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Calculating moles using volume, density, molar mass, pressure and temperature

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Acid rain is a growing worldwide environmental problem. Naturally, rainwater should have a pH of not less than 5.5, but in the northeastern United States for example, the average pH of the rainwater is about 4.5. The increased acidity of the rain kills plants and animals in lakes and streams, causes increased weathering and decomposition of limestone in statues and on buildings (a major problem for Greek antiquities), and creates problems with the production of fruit and vegetable crops. The major chemical involved is sulfur dioxide, SO2, which combines with rainwater to form sulfuric acid. Although sulfur dioxide has many sources including volcanoes and metal smelting, the main source is believed to be the burning of fossil fuel. The number of moles, n, of sulfur dioxide released from a coal-burning power plant can be determined from the density, d; volume, V; and the molar mass, Mm, of sulfur dioxide gas given off by the power plant.

If a given power plant released sulfur dioxide gas with a volume, V, of 1200 m3 at a density, d, of 2.86 kg/m3 at standard pressure and temperature, how many moles of sulfur dioxide are released?

Express your answer in moles to three significant figures.

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This question is one of conversions. To find the moles of SO2 gas, you need to find the total mass. 1200 m3 * 2.86 Kg/m3 = 3432 ...

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The solution explains in both narrative and calculations to arrive at the answer.

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Vapor Density & Ideal Gas Law

Please take a look at the attached lab report on vapor density. Please see the ** items regarding percentage error and calculation of R. I can't figure out how to do the percentage error of my trials and the calculations for the R values are confusing. Thanks for your help.

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Vapor Density and the Ideal Gas Law
Lab Conducted: October 10, 2005

Purpose: To use the Ideal Gas Law (PV=nRT) to calculate the molar mass (M) of an unknown real vapor and to determine its identity as either Methanol, Ethanol, Acetone, Pentane or Cyclohexane.

Procedure: Boiled 0.5L of water and inserted a flask of an unknown liquid which was covered with a foil cap that had a small hole in it. The unknown substance was heated in three separate trials to determine the volume of gas that evaporated through the hole in the foil cap.

Calculations:

Pressure (P) = 753 mmHg/760 mmHg = 0.990789 atm
Temperature (T) = 99.74˚Celcius + 273.15 = 373.89˚Kelvin
Constant R = 0.082057

Trial #1
Volume of flask = 262 mL = 0.262 liters

Mass of flask before heating = 123.610 grams
Mass of flask after heating = 124.590 grams
Difference = mass of substance = 0.980 grams

n = PV = (0.990789)(0.262)_ = 0.0084610 moles
RT (0.082057)(373.89)

Molar Mass = 0.980 grams/.0084610 = 115.826 grams/mole

Trial #2
Volume of flask = 298 mL = 0.298 liters

Mass of flask before heating = 113.487 grams
Mass of flask after heating = 114.344 grams
Difference = mass of substance = 0.857 grams

n = PV = (0.990789)(0.298)_ = 0.0096236 moles
RT (0.082057)(373.89)

Molar Mass = 0.857 grams/.0096236 = 89.052 grams/mole

Trial #3
Volume of flask = 262 mL = 0.262 liters

Mass of flask before heating = 123.610 grams
Mass of flask after heating = 124.410 grams
Difference = mass of substance = 0.800 grams

n = PV = (0.990789)(0.262)_ = 0.008461 moles
RT (0.082057)(373.89)

Molar Mass = 0.800 grams/.008461 = 94.5515 grams/mole

Molar Masses of Possible Substances
Methanol CH3OH 32 g/mol
Ethenol C2H5OH 36 g/mol
Acetone CH3CH2CO 57 g/mol
Pentane C5H12 72 g/mol
Cyclohexane C6H12 84 g/mol

Conclusion/Discussion

It is likely that the unknown substance is Cyclohexane because the average of molar mass from the three trials is 99.8 g/mol [(94.5515+89.052+115.826)/3] and the largest molar mass of the possible substances is 84 g/mol.

**Percentage Error of molar mass calculations:

**Maximum Value, Minimum Value and Average value of R with uncertainty range to the average value

R = MP/T
m/V

Assume uncertainties are as follows: Pressure = +/- 0.1 cmHg, Temperature = +/-0.3˚C, Volume = +/-0.0004 L, mass = +/- 0.001

Lab Book Questions

1. Weighing the flask with the foil cap makes the measurement more accurate as the foil cap has mass.

2. It will create error in the calculation of the mass of the substance.

3. The temperature value from the table is for pure water. We actually used tap water in the experiment which will change the boiling point of water because of other substances in the non-pure water.

4a. 1.0261 g

4b. 250 mL

4c. n = PV = (0.99408)(0.250)_ = 0.00813 moles
RT (0.082057)(372.59)

Molar Mass = 1.0261 grams/.00813 = 126.2 grams/mole

5. I believe the signs would be opposite which would cancel the error arising from the neglect of the vapor.
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