1. Van't Hoff factors depend on the concentrations of the dissolved solute species. Why would a dilute solution have a Van't Hoff factor closer to the ideal value?
a. because in dilute solutions solute species are less likely to bump into each other and pair up.
b. because in dilute solutions solute species are more likely to bump into each other and pair up.
c. because in dilute solutions, the average kinetic energies of solute species is greater therefore making solute collisions less effective.
d. because in dilute solutions there are more holes for solute species to hide in.
2. How many milligrams of nitrogen gas are dissolved in 4.00 liters of water under atmospheric conditions? Assume that the air above the water contains nitrogen with a partial pressure of 0.78 atm. (N2: KH = 6.1 x 10-4 M/atm)
a. 17.1 mg N2
b. 13.3 mg N2
c. 68.3 mg N2
d. 53.3 mg N2
3. Which of the following Van't Hoff factors is incorrect?
a. NaCl: i = 1.87
b. K2CO3: i = 2.45
c. C12H22O11: i = 1.00
d. HCl: i = 2.1
Thank you.
1. http://www.chemguide.co.uk/physical/phaseeqia/nonideal.html
2. C = KpP
Plug in K and P and solve for C in M. Then M = mols/L and solve for mols.l Then mols = g/molar mass and solve for grams.
3. Ideal values.
a = 2
b = 3
c
1
d = 2. d is the only one HIGHER than the ideal.
1. The Van't Hoff factor, denoted by "i," is a measure of the number of particles that a solute molecule dissociates into when dissolved in a solvent. It depends on the concentration of dissolved solute species. In a dilute solution, the concentration of solute species is low, meaning there are fewer solute molecules present.
(a) The statement in option a is incorrect. In dilute solutions, solute species are less likely to bump into each other and pair up because of their low concentration.
(b) The statement in option b is also incorrect. In dilute solutions, solute species are less likely to bump into each other and pair up because of their low concentration.
(c) The statement in option c is incorrect as well. The average kinetic energies of solute species do not play a direct role in determining the Van't Hoff factor.
(d) The statement in option d is incorrect. The number of "holes" for solute species has no influence on the Van't Hoff factor.
Therefore, none of the provided options correctly explain why a dilute solution would have a Van't Hoff factor closer to the ideal value.
2. To determine the amount of nitrogen gas dissolved in water, we can use Henry's law. Henry's law states that the concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid. The proportionality constant is given by the Henry's law constant (KH) for the specific gas and solvent system.
Given:
- Volume of water (V): 4.00 L
- Partial pressure of nitrogen gas (P): 0.78 atm
- Henry's law constant for nitrogen gas in water (KH): 6.1 x 10^(-4) M/atm
The amount of nitrogen gas dissolved in water can be calculated using the formula:
Mass of solute (in moles) = Concentration (in Molarity) × Volume of solvent (in liters)
First, we need to convert the pressure to Molarity using Henry's law equation:
Concentration of nitrogen gas (in Molarity) = KH × Partial pressure of nitrogen gas
Concentration of nitrogen gas = (6.1 x 10^(-4) M/atm) × (0.78 atm) = 4.758 x 10^(-4) M
Now, we can calculate the mass of nitrogen gas dissolved in water:
Mass of nitrogen gas = Concentration of nitrogen gas × Volume of water
Mass of nitrogen gas = (4.758 x 10^(-4) M) × (4.00 L)
To convert moles to milligrams, we need to multiply by the molar mass of nitrogen gas, which is approximately 28 g/mol:
Mass of nitrogen gas = (4.758 x 10^(-4) M) × (4.00 L) × (28 g/mol) × (1000 mg/g)
Calculating the expression above yields:
Mass of nitrogen gas ≈ 17.1 mg
Therefore, the correct answer is option a) 17.1 mg N2.
3. The Van't Hoff factor, denoted by "i," is supposed to represent the extent of dissociation of a solute in a solvent. For ionic compounds, such as NaCl and K2CO3, the Van't Hoff factors can be calculated based on the number of ions that form when the compounds dissociate.
(a) NaCl completely dissociates into Na+ and Cl- ions, resulting in two ions. Thus, the correct Van't Hoff factor for NaCl is i = 2, not 1.87. Therefore, option a is incorrect.
(b) K2CO3 dissociates into two K+ ions and one CO3(2-) ion. This gives a total of three ions when the compound dissociates, so the correct Van't Hoff factor for K2CO3 is i = 3/2 or 1.5. Therefore, option b is correct.
(c) C12H22O11 is a covalent compound (a sugar) and does not dissociate into ions when dissolved. Therefore, the Van't Hoff factor for C12H22O11 should be 1. The statement in option c is correct.
(d) HCl dissociates into H+ and Cl- ions, resulting in two ions. Thus, the Van't Hoff factor for HCl should be i = 2.1. Therefore, option d is correct.
The incorrect Van't Hoff factor is option a) NaCl: i = 1.87.
I hope this helps! Let me know if you have any further questions.
1. The correct answer is a. because in dilute solutions, solute species are less likely to bump into each other and pair up. In dilute solutions, the concentration of solute species is low, which means there are fewer solute particles to interact with each other and form pairs. This leads to a Van't Hoff factor closer to the ideal value.
2. To calculate the amount of nitrogen gas dissolved in water, we can use Henry's Law. The equation is given as:
n = KH * P
Where:
n: amount of solute (in moles)
KH: Henry's Law constant (in M/atm)
P: partial pressure of the solute gas (in atm)
First, let's convert the given volume of water to liters:
4.00 liters
Now, we can substitute the values into the equation:
n = (6.1 x 10^-4 M/atm) * (0.78 atm)
n = 4.758 x 10^-4 moles
To convert moles to milligrams, we need to know the molar mass of nitrogen gas (N₂):
Molar mass of N₂ = 14.01 g/mol
Now, let's calculate the amount of nitrogen gas in milligrams:
n (in grams) = (4.758 x 10^-4 moles) * (28.02 g/mol)
n (in grams) = 0.0133 grams
n (in milligrams) = (0.0133 grams) * (1000 mg/g)
n (in milligrams) = 13.3 mg
Therefore, the correct answer is b. 13.3 mg N₂.
3. The correct answer is d. HCl: i = 2.1. The Van't Hoff factor (i) represents the number of particles into which a compound dissociates or associates when it dissolves in the solvent. In the case of HCl, it fully dissociates into H⁺ and Cl⁻ ions. Therefore, the Van't Hoff factor for HCl should be 2.