Gas Laws

We are given the following information:

• Henry's law constant for in water at 298 K, atm
• Temperature, T = 298 K
• Mole fraction of in air,
• Total pressure of air, atm
• Number of moles of water, moles

We need to find the number of moles of from air dissolved in 10 moles of water.

Step 1: Calculate the partial pressure of in the air.

According to Dalton's law of partial pressures, the partial pressure of a gas in a mixture is the product of its mole fraction and the total pressure.

atm

atm

Step 2: Apply Henry's law to find the mole fraction of dissolved in water.

Henry's law relates the partial pressure of a gas above a liquid to the mole fraction of the gas dissolved in the liquid:

Where is the mole fraction of dissolved in water.

Rearranging the formula to solve for :

Step 3: Calculate the number of moles of dissolved in water.

The mole fraction of in the solution is defined as:

Where is the number of moles of dissolved and is the number of moles of water.

Since the solubility of in water is very low (indicated by the small mole fraction ), the number of moles of dissolved ( ) is much smaller than the number of moles of water ( ). Therefore, we can approximate the denominator:

So, the mole fraction expression simplifies to:

Now, we can solve for :

moles

moles

moles

The final answer is .

We can use the ideal gas law to solve this problem:

Ideal Gas Law:

Let the initial volume be , pressure be , and temperature be . The initial conditions are:

After the changes: - The temperature is doubled: - The pressure is halved: The new volume can be found using the ideal gas law: Substituting the changes: Simplifying: Thus, the volume of the gas will be 4 times the original volume when the temperature is doubled and the pressure is halved.

The correct answer is (B) : will be 4 times the original volume.

Given the Henry's law constant ( ) values (in bar) for the gases:
Argon (I): 40.3
Carbon dioxide (II): 1.67
Formaldehyde (III):
Methane (IV): 0.413

According to Henry's law, the solubility of a gas in a liquid is inversely proportional to its value. Hence, the solubility increases as decreases.

Argon (I) has the highest value, so it has the lowest solubility.
Carbon dioxide (II) has a moderate value, so it has a moderate solubility.
Formaldehyde (III) has the lowest value, so it has the highest solubility.
Methane (IV) has a value higher than formaldehyde but lower than argon, so its solubility lies between carbon dioxide and argon.

Therefore, the increasing order of solubility is:

The correct answer is (A) : I < II < IV < III.

Let's evaluate each statement:

1. value is same for a gas in any solvent: This is incorrect. The Henry's law constant varies with the type of solvent. It is specific to the gas-solvent combination.

2. Higher the value, more the solubility of gas: This is incorrect. According to Henry's law, a higher value corresponds to a lower solubility of the gas. The solubility of a gas in a solvent is inversely proportional to .

3. K_H value increases on increasing the temperature of the solution: This is correct. As the temperature increases, the solubility of gases generally decreases, which causes the Henry's law constant to increase. This is because gases become less soluble at higher temperatures.

4. Easily liquefiable gases usually have lesser K_H values: This is incorrect. Gases that are easily liquefiable, such as ammonia, generally have higher solubility in a solvent, which corresponds to a lower value.

Therefore, the correct answer is (C): value increases on increasing the temperature of the solution.

Correct Answer: 3 litres

Explanation:
We use the Ideal Gas Equation:
PV = nRT

Where:
• P = Pressure = 0.821 atm
• V = Volume (what we need to find)
• n = Number of moles of CO
• R = 0.0821 L·atm·K⁻¹·mol⁻¹
• T = Temperature in Kelvin = 27°C + 273 = 300 K

First, calculate the number of moles (n):
Molar mass of CO = 12 (C) + 16 (O) = 28 g/mol


Now plug into the equation:



So, the volume is 3 litres.