

Procedure:

Part 1: Ideal Gas Law - Pressure vs. Volume

a) Use the ideal gas model to predict the pressure of air at 5 different volumes below 20 mL (temperature constant). Equation [2]

b) Using a syringe, tubing and an absolute pressure sensor in data studio, measure an initial volume and pressure - p₁V₁ (Initial volume should be about 20mL.)

c) Compress the syringe to each of the 5 volumes chosen prior and record the corresponding pressure. These are your experimental values.

d) Use a percent difference to calculate the predicted values with the experimental values.

e) Plot pressure vs. volume to determine whether your data supports the ideal gas model. Analyze and interpret your data.

Part 2: Ideal Gas Law - Pressure vs. Temperature

a) Submerge acanister with air at constant volume into a hot water bath. Using an absolute pressure sensor and temperature sensor, record pressure of the air and the temperatue of the water (which is ideally the same temperatue of the air).

b) With ice, slowly decrease the temperature of the water and carefully record the pressure and temperature and several point down to -10'C.

c) Plot your points on a pressure vs. temperature graph and apply a iinear fit to get the equation of the line and its slope.

d) Use this equation to calculate Absolute Zero (when pressure = 0)

e) Use the slope to calculate the Ideal Gas Constant - Equation [5].

f) Use a percent difference to compare the ideal gas constant and absolute zero from your measurement to their accepted values

Sample Data:

Part 1: Initial Volume, V1 = 20mL ; Initial Pressure, p1 = 101.0 kPa

Table of Results:

Volume(mL)	Predictions Pressure (kPa)	Experimental Pressure (kPa)	% dffirence
18	112.2	111.6	0.55%
15	134.7	132.0	1.90%
10	202.0	191.4	5.0%
8	252.5	232.9	7.8%
5	404.0	342.8	15%

Part 2 ;

Data:

Temperature (C)	Pressure (Pa)
48.24	100470
27.59	95160
21.69	93630
15.55	91800
12.21	91000

Table of Results:

	Theoretical/Accepted Value	Experimental Value	Percent Difference
Absolute Zero	-273.15 C	-333.19 C	22.0%
Ideal Gas Constant,R	8.31 J/molK	6.29 J/molK	24.3%

Data Analysis: Sample Calculations

Part 1 - predicting pressure

Part 2 calculating Absolute Zero

For P = 0 =>

Part 2 - calculating Ideal Gas Constant