Chemistry

1.       At 25.0  0C, the vapor pressure of pure water is 25.756 mmHg. What is the vapor pressure of water at 35.0 0C. The molar enthalpy of vaporization of water is 40.66 kJ/mol.

The relationship between vapor pressure at one temperature, with the vapor pressure at a different temperature is given by the Clausius-Clapeyron equation:

Where  is the enthalpy of vaporization, the amount of heat needed to vaporize 1 mole of a substance. And R is the gas constant. There are many units of the gas constant, since our units here are J, mol, and K, we will use:

Our temperature must be in Kelvin for units to cancel:

 K

 K

We must also convert  in J/mol since R is in J/(mol.K).

Now we can put the values in our equation

; to remove the ln, we must raise the number to e.

: The new pressure is higher, at higher temperature. Since higher temperatures more gas are evaporated, hence higher vapor pressure.

2.       While doing a lab on a hot day, you realize that the vapor pressure of acetone is 400 torr. If you know that the vapor pressure of acetone at room temperature (25.0 0C) is 230 torr. What is the current temperature in the lab? The molar enthalpy of vaporization of acetone is 29.1 kJ/mol.

The relationship between vapor pressure at one temperature, with the vapor pressure at a different temperature is given by the Clausius-Clapeyron equation:

Where  is the enthalpy of vaporization, the amount of heat needed to vaporize 1 mole of a substance. And R is the gas constant. There are many units of the gas constant, since our units here are J, mol, and K, we will use:

Our temperature must be in Kelvin for units to cancel:

 K

We must also convert  in J/mol since R is in J/(mol.K).

Now we can put the values in our equation

 I am going to move all the numbers in front of the parentheses to the other side

l. Now everything on the left is just a number, I can plug in a calculator:

 Now isolate

; Therefore

The temperature must be higher to produce high vapor pressure.  

 

3.       The vapor pressure of an aqueous solution is found to be 24.9 mmHg at 250C. The solution was made by dissolving 100 g of NaCl into 100 g of methanol (CH3OH) solvent. What is the pressure of pure methanol?

The relationship between vapor pressure of pure solvent and vapor pressure of a solution is given by Roult’s Law:

Where, Xsolvent is the fraction of free solvent molecule. The molecule free of the solute and able to evaporate.  

We need to find the moles of solute and solvent. For that we need the molar masses:

NaCl = 22.99 g/mol + 35.45 g/mol = 58.44 g/mol

CH3OH = (12.01 g/mol)+(4 x 1.01 g/mol)+(15.99 g/mol)=32.04 g/mol

Now we can find the moles of each:

Then the pressure of the solution is

Adding solute to the solvent lowers the vapor pressure, because solute interacts with solvent molecules, which leaves fewer free solvent molecules to evaporate, hence lowering the vapor pressure.

 

 

 

 

 

 

 

 

4.       You are tasked with finding the molar mass of an unknown compound. You decide to use boiling point elevation to do that. When you dissolve 50.0 g of the compound into 100 g of water, the solution boiling point is suddenly 112 0C. What is the molar mass of the unknown compound? Assume normal boiling point of water is 100 0C and Kb = 0.52 0C/m.

We just saw in question 3 that adding solute to the solvent causes the lowering of vapor pressure. Boiling point happens when the vapor pressure equals the outside pressure. If the vapor pressure lowers, we will need to heat the solution at a higher temperature to reach the outside pressure. Boling point elevation is given by: . Where i is a factor that counts how many species a solute break into. This is the case only for electrolyte, i.e. ionic compounds. Kb is a constant for a specific solvent, and m is molality given by:

The boiling temperature rises from 100 0C to 112 0C, hence .

Hence putting in the values we can find m. Since, it doesn’t specify we will assume that the unknown compound is a covalent molecule so i=1.

. Then

Using the molality and the given mass of the solvent we can find the moles of solute. Since

Since;       

 

Then:

 

 

5.       A solution is made by dissolving 100 g of essentially nonvolatile ethylene glycol (C2H6O2) in 500 g of water. What is the resulting freezing point of the solution? (Kf = 1.86 0C/m).

Another property that changes when we add solute to the solvent is the freezing point. Freezing occurs when we remove energy from a liquid and lower its temperature until it becomes solid. Since a solution is more disordered than a pure solvent, more energy must be removed to freeze solution than a pure solvent, leading to lowering of freezing point. Freezing point depression is given by: . Where i is a factor that counts how many species a solute break into. This is the case only for electrolyte, i.e. ionic compounds only. Our solute is made of only nonmetals, so it is covalent hence i=1. Kf is a constant for a given solvent, and m is molality given by:

We must find the moles of the solute first, for that we need the molar mass of ethylene glycol

C2H6O2 = (6 x 12.01 g/mol)+(6 x 1.01 g/mol)+(2 x 15.99 g/mol)=110.1 g/mol

Then:       

Then we can find the molality, but we must have our solvent in kg

Since water usually freezes at 0.0 0C, the new freezing point will be -3.39 0C.

 

 

 

 

 

6.       The easiest and most accurate method to finding the molar mass of a compound is to measure the osmotic pressure when such compound dissolves in water. Let’s say you are in a lab and find a mysterious solid on a tray. You would like to find its molar mass as a first step into identifying it. You take a 10.0 g sample and dissolve it in 100 mL of water. Your record the osmotic pressure of 2.2 torr at 200C. What is the molar mass of your sample? Assume that your sample is a nonelectrolyte, that is it doesn’t break into ions when dissolved in water.

 

Another property that is different from a solution and a pure solvent is osmotic pressure. If you have two solutions of different concentrations of solute, separated by a semi-permeable membrane, water will move from the most dilute solution (less solute) to the most concentrated (more solute) until the concentration is equal. This movement of water from one side to the other due to concentration difference is osmosis.  To stop this water movement, a certain pressure must be applied. This pressure is known as osmotic pressure and is given by

 

 

Where i is a factor that counts how many species a solute break into. This is the case only for electrolytes, i.e. ionic compounds only. M is the concentration of is the solution:

 

 R is the gas constant, T temperature in Klevin. П is the osmotic pressure. Given the osmotic pressure and temperature we can find the Molarity. Since the sample is nonelectrolyte i=1.

 

Temperature must be in Kelvin:

Since pressure is in torr, R must be in torr:

 

Hence using:

Then:

 

Since we have M, we can find moles of solute:

Volume must be in L:

 

Since;       

 

Then:

 

7.       Calculate the change in internal energy (ΔE) for the combustion reaction of a gas that releases 210.0 kJ of heat to its surroundings and does 65.5 kJ of work on its surroundings?

The most important thing is to pick the correct signs. If heat LEAVES the system, q is negative. If heat ENTERS the system q is positive. If work is done BY the system w is negative if work is done ON the system w is positive

Heat is released, so q = -210.0 kJ, and the system does work so w = -65.5 kJ

 

8.       Calculate the change in internal energy (ΔE) for the chemical reaction that releases 90.7 kJ of heat to its surroundings and does no work on them?

Using question 7. Heat is released so q = -90.7 kJ, and no work is done so w=0

 

9.       An air ballon initially contains 0.250 L of air in the morning, as the temperature outside rises during the day the ballon absorbs 20.0 kJ of heat.

                          

a.     What is the value with sign for the heat, q, absorbed? Meaning is q = +20.0 kJ or -20.0 kJ. Explain

Since the system absorbs heat, q comes into the system so the q=+20.0 kJ

b.     If as a result of absorbing 20.0 kJ, the ballon expands to a volume of 0.350 L, what is the work due to this expansion, in kJ. (Hint: 101.3 J = 1 L atm)

 

ΔV is the change in volume: : where Vf is the final volume, and Vi is the initial volume.

Then

Therefore:

Converting work into Joule using the conversion factor given, then to kJ

 

 

 

c.     From your answer in b, is the work done by the system to the surrounding, or does the surrounding do work on the system? Explain.   

The work is negative, so the work is leaving the system. This is what we expected since as the system expands it pushes the surrounding a distance d.

 

d.     What is the change in internal energy of the whole process? Is the process overall exothermic or endothermic?  

So:

So, since the internal energy is positive, the overall process is endothermic.

 

 

10.  A 150 g piece of iron (Fe) (heat capacity of iron, Cp = 25.09 J/ (mol. 0C)) was heated at a temperature of 47.0 0C and then placed in contact with a 275 g piece of copper (Cu) at 20.0 0C (heat capacity of copper, Cp = 25.46 J/ (mol. 0C)). What was the final temperature of the two pieces of metal?

The heat lost by the hot object (iron), so q of iron (q of iron is negative) is gained by the colder object Copper. The final T MUST be between the two temperatures.

 

We have the formulas of q at the back of the exam. Since we are given specific heats in J/(mol. 0C), we need to convert our masses into moles:

 

 

 

Now equating the two heats

Let’s multiply to remove the parentheses, we get:

 

 

3 0C. In the middle of the two temperatures.

 

 

 

 

 

 

 

11.  A 50.0 g of an aluminum sphere initially at 65.0 0C is immersed in a 20.0 g bucket of water initially at 23.0 0C. At thermal equilibrium, the temperature if the system was measured as 25.0 0C. What is the specific heat of aluminum? The molar heat capacity of water is 75.3 J/ (mol. 0C).

 

Similar to problem 10. The heat lost by the hot object (aluminum), so q of aluminum is negative, and that heat is gained by the colder object water. The final T MUST be between the two temperatures. And it is at 25.0 0C

 

 

We have the formulas of q at the back of the exam. Since we are given specific heats in J/(mol. 0C), we need to convert our masses into moles:

 

 

 

 

Now equating the two heats and solve for the unknown

Cs = 5.65 J/(mol . 0C)

 

 

 

 

 

 

 

 

 

12.  Below are four different covalent molecules:

 

H2CO = Molecule is made of C-H that are non polar, and C=O which is polar, so the molecule is polar and has dipole-dipole intermolecular forces.

 

H3COH = the molecule is made of C-H bonds that are nonpolar, then we have C-O bond that is polar, and then O-H bond that is special polar. The predominant intermolecular force is hydrogen bonding

 

CH4 = molecule is made of C-H bonds only, which are nonpolar. So, the molecule has only London Dispersion forces.

 

CH3CH3= This molecule is made of C-H and C-C bonds which are nonpolar bonds. So, the molecule only has London dispersion forces, although since it is slightly bigger than CH4 its London dispersion forces are stronger.

A.     For each molecule indicates what are the predominant intermolecular forces.

 

See above

B.     Which compound has the highest boiling point? Explain

 

Highest boiling point means, means more energy is needed to vaporize it, means stronger intermolecular forces. The strongest intermolecular forces are hydrogen bonding, so H3COH has the highest boiling point.

 

C.    Which compound is the most soluble in water? Explain

 

Since water is polar with hydrogen bonding, the most soluble molecules in water are polar, and even more soluble if that molecule can form hydrogen bonding with water. So, then H3COH is most soluble

 

 

D.    Which compound will have the highest vapor pressure? Explain.

 

Highest vapor pressure means it is easy to get the molecule into a gas phase. Meaning lower boiling point, and weaker intermolecular forces. The weakest intermolecular forces are London dispersion forces (LDF). Those LDF are even weaker if the molecule is small. Hence CH4 has the highest vapor pressure.1.       At 25.0  0C, the vapor pressure of pure water is 25.756 mmHg. What is the vapor pressure of water at 35.0 0C. The molar enthalpy of vaporization of water is 40.66 kJ/mol.

The relationship between vapor pressure at one temperature, with the vapor pressure at a different temperature is given by the Clausius-Clapeyron equation:

Where  is the enthalpy of vaporization, the amount of heat needed to vaporize 1 mole of a substance. And R is the gas constant. There are many units of the gas constant, since our units here are J, mol, and K, we will use:

Our temperature must be in Kelvin for units to cancel:

 K

 K

We must also convert  in J/mol since R is in J/(mol.K).

Now we can put the values in our equation

; to remove the ln, we must raise the number to e.

: The new pressure is higher, at higher temperature. Since higher temperatures more gas are evaporated, hence higher vapor pressure.

2.       While doing a lab on a hot day, you realize that the vapor pressure of acetone is 400 torr. If you know that the vapor pressure of acetone at room temperature (25.0 0C) is 230 torr. What is the current temperature in the lab? The molar enthalpy of vaporization of acetone is 29.1 kJ/mol.

The relationship between vapor pressure at one temperature, with the vapor pressure at a different temperature is given by the Clausius-Clapeyron equation:

Where  is the enthalpy of vaporization, the amount of heat needed to vaporize 1 mole of a substance. And R is the gas constant. There are many units of the gas constant, since our units here are J, mol, and K, we will use:

Our temperature must be in Kelvin for units to cancel:

 K

We must also convert  in J/mol since R is in J/(mol.K).

Now we can put the values in our equation

 I am going to move all the numbers in front of the parentheses to the other side

l. Now everything on the left is just a number, I can plug in a calculator:

 Now isolate

; Therefore

The temperature must be higher to produce high vapor pressure.  

 

3.       The vapor pressure of an aqueous solution is found to be 24.9 mmHg at 250C. The solution was made by dissolving 100 g of NaCl into 100 g of methanol (CH3OH) solvent. What is the pressure of pure methanol?

The relationship between vapor pressure of pure solvent and vapor pressure of a solution is given by Roult’s Law:

Where, Xsolvent is the fraction of free solvent molecule. The molecule free of the solute and able to evaporate.  

We need to find the moles of solute and solvent. For that we need the molar masses:

NaCl = 22.99 g/mol + 35.45 g/mol = 58.44 g/mol

CH3OH = (12.01 g/mol)+(4 x 1.01 g/mol)+(15.99 g/mol)=32.04 g/mol

Now we can find the moles of each:

Then the pressure of the solution is

Adding solute to the solvent lowers the vapor pressure, because solute interacts with solvent molecules, which leaves fewer free solvent molecules to evaporate, hence lowering the vapor pressure.

 

 

 

 

 

 

 

 

4.       You are tasked with finding the molar mass of an unknown compound. You decide to use boiling point elevation to do that. When you dissolve 50.0 g of the compound into 100 g of water, the solution boiling point is suddenly 112 0C. What is the molar mass of the unknown compound? Assume normal boiling point of water is 100 0C and Kb = 0.52 0C/m.

We just saw in question 3 that adding solute to the solvent causes the lowering of vapor pressure. Boiling point happens when the vapor pressure equals the outside pressure. If the vapor pressure lowers, we will need to heat the solution at a higher temperature to reach the outside pressure. Boling point elevation is given by: . Where i is a factor that counts how many species a solute break into. This is the case only for electrolyte, i.e. ionic compounds. Kb is a constant for a specific solvent, and m is molality given by:

The boiling temperature rises from 100 0C to 112 0C, hence .

Hence putting in the values we can find m. Since, it doesn’t specify we will assume that the unknown compound is a covalent molecule so i=1.

. Then

Using the molality and the given mass of the solvent we can find the moles of solute. Since

Since;       

 

Then:

 

 

5.       A solution is made by dissolving 100 g of essentially nonvolatile ethylene glycol (C2H6O2) in 500 g of water. What is the resulting freezing point of the solution? (Kf = 1.86 0C/m).

Another property that changes when we add solute to the solvent is the freezing point. Freezing occurs when we remove energy from a liquid and lower its temperature until it becomes solid. Since a solution is more disordered than a pure solvent, more energy must be removed to freeze solution than a pure solvent, leading to lowering of freezing point. Freezing point depression is given by: . Where i is a factor that counts how many species a solute break into. This is the case only for electrolyte, i.e. ionic compounds only. Our solute is made of only nonmetals, so it is covalent hence i=1. Kf is a constant for a given solvent, and m is molality given by:

We must find the moles of the solute first, for that we need the molar mass of ethylene glycol

C2H6O2 = (6 x 12.01 g/mol)+(6 x 1.01 g/mol)+(2 x 15.99 g/mol)=110.1 g/mol

Then:       

Then we can find the molality, but we must have our solvent in kg

Since water usually freezes at 0.0 0C, the new freezing point will be -3.39 0C.

 

 

 

 

 

6.       The easiest and most accurate method to finding the molar mass of a compound is to measure the osmotic pressure when such compound dissolves in water. Let’s say you are in a lab and find a mysterious solid on a tray. You would like to find its molar mass as a first step into identifying it. You take a 10.0 g sample and dissolve it in 100 mL of water. Your record the osmotic pressure of 2.2 torr at 200C. What is the molar mass of your sample? Assume that your sample is a nonelectrolyte, that is it doesn’t break into ions when dissolved in water.

 

Another property that is different from a solution and a pure solvent is osmotic pressure. If you have two solutions of different concentrations of solute, separated by a semi-permeable membrane, water will move from the most dilute solution (less solute) to the most concentrated (more solute) until the concentration is equal. This movement of water from one side to the other due to concentration difference is osmosis.  To stop this water movement, a certain pressure must be applied. This pressure is known as osmotic pressure and is given by

 

 

Where i is a factor that counts how many species a solute break into. This is the case only for electrolytes, i.e. ionic compounds only. M is the concentration of is the solution:

 

 R is the gas constant, T temperature in Klevin. П is the osmotic pressure. Given the osmotic pressure and temperature we can find the Molarity. Since the sample is nonelectrolyte i=1.

 

Temperature must be in Kelvin:

Since pressure is in torr, R must be in torr:

 

Hence using:

Then:

 

Since we have M, we can find moles of solute:

Volume must be in L:

 

Since;       

 

Then:

 

7.       Calculate the change in internal energy (ΔE) for the combustion reaction of a gas that releases 210.0 kJ of heat to its surroundings and does 65.5 kJ of work on its surroundings?

The most important thing is to pick the correct signs. If heat LEAVES the system, q is negative. If heat ENTERS the system q is positive. If work is done BY the system w is negative if work is done ON the system w is positive

Heat is released, so q = -210.0 kJ, and the system does work so w = -65.5 kJ

 

8.       Calculate the change in internal energy (ΔE) for the chemical reaction that releases 90.7 kJ of heat to its surroundings and does no work on them?

Using question 7. Heat is released so q = -90.7 kJ, and no work is done so w=0

 

9.       An air ballon initially contains 0.250 L of air in the morning, as the temperature outside rises during the day the ballon absorbs 20.0 kJ of heat.

                          

a.     What is the value with sign for the heat, q, absorbed? Meaning is q = +20.0 kJ or -20.0 kJ. Explain

Since the system absorbs heat, q comes into the system so the q=+20.0 kJ

b.     If as a result of absorbing 20.0 kJ, the ballon expands to a volume of 0.350 L, what is the work due to this expansion, in kJ. (Hint: 101.3 J = 1 L atm)

 

ΔV is the change in volume: : where Vf is the final volume, and Vi is the initial volume.

Then

Therefore:

Converting work into Joule using the conversion factor given, then to kJ

 

 

 

c.     From your answer in b, is the work done by the system to the surrounding, or does the surrounding do work on the system? Explain.   

The work is negative, so the work is leaving the system. This is what we expected since as the system expands it pushes the surrounding a distance d.

 

d.     What is the change in internal energy of the whole process? Is the process overall exothermic or endothermic?  

So:

So, since the internal energy is positive, the overall process is endothermic.

 

 

10.  A 150 g piece of iron (Fe) (heat capacity of iron, Cp = 25.09 J/ (mol. 0C)) was heated at a temperature of 47.0 0C and then placed in contact with a 275 g piece of copper (Cu) at 20.0 0C (heat capacity of copper, Cp = 25.46 J/ (mol. 0C)). What was the final temperature of the two pieces of metal?

The heat lost by the hot object (iron), so q of iron (q of iron is negative) is gained by the colder object Copper. The final T MUST be between the two temperatures.

 

We have the formulas of q at the back of the exam. Since we are given specific heats in J/(mol. 0C), we need to convert our masses into moles:

 

 

 

Now equating the two heats

Let’s multiply to remove the parentheses, we get:

 

 

3 0C. In the middle of the two temperatures.

 

 

 

 

 

 

 

11.  A 50.0 g of an aluminum sphere initially at 65.0 0C is immersed in a 20.0 g bucket of water initially at 23.0 0C. At thermal equilibrium, the temperature if the system was measured as 25.0 0C. What is the specific heat of aluminum? The molar heat capacity of water is 75.3 J/ (mol. 0C).

 

Similar to problem 10. The heat lost by the hot object (aluminum), so q of aluminum is negative, and that heat is gained by the colder object water. The final T MUST be between the two temperatures. And it is at 25.0 0C

 

 

We have the formulas of q at the back of the exam. Since we are given specific heats in J/(mol. 0C), we need to convert our masses into moles:

 

 

 

 

Now equating the two heats and solve for the unknown

Cs = 5.65 J/(mol . 0C)

 

 

 

 

 

 

 

 

 

12.  Below are four different covalent molecules:

 

H2CO = Molecule is made of C-H that are non polar, and C=O which is polar, so the molecule is polar and has dipole-dipole intermolecular forces.

 

H3COH = the molecule is made of C-H bonds that are nonpolar, then we have C-O bond that is polar, and then O-H bond that is special polar. The predominant intermolecular force is hydrogen bonding

 

CH4 = molecule is made of C-H bonds only, which are nonpolar. So, the molecule has only London Dispersion forces.

 

CH3CH3= This molecule is made of C-H and C-C bonds which are nonpolar bonds. So, the molecule only has London dispersion forces, although since it is slightly bigger than CH4 its London dispersion forces are stronger.

A.     For each molecule indicates what are the predominant intermolecular forces.

 

See above

B.     Which compound has the highest boiling point? Explain

 

Highest boiling point means, means more energy is needed to vaporize it, means stronger intermolecular forces. The strongest intermolecular forces are hydrogen bonding, so H3COH has the highest boiling point.

 

C.    Which compound is the most soluble in water? Explain

 

Since water is polar with hydrogen bonding, the most soluble molecules in water are polar, and even more soluble if that molecule can form hydrogen bonding with water. So, then H3COH is most soluble

 

 

D.    Which compound will have the highest vapor pressure? Explain.

 

Highest vapor pressure means it is easy to get the molecule into a gas phase. Meaning lower boiling point, and weaker intermolecular forces. The weakest intermolecular forces are London dispersion forces (LDF). Those LDF are even weaker if the molecule is small. Hence CH4 has the highest vapor pressure.