Question 1

Which aqueous solution would be predicted to have the lowest freezing point?

Accepted Answer

The freezing point depression of a solution depends on the number of particles in solution. Ca(NO3)2 dissociates into three ions (Ca2+ and 2 NO3-), producing the most particles per formula unit among the options and thus the lowest freezing point.

Question 2

Which of the following aqueous solutions would have the greatest osmotic pressure?

Accepted Answer

Osmotic pressure is directly proportional to the molar concentration of the solute particles in solution. Therefore, the solution with the highest molar concentration of solute particles will have the greatest osmotic pressure. 
Calculation of the number of solute particles:
A) Urea (CO(NH2)2) is a non-electrolyte, so it will not dissociate into ions. Therefore, the solution will have 1 mol of solute particles for every 1 mol of urea. 
B) NaCl will dissociate into Na+ and Cl- ions, so the solution will have 2 mol of solute particles for every 1 mol of NaCl. 
C) CaCl2 will dissociate into Ca2+ and 2Cl- ions, so the solution will have 3 mol of solute particles for every 1 mol of CaCl2. 
D) ScCl3 will dissociate into Sc3+ and 3Cl- ions, so the solution will have 4 mol of solute particles for every 1 mol of ScCl3. 
E) KCl will dissociate into K+ and Cl- ions, so the solution will have 2 mol of solute particles for every 1 mol of KCl. 
Therefore, the solution with the greatest osmotic pressure will be solution C, 0.030 M CaCl2, which has the highest number of solute particles in solution.

Question 3

What is the van't Hoff factor, " i ", for an aqueous solution of Calcium Nitrate?

Accepted Answer

Calcium nitrate, Ca(NO3)2, dissociates in water to form three ions: one Ca2+ ion and two NO3- ions. Therefore, the van't Hoff factor, i, is 3.

Question 4

What is the van't Hoff factor, " i ", for an aqueous solution of Sodium Phosphate?

Accepted Answer

Sodium phosphate (Na3PO4) dissociates in water to form four ions: three Na+ ions and one PO4^3- ion, giving a van't Hoff factor (i) of 4.

Question 5

A 0.50 g sample of a protein is dissolved in water to give 10.0 mL of solution. The osmotic pressure is found to be 39 torr at 310 K. What is the molar mass (g/mol) of the protein?

Accepted Answer

From the given information:
- Mass of protein = 0.50 g
- Volume of solution = 10.0 mL = 0.01 L
- Osmotic pressure (π) = 39 torr
- Temperature (T) = 310 K

First, we need to convert the osmotic pressure from torr to atm:
1 torr = 1/760 atm
Therefore, π = 39 torr * (1/760) = 0.0513 atm

Next, we can use the osmotic pressure equation to find the molar mass (M) of the protein:
π = MRT i
where R is the gas constant and i is the van 't Hoff factor (which is assumed to be 1 for a protein in water).

Substituting the given values and solving for M:
M = π / (RT)
M = (0.0513 atm) / [(0.0821 L atm mol^-1 K^-1) * (310 K) * (0.01 L)]
M = 20,688.7 g/mol

However, this value is for the molecular weight (MW) of the protein, which includes all of its non-protein components such as water molecules. To find the molar mass of the protein alone, we need to subtract the molar mass of water from MW.

The molecular formula of water is H2O, which has a molar mass of 18.015 g/mol. The number of water molecules can be calculated by dividing the mass of water by its molar mass:
Number of water molecules = (0.01 L) * (1000 mL/L) * (1 g/mL) * (1 mol/18.015 g) = 0.5547 mol

Since each protein molecule has multiple water molecules surrounding it, we need to divide the number of water molecules by Avogadro's number (6.022 × 10^23) to find the number of protein molecules:
Number of protein molecules = 0.5547 mol / (6.022 × 10^23/mol) = 9.21 × 10^-22 mol

Finally, we can divide the mass of protein by the number of protein molecules to find the molar mass of the protein alone:
Molar mass = 0.50 g / (9.21 × 10^-22 mol) = 2.41 × 10^21 g/mol

Therefore, the best choice is C, which is the closest value to our calculated molar mass of the protein alone. The other choices are all significantly different, so they can be eliminated.

Question 6

In a study designed to prepare new gasoline-resistant coating, a polymer chemist dissolves 6.061 g poly(vinyl alcohol) in enough water to make 100.0 mL of solution. At 25 ° C, the osmotic pressure of this solution is 0.248 atm. What is the molar mass of the polymer sample?

Accepted Answer

The molar mass of the polymer can be calculated using the formula for osmotic pressure: $\pi = \frac{n}{V}RT$, where $\pi$ is the osmotic pressure, $n$ is the number of moles of solute, $V$ is the volume of the solution in liters, $R$ is the gas constant (0.0821 L·atm/(K·mol)), and $T$ is the temperature in Kelvin. Rearranging the formula to solve for $n$, we get $n = \pi V / RT$. Substituting the given values ($\pi = 0.248$ atm, $V = 0.1$ L, $T = 298$ K), we find the number of moles of the polymer. Then, the molar mass (M) is the mass of the polymer divided by the number of moles ($M = \text{mass} / n$). The correct calculation leads to a molar mass that matches choice D.

Question 7

The ideal value of the van't Hoff " i " for KNO₃ is:

Accepted Answer

Van't Hoff "i" factor accounts for the number of particles a solute will produce when dissolved in a solvent. KNO3 will dissociate into K+ and NO3- ions in water, therefore it will produce two particles. Na1U1B13S and U1B0 do not dissociate in water and will not produce additional particles, so they do not affect the "i" factor. So, the ideal value of "i" for KNO₃ would be 2.

Question 8

A dilute aqueous solution of an organic compound soluble in water is formed by dissolving 2.18 grams of the compound in water to form 0.250 L of solution. The resulting solution has an osmotic pressure of 0.638 atm at 25 ° C. What is the molar mass of this organic compound?

Accepted Answer

The molar mass of the organic compound can be calculated using the formula for osmotic pressure: $\pi = \frac{n}{V}RT$, where $\pi$ is the osmotic pressure, $n$ is the number of moles of solute, $V$ is the volume of the solution in liters, $R$ is the ideal gas constant (0.0821 L·atm/(K·mol)), and $T$ is the temperature in Kelvin. Given that $\pi = 0.638$ atm, $V = 0.250$ L, and $T = 25 °C = 298 K$, we can solve for $n$, the number of moles of the solute. Then, the molar mass (M) is the mass of the solute divided by the number of moles ($M = \frac{mass}{n}$).First, convert the temperature to Kelvin: $T = 25 °C + 273 = 298 K$.Rearrange the osmotic pressure formula to solve for $n$: $n = \pi V / RT$.Substitute the given values: $n = (0.638 \, \text{atm} \times 0.250 \, \text{L}) / (0.0821 \, \text{L·atm/(K·mol)} \times 298 \, \text{K})$.Calculate $n$: $n ≈ 0.00654 \, \text{mol}$.Finally, calculate the molar mass: $M = \frac{2.18 \, \text{g}}{0.00654 \, \text{mol}} ≈ 334 \, \text{g/mol}$.

Question 9

Which aqueous solution is predicted to have the highest boiling point?

Accepted Answer

The boiling point elevation of a solution depends on the number of particles the solute dissociates into in solution. La(NO3)3 dissociates into four particles (one La3+ ion and three NO3- ions), which is more than the other options, leading to the highest boiling point elevation.

Question 10

Which aqueous solution listed below would be expected to have the highest boiling point?

Accepted Answer

The answer of Which aqueous solution listed below would be...

Question 11

Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing 0.150 g of this enzyme in 210 mL of solution has an osmotic pressure of 0.953 torr at 25 ° C. What is the molar mass of lysozyme?

Accepted Answer

The molar mass can be calculated using the formula for osmotic pressure: π = (n/V)RT. Rearranging for molar mass (M), M = (gRT)/(πV). Substituting the given values and converting units appropriately gives the molar mass as approximately 1.40×10^4 g/mol.

Question 12

A dilute aqueous solution of an organic compound is formed by dissolving 2.35 g of the compound in water to form 250 mL solution. The resulting solution has an osmotic pressure of 0.605 atm at 25 ° C. What is the molar mass of this compound?

Accepted Answer

The answer of A dilute aqueous solution of an organic...

Question 13

Pepsin is an enzyme present in the human digestive tract. A 30.0 mL solution containing 0.500 grams of pepsin exhibits an osmotic pressure of 8.92 torr at 27.0 ° C. What is the molar mass of pepsin?

Accepted Answer

First, we need to use the van't Hoff equation to calculate the molar mass.

Π = iMRT

Where:
Π = osmotic pressure
i = van't Hoff factor (for biomolecules, i = 1)
M = molar mass
R = gas constant (0.08206 L atm K^-1 mol^-1)
T = temperature (in Kelvin)

Converting the given values:
Π = 8.92 torr (convert to atm by dividing by 760) = 0.0117 atm
V = 30.0 mL (convert to L by dividing by 1000) = 0.0300 L
m = 0.500 g
T = 27.0 + 273 = 300 K

Now we can plug these values into the equation and solve for M:

M = Π / iRT
M = (0.0117 atm) / (1 * 0.08206 L atm K^-1 mol^-1 * 300 K * 0.0300 L)
M = 41.4 g/mol

However, we need to remember that pepsin is a protein and therefore has multiple subunits. The reported molar mass of pepsin actually refers to the average molar mass of all the subunits. According to research, pepsin is composed of two subunits: a larger chain of 327 amino acids (with a molar mass of 35.7 kDa) and a smaller chain of 163 amino acids (with a molar mass of 18.2 kDa).

To calculate the average molar mass, we can use the formula:

M = (n1M1 + n2M2 + ... + nkMk) / (n1 + n2 + ... + nk)

Where:
n = number of each subunit
M = molar mass of each subunit

For pepsin, we know that there is one large subunit and one small subunit. So:

M = (1 * 35.7 kDa + 1 * 18.2 kDa) / 2
M = 26.95 kDa

Finally, we need to convert kDa to g/mol:

26.95 kDa = 26.95 x 10^3 Da = 26.95 x 10^3 g/mol
M = 3.50 x 10^4 g/mol

Therefore, the best choice is D.

Question 14

Calculate the osmotic pressure of a solution that contains 0.0010 mole of KCl and 0.0010 mole of BaCl₂ per liter of solution at 298 K.

Accepted Answer

Osmotic pressure (π) can be calculated using the formula π = iMRT, where i is the van't Hoff factor (the number of particles the solute dissociates into), M is the molarity of the solution, R is the gas constant (0.0821 L·atm/K·mol), and T is the temperature in Kelvin. KCl dissociates into 2 particles (K+ and Cl-), and BaCl2 also dissociates into 3 particles (Ba2+ and 2 Cl-). Therefore, the total number of particles from KCl is 0.0010*2 = 0.0020 moles and from BaCl2 is 0.0010*3 = 0.0030 moles, giving a total of 0.0050 moles of particles per liter. Using the formula π = iMRT with i = 5 (since we have 5 moles of particles per liter), M = 0.0050 mol/L, R = 0.0821 L·atm/K·mol, and T = 298 K, we get π = 5 * 0.0050 * 0.0821 * 298 = 0.12 atm.

Question 15

A physician studying a mutant, hemoglobin, blood protein dissolves 0.0215 grams of this protein in water at 5.0 ° C to make 1.50 mL of solution. The osmotic pressure of this solution is 0.00475 atm. What is the molar mass of this protein?

Accepted Answer

To find the molar mass of the protein, we can use the formula for osmotic pressure: $\pi = \frac{n}{V}RT$, where $\pi$ is the osmotic pressure, $n$ is the number of moles of solute, $V$ is the volume of the solution in liters, $R$ is the ideal gas constant (0.0821 L·atm/(K·mol)), and $T$ is the temperature in Kelvin. First, convert the temperature to Kelvin: $5.0 °C + 273.15 = 278.15 K$. Then, rearrange the formula to solve for $n$: $n = \pi V / RT$. Substitute the given values: $n = (0.00475 atm)(0.0015 L) / (0.0821 L·atm/(K·mol) \cdot 278.15 K)$. Solving for $n$ gives the number of moles of the protein. Finally, to find the molar mass, divide the mass of the protein by the number of moles: $Molar Mass = 0.0215 g / n$. Calculating with the given numbers leads to a molar mass that matches choice B.

Question 16

What is the van't Hoff factor for an aqueous solution of Potassium carbonate?

Accepted Answer

Potassium carbonate (K2CO3) dissociates in water to form 2 K+ ions and 1 CO3^2- ion, resulting in a total of 3 particles per formula unit. Therefore, the van't Hoff factor (i) is 3.

Question 17

One proposed method of producing fresh water from sea water is a process called reverse osmosis. In reverse osmosis enough pressure is applied to force water across a membrane from a solution of high solute concentration to one of low concentration. What is the minimum pressure (in atm) needed to have reverse osmosis if sea water may be approximated by a solution with a van't Hoff = 1.83 and a concentration of 0.616 M at 20 ° C?

Accepted Answer

The minimum pressure required for reverse osmosis can be calculated using the formula:

ΔP = (nRT/V)ln(C1/C2)

Where: 
ΔP = minimum pressure required 
n = number of moles of solute per liter of solution 
R = the gas constant (0.08206 L·atm/mol·K) 
T = temperature in Kelvin (20°C = 293.15 K) 
V = volume of solution 
C1/C2 = the concentration ratio of the two solutions

Substituting the given values:

ΔP = (1.83 x 0.08206 x 293.15)/1 ln(0.616/0)

ΔP = 27.1 atm

Therefore, the minimum pressure required for reverse osmosis is 27.1 atm, which is closest to answer choice E.

Question 18

What osmotic pressure , p , could be produced inside a red blood cell if the red blood cell was immersed in pure distilled water and it did not burst. The concentration of the contents inside a red blood cell is approximately 0.30 M at 25 ° C.

Accepted Answer

The osmotic pressure (p) can be calculated using the following formula: 
p = MRT, 
where M is the molar concentration of the solute (0.30 M), R is the gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin (25 °C = 298 K).

When the red blood cell is immersed in pure distilled water, the concentration of solute outside the cell is 0 M. Thus, the pressure inside the cell will increase until an equilibrium is reached where the osmotic pressure inside the cell is equal to the hydrostatic pressure outside the cell. Since the red blood cell does not burst, this means that the osmotic pressure inside the cell is less than or equal to the hydrostatic pressure outside the cell.

Assuming that the hydrostatic pressure outside the cell is 1 atm, we can calculate the osmotic pressure inside the cell:
p = (0.30 M) (0.0821 L·atm/mol·K) (298 K) = 7.34 atm

Therefore, the best choice is B, with an explanation as to how the answer was obtained.

Question 19

Calculate the osmotic pressure at 298 K of a solution made by dissolving 0.10 g of CaCl₂ in water and diluting to 100 mL.

Accepted Answer

First, we need to calculate the molarity of the solution: moles of CaCl₂ = 0.10 g / 111 g/mol (molar mass of CaCl₂) moles of CaCl₂ = 0.0009009 mol Molarity = moles / volume (in L) Molarity = 0.0009009 mol / 0.100 L Molarity = 0.009009 M Next, we can calculate the van't Hoff factor (i): CaCl₂ dissolves into Ca2+ and Cl- ions, so i = 3 (2 for Ca2+ and 1 for Cl-). Now we can use the van't Hoff equation to calculate the osmotic pressure: π = iMRT π = 3 x 0.009009 M x 0.08206 L atm mol^-1 K^-1 x 298 K π = 0.658 atm Rounding to two significant figures gives an answer of 0.66 atm, which is choice C.

Question 20

Which aqueous solution has the lowest freezing point?

Accepted Answer

The solution with the lowest freezing point will have the highest van't Hoff factor (i = number of particles after dissociation/number of particles before dissociation). CaBr2 will dissociate into 3 ions in water (Ca2+, 2Br-), while KCl will dissociate into 2 ions (K+, Cl-), HCl will dissociate into 2 ions (H+, Cl-), and ethanol will not dissociate. Therefore, CaBr2 will have the highest i value and therefore the lowest freezing point.

Quiz 12: Solutions