# Murder Mystery Summative

## Scenario 1:

• In Joe Titan's room, a cup was found filled with an odorless, colorless liquid. This liquid was 11.19% hydrogen and 88.81% oxygen, and had a molar mass of 18.0g/mol.
• So, I took 11.19g H and divided it by 1.008g/mol, the molar mass of hydrogen. This told me that the sample of liquid contained 11.1 moles of hydrogen.
• Next, I took 88.81g O and divided it by 15.9994g/mol, the molar mass of oxygen. This told me that the sample of liquid contained 5.55 moles of oxygen.
• The smaller amount of moles in the liquid was oxygen- 5.55 moles. So, I divided both 11.1mol and 5.55mol by 5.55. For hydrogen, this got me 2, and for oxygen, I got 1.
• I used these numbers to determine the empirical formula, which is H2O.
• Next, I found the mass of the empirical formula by adding the masses of two moles of hydrogen and one mole of oxygen. This would be 1.008g/mol + 1.008g/mol + 15.9994g/mol. The empirical mass ended up being 18g.
• Lastly, I divided the molar mass- 18.0g/mol- by the empirical mass, and got 1. 1 x H2O would be H2O, showing me that the molecular formula of the liquid in Joe Titan's cup was H2O.

## H2O- water

A colorless, odorless liquid. No safety concerns apply. It is nontoxic and essential for life. In order to overdose on water, one would need to drink multiple liters. Joe Titan was found with only 800mL of water in his system, or 0.8L, a safe amount. (chemspider, pubchem, webmd)

## Scenario 2:

• Recently, Joe Titan had been taking large quantities of pain killers. At the scene, a nearly empty bottle of a drug was found. Analysis of the drug concluded that it was comprised of 302.76mg carbon, 35.18mg hydrogen and 62.04mg oxygen, and that its molar mass was 206g/mol.
• In order to identify the drug, I first did 302.76mg C divided by 12,011mg/mol (the molar mass of carbon). This told me that the drug contained 0.0252068937 moles of carbon.
• Then, I did 35.18mg H divided by 1,008mg/mol (the molar mass of hydrogen). This told me that the drug contained 0.0349007937 moles of hydrogen.
• Next, I did 62.04mg O divided by 15,999.4mg/mol (the molar mass of oxygen). This told me that the drug contained 0.0038776454 moles of oxygen.
• The smallest number of moles out of the three was oxygen, 0.0038776454 moles. So, I did 0.0252068937 (C), 0.0343007937 (H) and 0.0038776454 (O) divided by 0.0038776454.
• For carbon, this got me 6.5, for hydrogen it got me 9, and for oxygen it got me 1. I multiplied all of these numbers by 2 to get rid of decimals in order to determine the empirical formula, C13H18O2.
• To determine the mass of the empirical formula I added the molar masses of 13 moles of carbon, 18 moles of hydrogen and 2 moles of oxygen. This would be 13(12.011g/mol) + 18(1.008g/mol) + 2(15.9994g/mol). I found that the empirical mass was 206g.
• Lastly, I divided the molar mass of the drug- 206g/mol -by the empirical mass. 206 divided by 206 is 1, so the molecular formula of the drug is 1 x C13H18O2, which would be C13H18O2.

## C13H18O2- Ibuprofen

A white powder which can cause safety concerns such as heartburn and nausea/vomiting, and loss of consciousness in the event of an overdose. The safe dosage of ibuprofen for an adult with osteoarthritis is a maximum of 3,200mg or 3.2g per day. Dosages higher than that have not been tested and are not recommended. Prolonged use of the drug can increase risk of heart attack and stroke. At the scene, Joe Titan was found with over 30g of ibuprofen in his system, which is almost 10 times the maximum daily amount. This would be 30,000mg or 75 of the 400mg pills. Overdose on ibuprofen can cause fatal heart attack or stroke in high dosages. (drugs.com, pubchem)

## Scenario 3:

• A chemical, given to Joe Titan by his wife, was found dissolved in his blood. 5.26g of this chemical was dissolved in 5.1L of blood, with a molarity of 0.00573M. Additionally the chemical was 40.001% carbon, 6.714% hydrogen and 53.285% oxygen.
• First, I needed to find out the molar mass of the chemical. To do so, I used the formula ML = mol. This was (0.00573M)(5.1L), and it equaled 0.029223mol, meaning that there were 0.029223 moles of the chemical in Joe Titan's blood. Next, I used the formula g/mol to determine the molar mass of the chemical. Since there were 5.26g of the chemical in Joe's blood, this was 5.26g divided by 0.029223mol. The rseult was 180g/mol, meaning that the chemical in Joe Titan's blood had a molar mass of 180g/mol.
• Then, I had to determine the empirical formula of the chemical. So, I first did 10.001gC divided by 12.011g/mol (the molar mass of carbon). This told me that there were 3.33mol carbon.
• Next, I did 6.714gH divided by 1.008g/mol (the molar mass of hydrogen). This told me that there were 6.66mol hydrogen.
• Then, I did 53.285gO divided by 15.9994g/mol (the molar mass of oxygen). This told me that there were 3.33mol oxygen.
• The lowest amount of moles was both carbon and oxygen, with 3.33mol. So, I did 3.33mol (C), 6.66mol (H) and 3.33mol (O) divided by 3.33. For carbon, this got me 1, for hydrogen it got me 2 and for oxygen it also got me 1.
• I used these numbers to determine the empirical formula of the chemical, CH2O.
• Next I found the mass of the empirical formula by adding the molar masses of 1 mole of carbon, 1 moles of hydrogen and 1 mole of oxygen. This was 12.011g/mol + 2(1.008g/mol) + 15.9994g/mol. The empirical mass ended up being 30g.
• Since I discovered that the molar mass of the drug was 180g/mol, I did 180g/mol divided by the empirical mass, 30g. This got me 6. So, I multiplied CH2O by 6, and got that the molecular formula of the chemical was C6H12O6.

## C6H12O6- Glucose

A primary source of energy for living organisms, naturally occurring in fruits and plants and found in candy. Can cause hyperglycemia in those with diabetes. Hyperglycemia can occur if the blood glucose level is above 130mg/dL. Joe titan had a blood glucose level of 5.26g/5.1L, which would convert to 0.00526mg/0.51dL. If we use a proportion, we can discover that his blood glucose level would only be 0.01mg/dL, which is very far below the level which would cause hyperglycemia. Because of this, the amount of glucose in Joe Titan's body poses no harm to his health. (pubchem, endocrineweb.com)

## Scenario 4:

• A drug bottle in Joe Titan's cabinet was found with pills containing 1.023x1024 atoms of carbon, 8.428x1023 atoms of hydrogen, 2.408x1023 atoms of oxygen and 6.02x1022 atoms of sulfur. The molar mass of the drug was 314.38g/mol.
• First, I needed to determine the amount of moles of each element. I did this using dimensional analysis, dividing each amount of atoms by 6.02x1023.
• 1.023x1024 atoms C divided by 6.02x1023 was 1.6944mol.
• 8.428x1023 atoms H divided by 6.02x1023 was 1.4mol.
• 2.408x1023 atoms O divided by 6.02x1023 was 0.4mol.
• 6.02x1022 atoms S divided by 6.02x1023 was 0.1 mol.
• Because the smallest number of moles was sulfur with 0.1mol, I took 1.6944mol (C), 1.4mol (H), 0.4mol (O) and 0.1mol (S) and divided them by 0.1. For carbon, I got 17, for hydrogen, I got 14, for oxygen, I got 4 and for sulfur I got 1.
• I used these numbers to determine the empirical formula, which was C17H14O4S. To find the mass of the empirical formula, I added together the molar masses of 17mol carbon, 14mol hydrogen, 4mol oxygen and a mole of sulfur. This was 17(12.011g/mol) + 14(1.008g/mol) + 4(15.994g/mol) + 32.066g/mol. I found that the empirical mass of the drug was 314.36g.
• Because the molar mass of the drug was 314.36g/mol, I did 314.36g/mol divided by 314.36g, and got 1. 1 x C17H14O4S is C17H14O4S, so the molecular formula of the drug is C17H14O4S.

## C17H14O4S- Rofecoxib

A white/yellow powder used for osteoarthritis relief, withdrawn from the US market in 2004 for its increased risk of cardiovascular events. The maximum daily dosage for adults with osteoarthritis is 25mg. Joe Titan was discovered with less than 2.5mg in his system, which is only 10% of the daily dosage. This shows that Joe was not taking very much of the drug and was probably not taking the drug regularly. Despite this, the drug is still dangerous. (drugs.com).

## Scenario 5:

• Joe had recently been researching a hydrocarbon. This hydrocarbon was comprised of 14.37% hydrogen and 85.63% carbon. Its density was 0.967 g/L at 0.834 atm and 21 degrees Celsius.
• To find the molar mass, I used the formula mm = DRT/P. This was mm = (0.967g/L)(0.0821)(294 degrees Kelvin) divided by 0.834atm. The answer was 27.99g/mol, telling me that the molar mass of the gas was 27.99g/mol.
• Next, I found the empirical formula. To do this, I first divided 14.37g H by 1.008g/mol (the molar mass of hydrogen). This told me that there were 14.26mol hydrogen in the gas.
• Then, I did 85.63g C divided by 12.011g/mol (the molar mass of carbon). This told me that there were 7.13mol carbon in the gas.
• The smallest number of moles was carbon with 7.13mol, so I did both 14.26mol (H) and 7.13mol (C) divided by 7.13. For hydrogen, I got 2, and for carbon, I got 1.
• I used these numbers to determine the molecular formula, which was CH2. Then, I fount the mass of the empirical formula by adding the masses of 1 mole of carbon and 2 moles of hydrogen. This was 12.011g/mol + 1.008g/mol + 1.008g/mol, and it equaled 14.03g.
• Since I found that the molar mass of the gas was 27.99g/mol, I did 27/99g/mol divided by 14.03g, and I got 2.
• So, I multiplied CH2 by 2, giving me the molecular formula, which is C2H4.

## C2H4- Ethylene:

Ethylene is a colorless gass used in fuels which can cause drowsiness, dizziness, and unconsciousness. It can cause suffocation in confined areas. No evidence of toxic effects of exposure to humans has been reported. The acute toxicity of it is low, but very high concentrations of it can cause asphyxiation. Only a trace amount of the chemical was found in Joe Titan's body, indicating that the probability of asphyxiation is not likely. (pubchem, inchem)

## Conclusion:

From my investigations, I can conclude that Joe Titan was killed by the large amount of ibuprofen he had taken. Although ibuprofen is not dangerous if taken correctly, any drug can severely harm a person in too high of a dosage. Unsafe usage of ibuprofen can result in increased risk for heart attack or stroke, and can cause internal bleeding. The prolonged use of ibuprofen also causes liver and kidney problems. Joe Titan had taken a huge amount- 30g- almost 10 times the safe amount (3.2g) of ibuprofen. This means that he had taken at least 75 pills, which is an overdose. This is what leads me to believe that he was killed by the ibuprofen. Such a large amount of the drug is completely unsafe and there is no doubt that it had health consequences. Plus, his usage of ibuprofen put him at a much higher risk than any of the other chemicals found at the scene. Although rofecoxib also seems suspicious, he was not taking very much of it, and taking 30g of any drug is a very high overdose.